%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU720^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:46:42 AM UTC 2026
% Result : Theorem 59.05s 10.07s
% Output : CNFRefutation 59.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 241
% Syntax : Number of formulae : 4479 (1609 unt; 0 typ; 240 def)
% Number of atoms : 36492 (14852 equ; 0 cnn)
% Maximal formula atoms : 240 ( 8 avg)
% Number of connectives : 74590 (15255 ~;14183 |; 50 &;44192 @)
% ( 14 <=>; 896 =>; 0 <=; 0 <~>)
% Maximal formula depth : 247 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2508 (2508 >; 0 *; 0 +; 0 <<)
% Number of symbols : 436 ( 433 usr; 243 con; 0-4 aty)
% Number of variables : 16220 (1228 ^;14957 !; 35 ?;16220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_ap2apEq1,type,
ap2apEq1: $o ).
thf(tp_ap2apEq2,type,
ap2apEq2: $o ).
thf(tp_ap2p,type,
ap2p: $o ).
thf(tp_apProp,type,
apProp: $o ).
thf(tp_app,type,
app: $o ).
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_beta1,type,
beta1: $o ).
thf(tp_beta2,type,
beta2: $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_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_binunionT_lem,type,
binunionT_lem: $o ).
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_brelnall2,type,
brelnall2: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_cartprodpairmemEL,type,
cartprodpairmemEL: $o ).
thf(tp_cartprodpairmemER,type,
cartprodpairmemER: $o ).
thf(tp_cartprodpairsurjEq,type,
cartprodpairsurjEq: $o ).
thf(tp_cartprodsndin,type,
cartprodsndin: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $o ).
thf(tp_complementTI1,type,
complementTI1: $o ).
thf(tp_complementT_lem,type,
complementT_lem: $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_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrEL1,type,
dpsetconstrEL1: $o ).
thf(tp_dpsetconstrEL2,type,
dpsetconstrEL2: $o ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $o ).
thf(tp_dpsetconstrERa,type,
dpsetconstrERa: $o ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_dpsetconstrSub,type,
dpsetconstrSub: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_dsetconstr__Cong,type,
dsetconstr__Cong: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptyset__Cong,type,
emptyset__Cong: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqbreln,type,
eqbreln: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_eta1,type,
eta1: $o ).
thf(tp_eta2,type,
eta2: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1E2,type,
ex1E2: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_exuE3u,type,
exuE3u: $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $o ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_ifSingleton,type,
ifSingleton: $o ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iffalseProp1,type,
iffalseProp1: $o ).
thf(tp_iffalseProp2,type,
iffalseProp2: $o ).
thf(tp_ifp,type,
ifp: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_iftrueProp1,type,
iftrueProp1: $o ).
thf(tp_iftrueProp2,type,
iftrueProp2: $o ).
thf(tp_iftrueorfalse,type,
iftrueorfalse: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2lamEq,type,
lam2lamEq: $o ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powersetTE1,type,
powersetTE1: $o ).
thf(tp_powersetTI1,type,
powersetTI1: $o ).
thf(tp_powersetT_lem,type,
powersetT_lem: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY599,type,
sK100_SY599: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK101_SY1227,type,
sK101_SY1227: $i > $i > $i > $i > $i ).
thf(tp_sK102_SY1143,type,
sK102_SY1143: $i > $i > $i > $i > $i ).
thf(tp_sK103_SY1143,type,
sK103_SY1143: $i > $i > $i > $i > $i ).
thf(tp_sK104_SY1204,type,
sK104_SY1204: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK105_SY1143,type,
sK105_SY1143: $i > $i > $i > $i > $i ).
thf(tp_sK106_SY1238,type,
sK106_SY1238: $i > $i > $i > $i > $i ).
thf(tp_sK107_SY1239,type,
sK107_SY1239: $i > $i > $i > $i > $i ).
thf(tp_sK108_SY1180,type,
sK108_SY1180: $i > $i > $i > $i ).
thf(tp_sK109_SY1221,type,
sK109_SY1221: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK10_SY674,type,
sK10_SY674: $i > $i > $i ).
thf(tp_sK110_SY1222,type,
sK110_SY1222: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK111_SY1244,type,
sK111_SY1244: $i > $i > $i > $i > $i ).
thf(tp_sK112_SY1180,type,
sK112_SY1180: $i > $i > $i > $i ).
thf(tp_sK113_SY1234,type,
sK113_SY1234: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1220,type,
sK114_SY1220: $i > $i > $i > $i ).
thf(tp_sK115_SY1250,type,
sK115_SY1250: $i > $i > $i > $i ).
thf(tp_sK116_SY646,type,
sK116_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK117_SY126,type,
sK117_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK118_SY1240,type,
sK118_SY1240: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK119_SY1241,type,
sK119_SY1241: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY684,type,
sK11_SY684: ( $i > $o ) > $i > $i ).
thf(tp_sK120_SY1258,type,
sK120_SY1258: $i > $i > $i > $i ).
thf(tp_sK121_SY646,type,
sK121_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK122_SY126,type,
sK122_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK123_SY1245,type,
sK123_SY1245: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK124_SY1242,type,
sK124_SY1242: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK125_SY1248,type,
sK125_SY1248: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK126_SY1249,type,
sK126_SY1249: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK127_SY1246,type,
sK127_SY1246: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK128_SY1254,type,
sK128_SY1254: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK129_SY1255,type,
sK129_SY1255: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY730,type,
sK12_SY730: $i > $i > $i ).
thf(tp_sK130_SY1256,type,
sK130_SY1256: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK131_SY1257,type,
sK131_SY1257: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK132_SY1262,type,
sK132_SY1262: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK133_SY1263,type,
sK133_SY1263: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK134_SY646,type,
sK134_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK135_SY126,type,
sK135_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK136_SY1264,type,
sK136_SY1264: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK137_SY646,type,
sK137_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK138_SY126,type,
sK138_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK139_SY646,type,
sK139_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK13_SY748,type,
sK13_SY748: $i > $i > $i ).
thf(tp_sK140_SY126,type,
sK140_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK141_SY646,type,
sK141_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK142_SY126,type,
sK142_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK143_SY1270,type,
sK143_SY1270: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK144_SY646,type,
sK144_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK145_SY126,type,
sK145_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK146_SY646,type,
sK146_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK147_SY126,type,
sK147_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK148_SY646,type,
sK148_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK149_SY126,type,
sK149_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY760,type,
sK14_SY760: ( $i > $o ) > $i > $i ).
thf(tp_sK150_SY646,type,
sK150_SY646: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK151_SY126,type,
sK151_SY126: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY1276,type,
sK152_SY1276: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK153_SY1280,type,
sK153_SY1280: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK154_SY1281,type,
sK154_SY1281: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK155_SY1282,type,
sK155_SY1282: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK156_SY1290,type,
sK156_SY1290: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK157_SY1291,type,
sK157_SY1291: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK158_SY1292,type,
sK158_SY1292: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK159_SY1299,type,
sK159_SY1299: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY786,type,
sK15_SY786: ( $i > $o ) > $i > $i ).
thf(tp_sK16_SY798,type,
sK16_SY798: $i > $i > $i ).
thf(tp_sK17_SY858,type,
sK17_SY858: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK18_SY914,type,
sK18_SY914: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK19_SY923,type,
sK19_SY923: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY1103,type,
sK20_SY1103: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK21_SY956,type,
sK21_SY956: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK22_SY971,type,
sK22_SY971: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK23_SY252,type,
sK23_SY252: $i > $i ).
thf(tp_sK24_SY732,type,
sK24_SY732: ( $i > $o ) > $i > $i ).
thf(tp_sK25_SY310,type,
sK25_SY310: $i > $i ).
thf(tp_sK26_SY1013,type,
sK26_SY1013: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK27_SY1122,type,
sK27_SY1122: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK28_SY868,type,
sK28_SY868: $i > $i > $i ).
thf(tp_sK29_SY1067,type,
sK29_SY1067: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK30_SY686,type,
sK30_SY686: ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY733,type,
sK31_SY733: ( $i > $o ) > $i > $i ).
thf(tp_sK32_SY1112,type,
sK32_SY1112: ( $i > $o ) > $i > $i ).
thf(tp_sK33_SY1113,type,
sK33_SY1113: ( $i > $o ) > $i > $i ).
thf(tp_sK34_SY1116,type,
sK34_SY1116: $i > ( $i > $o ) > $i ).
thf(tp_sK35_SY836,type,
sK35_SY836: $i > $i > $i ).
thf(tp_sK36_SY1059,type,
sK36_SY1059: $i > $i > $i > $i ).
thf(tp_sK37_SY55,type,
sK37_SY55: $i > $i > $i ).
thf(tp_sK38_SY1101,type,
sK38_SY1101: $o > $i > $i > $i ).
thf(tp_sK39_SX0,type,
sK39_SX0: $i > $i > $i ).
thf(tp_sK3_SY2,type,
sK3_SY2: $i ).
thf(tp_sK40_SX0,type,
sK40_SX0: $i > $i > $i ).
thf(tp_sK41_SY738,type,
sK41_SY738: $i > $i > $i ).
thf(tp_sK42_SY416,type,
sK42_SY416: $i > $i ).
thf(tp_sK43_SY599,type,
sK43_SY599: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK44_SY634,type,
sK44_SY634: $i > $i > $i ).
thf(tp_sK45_SY675,type,
sK45_SY675: $i > $i > $i ).
thf(tp_sK46_SY1157,type,
sK46_SY1157: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK47_SY498,type,
sK47_SY498: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY1161,type,
sK48_SY1161: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK49_SY1164,type,
sK49_SY1164: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK4_SY65,type,
sK4_SY65: $i > $i ).
thf(tp_sK50_SY951,type,
sK50_SY951: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK51_SY675,type,
sK51_SY675: $i > $i > $i ).
thf(tp_sK52_SY698,type,
sK52_SY698: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK53_SY1109,type,
sK53_SY1109: $i > $i > $i > $i ).
thf(tp_sK54_SY1115,type,
sK54_SY1115: $i > $i > $i > $i ).
thf(tp_sK55_SY1192,type,
sK55_SY1192: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY1128,type,
sK56_SY1128: $i > $i > $i > $i ).
thf(tp_sK57_SY899,type,
sK57_SY899: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK58_SY1099,type,
sK58_SY1099: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY1102,type,
sK59_SY1102: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY42,type,
sK5_SY42: $i > $i ).
thf(tp_sK60_SY1104,type,
sK60_SY1104: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY1137,type,
sK61_SY1137: $i > $i > $i > $i > $i ).
thf(tp_sK62_SY1108,type,
sK62_SY1108: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY1140,type,
sK63_SY1140: $i > $i > $i > $i > $i ).
thf(tp_sK64_SY1141,type,
sK64_SY1141: $i > $i > $i > $i > $i ).
thf(tp_sK65_SY1110,type,
sK65_SY1110: $i > ( $i > $o ) > $i ).
thf(tp_sK66_SY1114,type,
sK66_SY1114: $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY1156,type,
sK67_SY1156: $i > $i > $i > $i > $i ).
thf(tp_sK68_SY1119,type,
sK68_SY1119: $i > ( $i > $o ) > $i ).
thf(tp_sK69_SY1191,type,
sK69_SY1191: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY233,type,
sK6_SY233: $i > $i ).
thf(tp_sK70_SY1193,type,
sK70_SY1193: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK71_SY1194,type,
sK71_SY1194: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK72_SY1168,type,
sK72_SY1168: $i > $i > $i > $i > $i ).
thf(tp_sK73_SY1200,type,
sK73_SY1200: $i > $i > $i > $i > $i ).
thf(tp_sK74_SY1174,type,
sK74_SY1174: $i > $i > $i > $i ).
thf(tp_sK75_SY1201,type,
sK75_SY1201: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY1176,type,
sK76_SY1176: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK77_SY49,type,
sK77_SY49: $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY1178,type,
sK78_SY1178: $i > $i > $i ).
thf(tp_sK79_SY659,type,
sK79_SY659: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK7_SY596,type,
sK7_SY596: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK80_SY151,type,
sK80_SY151: $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY380,type,
sK81_SY380: $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY449,type,
sK82_SY449: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY500,type,
sK83_SY500: $i > ( $i > $o ) > $i ).
thf(tp_sK84_SY500,type,
sK84_SY500: $i > ( $i > $o ) > $i ).
thf(tp_sK85_SY49,type,
sK85_SY49: $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY151,type,
sK86_SY151: $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY380,type,
sK87_SY380: $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY394,type,
sK88_SY394: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY449,type,
sK89_SY449: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY642,type,
sK8_SY642: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK90_SY500,type,
sK90_SY500: $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY1129,type,
sK91_SY1129: $i > $i > $i > $i ).
thf(tp_sK92_SY1129,type,
sK92_SY1129: $i > $i > $i > $i ).
thf(tp_sK93_SY1143,type,
sK93_SY1143: $i > $i > $i > $i > $i ).
thf(tp_sK94_SY394,type,
sK94_SY394: $i > ( $i > $o ) > $i ).
thf(tp_sK95_SY394,type,
sK95_SY394: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY1129,type,
sK96_SY1129: $i > $i > $i > $i ).
thf(tp_sK97_SY599,type,
sK97_SY599: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK98_SY394,type,
sK98_SY394: $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY1195,type,
sK99_SY1195: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK9_SY657,type,
sK9_SY657: $i > $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_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $o ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setextT,type,
setextT: $o ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(tp_setminusELneg,type,
setminusELneg: $o ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusERneg,type,
setminusERneg: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(tp_setminusILneg,type,
setminusILneg: $o ).
thf(tp_setminusIRneg,type,
setminusIRneg: $o ).
thf(tp_setminusLsub,type,
setminusLsub: $o ).
thf(tp_setminusSubset1,type,
setminusSubset1: $o ).
thf(tp_setminusSubset2,type,
setminusSubset2: $o ).
thf(tp_setminusT_lem,type,
setminusT_lem: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $o ).
thf(tp_setukpairIL,type,
setukpairIL: $o ).
thf(tp_setukpairIR,type,
setukpairIR: $o ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_subbreln,type,
subbreln: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTI,type,
subsetTI: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theeq,type,
theeq: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,definition,
( ap2apEq2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(beta1,definition,
( beta1
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(beta2,definition,
( beta2
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binunionT_lem,definition,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,definition,
( brelnall2
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairsurjEq,definition,
( cartprodpairsurjEq
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(complementTI1,definition,
( complementTI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementT_lem,definition,
( complementT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dpsetconstrEL1,definition,
( dpsetconstrEL1
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,definition,
( dpsetconstrEL2
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrERa,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,definition,
( dpsetconstrSub
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqbreln,definition,
( eqbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(eta1,definition,
( eta1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(eta2,definition,
( eta2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1E2,definition,
( ex1E2
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(funcGraphProp1,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcGraphProp3,definition,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp4,definition,
( funcGraphProp4
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,definition,
( funcext2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(funcextLem,definition,
( funcextLem
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(ifSingleton,definition,
( ifSingleton
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iffalseProp1,definition,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,definition,
( iffalseProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(ifp,definition,
( ifp
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iftrueProp1,definition,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,definition,
( iftrueProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(iftrueorfalse,definition,
( iftrueorfalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam2lamEq,definition,
( lam2lamEq
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetTE1,definition,
( powersetTE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(powersetTI1,definition,
( powersetTI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetT_lem,definition,
( powersetT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setextT,definition,
( setextT
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ X ) ) )
=> ( X = Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusT_lem,definition,
( setminusT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(subbreln,definition,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTI,definition,
( subsetTI
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( subset @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theeq,definition,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(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
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setextAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
emptysetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
setadjoinAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
powersetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
setunionAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
omega0Ax = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(9,plain,
omegaSAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(10,plain,
omegaIndAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(11,plain,
replAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(12,plain,
foundationAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(13,plain,
wellorderingAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(14,plain,
descrp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(15,plain,
dsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(16,plain,
dsetconstrEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(17,plain,
dsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(18,plain,
exuE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(19,plain,
prop2setE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(20,plain,
emptysetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(21,plain,
emptysetimpfalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(22,plain,
notinemptyset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(23,plain,
exuE3e = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(24,plain,
setext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(25,plain,
emptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(26,plain,
noeltsimpempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(27,plain,
setbeta = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(28,plain,
nonemptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(29,plain,
nonemptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(30,plain,
nonemptyI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(31,plain,
setadjoinIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(32,plain,
emptyinunitempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(33,plain,
setadjoinIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(34,plain,
setadjoinE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(35,plain,
setadjoinOr = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(36,plain,
setoftrueEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(37,plain,
powersetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(38,plain,
emptyinPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(39,plain,
emptyInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(40,plain,
powersetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(41,plain,
setunionI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(42,plain,
setunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(43,plain,
subPowSU = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(44,plain,
exuE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(45,plain,
nonemptyImpWitness = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(46,plain,
uniqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(47,plain,
notinsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(48,plain,
eqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(49,plain,
singletonsswitch = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(50,plain,
upairsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(51,plain,
upairsetIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(52,plain,
upairsetIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(53,plain,
emptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(54,plain,
vacuousDall = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(55,plain,
quantDeMorgan1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(56,plain,
quantDeMorgan2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(57,plain,
quantDeMorgan3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(58,plain,
quantDeMorgan4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(59,plain,
prop2setI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(60,plain,
prop2set2propI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(61,plain,
notdexE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(62,plain,
notdallE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(63,plain,
exuI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(64,plain,
exuI3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(65,plain,
exuI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(66,plain,
inCongP = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(67,plain,
in__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(68,plain,
exuE3u = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(69,plain,
exu__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(70,plain,
emptyset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(71,plain,
setadjoin__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(72,plain,
powerset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(73,plain,
setunion__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(74,plain,
omega__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(75,plain,
exuEu = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(76,plain,
descr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(77,plain,
dsetconstr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(78,plain,
subsetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(79,plain,
eqimpsubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(80,plain,
eqimpsubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(81,plain,
subsetI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(82,plain,
emptysetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(83,plain,
subsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(84,plain,
subsetE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(85,plain,
notsubsetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(86,plain,
notequalI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(87,plain,
notequalI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(88,plain,
subsetRefl = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(89,plain,
subsetTrans = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(90,plain,
setadjoinSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(91,plain,
setadjoinSub2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(92,plain,
subset2powerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(93,plain,
setextsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(94,plain,
subsetemptysetimpeq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(95,plain,
powersetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(96,plain,
powersetE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(97,plain,
inPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(98,plain,
powersetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(99,plain,
sepInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(100,plain,
sepSubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(101,plain,
binunionIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(102,plain,
upairset2IR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(103,plain,
binunionIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(104,plain,
binunionEcases = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(105,plain,
binunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(106,plain,
binunionLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(107,plain,
binunionRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(108,plain,
binintersectI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(109,plain,
binintersectSubset5 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(110,plain,
binintersectEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(111,plain,
binintersectLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(112,plain,
binintersectSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(113,plain,
binintersectSubset3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(114,plain,
binintersectER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(115,plain,
disjointsetsI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(116,plain,
binintersectRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(117,plain,
binintersectSubset4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(118,plain,
binintersectSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(119,plain,
bs114d = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(120,plain,
setminusI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(121,plain,
setminusEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(122,plain,
setminusER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(123,plain,
setminusSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(124,plain,
setminusERneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(125,plain,
setminusELneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(126,plain,
setminusILneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(127,plain,
setminusIRneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(128,plain,
setminusLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(129,plain,
setminusSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(130,plain,
symdiffE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(131,plain,
symdiffI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(132,plain,
symdiffI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(133,plain,
symdiffIneg1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(134,plain,
symdiffIneg2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(135,plain,
secondinupair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(136,plain,
setukpairIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(137,plain,
setukpairIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(138,plain,
kpairiskpair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(139,plain,
kpairp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(140,plain,
singletonsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(141,plain,
singletoninpowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(142,plain,
singletoninpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(143,plain,
upairset2E = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(144,plain,
upairsubunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(145,plain,
upairinpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(146,plain,
ubforcartprodlem1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(147,plain,
ubforcartprodlem2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(148,plain,
ubforcartprodlem3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(149,plain,
cartprodpairin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(150,plain,
cartprodmempair1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(151,plain,
cartprodmempair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(152,plain,
setunionE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(153,plain,
setunionsingleton1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(154,plain,
setunionsingleton2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(155,plain,
setunionsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(156,plain,
singletonprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(157,plain,
ex1E1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(158,plain,
ex1I = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(159,plain,
ex1I2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(160,plain,
singletonsuniq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(161,plain,
setukpairinjL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(162,plain,
kfstsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(163,plain,
theprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(164,plain,
kfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(165,plain,
cartprodfstin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(166,plain,
setukpairinjL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(167,plain,
setukpairinjL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(168,plain,
setukpairinjR11 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(169,plain,
setukpairinjR12 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(170,plain,
setukpairinjR1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(171,plain,
upairequniteq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(172,plain,
setukpairinjR2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(173,plain,
setukpairinjR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(174,plain,
ksndsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(175,plain,
ksndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(176,plain,
kpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(177,plain,
cartprodsndin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(178,plain,
cartprodpairmemEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(179,plain,
cartprodpairmemER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(180,plain,
cartprodmempaircEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(181,plain,
cartprodfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(182,plain,
cartprodsndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(183,plain,
cartprodpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(184,plain,
dpsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(185,plain,
dpsetconstrSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(186,plain,
setOfPairsIsBReln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(187,plain,
dpsetconstrERa = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(188,plain,
dpsetconstrEL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(189,plain,
dpsetconstrEL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(190,plain,
dpsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(191,plain,
funcImageSingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(192,plain,
apProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(193,plain,
app = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(194,plain,
infuncsetfunc = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(195,plain,
ap2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(196,plain,
funcinfuncset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(197,plain,
lamProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(198,plain,
lamp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(199,plain,
lam2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(200,plain,
brelnall1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(201,plain,
brelnall2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(202,plain,
ex1E2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(203,plain,
funcGraphProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(204,plain,
funcGraphProp3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(205,plain,
funcGraphProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(206,plain,
funcextLem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(207,plain,
funcGraphProp4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(208,plain,
subbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(209,plain,
eqbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(210,plain,
funcext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(211,plain,
funcext2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(212,plain,
ap2apEq1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(213,plain,
ap2apEq2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(214,plain,
beta1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(215,plain,
eta1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(216,plain,
lam2lamEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(217,plain,
beta2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(218,plain,
eta2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(219,plain,
iffalseProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(220,plain,
iffalseProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(221,plain,
iftrueProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(222,plain,
iftrueProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(223,plain,
ifSingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(224,plain,
ifp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(225,plain,
theeq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(226,plain,
iftrue = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(227,plain,
iffalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(228,plain,
iftrueorfalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(229,plain,
binintersectT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(230,plain,
binunionT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(231,plain,
powersetT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(232,plain,
setminusT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(233,plain,
complementT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(234,plain,
setextT = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(235,plain,
subsetTI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(236,plain,
powersetTI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(237,plain,
powersetTE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(238,plain,
complementTI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(239,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
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(polarity_switch,[status(thm)],[239]) ).
thf(241,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY2 @ sK1_A )
& ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
& ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(242,plain,
complementTI1 = $true,
inference(copy,[status(thm)],[238]) ).
thf(243,plain,
powersetTE1 = $true,
inference(copy,[status(thm)],[237]) ).
thf(244,plain,
powersetTI1 = $true,
inference(copy,[status(thm)],[236]) ).
thf(245,plain,
subsetTI = $true,
inference(copy,[status(thm)],[235]) ).
thf(246,plain,
setextT = $true,
inference(copy,[status(thm)],[234]) ).
thf(247,plain,
complementT_lem = $true,
inference(copy,[status(thm)],[233]) ).
thf(248,plain,
setminusT_lem = $true,
inference(copy,[status(thm)],[232]) ).
thf(249,plain,
powersetT_lem = $true,
inference(copy,[status(thm)],[231]) ).
thf(250,plain,
binunionT_lem = $true,
inference(copy,[status(thm)],[230]) ).
thf(251,plain,
binintersectT_lem = $true,
inference(copy,[status(thm)],[229]) ).
thf(252,plain,
iftrueorfalse = $true,
inference(copy,[status(thm)],[228]) ).
thf(253,plain,
iffalse = $true,
inference(copy,[status(thm)],[227]) ).
thf(254,plain,
iftrue = $true,
inference(copy,[status(thm)],[226]) ).
thf(255,plain,
theeq = $true,
inference(copy,[status(thm)],[225]) ).
thf(256,plain,
ifp = $true,
inference(copy,[status(thm)],[224]) ).
thf(257,plain,
ifSingleton = $true,
inference(copy,[status(thm)],[223]) ).
thf(258,plain,
iftrueProp2 = $true,
inference(copy,[status(thm)],[222]) ).
thf(259,plain,
iftrueProp1 = $true,
inference(copy,[status(thm)],[221]) ).
thf(260,plain,
iffalseProp2 = $true,
inference(copy,[status(thm)],[220]) ).
thf(261,plain,
iffalseProp1 = $true,
inference(copy,[status(thm)],[219]) ).
thf(262,plain,
eta2 = $true,
inference(copy,[status(thm)],[218]) ).
thf(263,plain,
beta2 = $true,
inference(copy,[status(thm)],[217]) ).
thf(264,plain,
lam2lamEq = $true,
inference(copy,[status(thm)],[216]) ).
thf(265,plain,
eta1 = $true,
inference(copy,[status(thm)],[215]) ).
thf(266,plain,
beta1 = $true,
inference(copy,[status(thm)],[214]) ).
thf(267,plain,
ap2apEq2 = $true,
inference(copy,[status(thm)],[213]) ).
thf(268,plain,
ap2apEq1 = $true,
inference(copy,[status(thm)],[212]) ).
thf(269,plain,
funcext2 = $true,
inference(copy,[status(thm)],[211]) ).
thf(270,plain,
funcext = $true,
inference(copy,[status(thm)],[210]) ).
thf(271,plain,
eqbreln = $true,
inference(copy,[status(thm)],[209]) ).
thf(272,plain,
subbreln = $true,
inference(copy,[status(thm)],[208]) ).
thf(273,plain,
funcGraphProp4 = $true,
inference(copy,[status(thm)],[207]) ).
thf(274,plain,
funcextLem = $true,
inference(copy,[status(thm)],[206]) ).
thf(275,plain,
funcGraphProp2 = $true,
inference(copy,[status(thm)],[205]) ).
thf(276,plain,
funcGraphProp3 = $true,
inference(copy,[status(thm)],[204]) ).
thf(277,plain,
funcGraphProp1 = $true,
inference(copy,[status(thm)],[203]) ).
thf(278,plain,
ex1E2 = $true,
inference(copy,[status(thm)],[202]) ).
thf(279,plain,
brelnall2 = $true,
inference(copy,[status(thm)],[201]) ).
thf(280,plain,
brelnall1 = $true,
inference(copy,[status(thm)],[200]) ).
thf(281,plain,
lam2p = $true,
inference(copy,[status(thm)],[199]) ).
thf(282,plain,
lamp = $true,
inference(copy,[status(thm)],[198]) ).
thf(283,plain,
lamProp = $true,
inference(copy,[status(thm)],[197]) ).
thf(284,plain,
funcinfuncset = $true,
inference(copy,[status(thm)],[196]) ).
thf(285,plain,
ap2p = $true,
inference(copy,[status(thm)],[195]) ).
thf(286,plain,
infuncsetfunc = $true,
inference(copy,[status(thm)],[194]) ).
thf(287,plain,
app = $true,
inference(copy,[status(thm)],[193]) ).
thf(288,plain,
apProp = $true,
inference(copy,[status(thm)],[192]) ).
thf(289,plain,
funcImageSingleton = $true,
inference(copy,[status(thm)],[191]) ).
thf(290,plain,
dpsetconstrER = $true,
inference(copy,[status(thm)],[190]) ).
thf(291,plain,
dpsetconstrEL2 = $true,
inference(copy,[status(thm)],[189]) ).
thf(292,plain,
dpsetconstrEL1 = $true,
inference(copy,[status(thm)],[188]) ).
thf(293,plain,
dpsetconstrERa = $true,
inference(copy,[status(thm)],[187]) ).
thf(294,plain,
setOfPairsIsBReln = $true,
inference(copy,[status(thm)],[186]) ).
thf(295,plain,
dpsetconstrSub = $true,
inference(copy,[status(thm)],[185]) ).
thf(296,plain,
dpsetconstrI = $true,
inference(copy,[status(thm)],[184]) ).
thf(297,plain,
cartprodpairsurjEq = $true,
inference(copy,[status(thm)],[183]) ).
thf(298,plain,
cartprodsndpairEq = $true,
inference(copy,[status(thm)],[182]) ).
thf(299,plain,
cartprodfstpairEq = $true,
inference(copy,[status(thm)],[181]) ).
thf(300,plain,
cartprodmempaircEq = $true,
inference(copy,[status(thm)],[180]) ).
thf(301,plain,
cartprodpairmemER = $true,
inference(copy,[status(thm)],[179]) ).
thf(302,plain,
cartprodpairmemEL = $true,
inference(copy,[status(thm)],[178]) ).
thf(303,plain,
cartprodsndin = $true,
inference(copy,[status(thm)],[177]) ).
thf(304,plain,
kpairsurjEq = $true,
inference(copy,[status(thm)],[176]) ).
thf(305,plain,
ksndpairEq = $true,
inference(copy,[status(thm)],[175]) ).
thf(306,plain,
ksndsingleton = $true,
inference(copy,[status(thm)],[174]) ).
thf(307,plain,
setukpairinjR = $true,
inference(copy,[status(thm)],[173]) ).
thf(308,plain,
setukpairinjR2 = $true,
inference(copy,[status(thm)],[172]) ).
thf(309,plain,
upairequniteq = $true,
inference(copy,[status(thm)],[171]) ).
thf(310,plain,
setukpairinjR1 = $true,
inference(copy,[status(thm)],[170]) ).
thf(311,plain,
setukpairinjR12 = $true,
inference(copy,[status(thm)],[169]) ).
thf(312,plain,
setukpairinjR11 = $true,
inference(copy,[status(thm)],[168]) ).
thf(313,plain,
setukpairinjL = $true,
inference(copy,[status(thm)],[167]) ).
thf(314,plain,
setukpairinjL2 = $true,
inference(copy,[status(thm)],[166]) ).
thf(315,plain,
cartprodfstin = $true,
inference(copy,[status(thm)],[165]) ).
thf(316,plain,
kfstpairEq = $true,
inference(copy,[status(thm)],[164]) ).
thf(317,plain,
theprop = $true,
inference(copy,[status(thm)],[163]) ).
thf(318,plain,
kfstsingleton = $true,
inference(copy,[status(thm)],[162]) ).
thf(319,plain,
setukpairinjL1 = $true,
inference(copy,[status(thm)],[161]) ).
thf(320,plain,
singletonsuniq = $true,
inference(copy,[status(thm)],[160]) ).
thf(321,plain,
ex1I2 = $true,
inference(copy,[status(thm)],[159]) ).
thf(322,plain,
ex1I = $true,
inference(copy,[status(thm)],[158]) ).
thf(323,plain,
ex1E1 = $true,
inference(copy,[status(thm)],[157]) ).
thf(324,plain,
singletonprop = $true,
inference(copy,[status(thm)],[156]) ).
thf(325,plain,
setunionsingleton = $true,
inference(copy,[status(thm)],[155]) ).
thf(326,plain,
setunionsingleton2 = $true,
inference(copy,[status(thm)],[154]) ).
thf(327,plain,
setunionsingleton1 = $true,
inference(copy,[status(thm)],[153]) ).
thf(328,plain,
setunionE2 = $true,
inference(copy,[status(thm)],[152]) ).
thf(329,plain,
cartprodmempair = $true,
inference(copy,[status(thm)],[151]) ).
thf(330,plain,
cartprodmempair1 = $true,
inference(copy,[status(thm)],[150]) ).
thf(331,plain,
cartprodpairin = $true,
inference(copy,[status(thm)],[149]) ).
thf(332,plain,
ubforcartprodlem3 = $true,
inference(copy,[status(thm)],[148]) ).
thf(333,plain,
ubforcartprodlem2 = $true,
inference(copy,[status(thm)],[147]) ).
thf(334,plain,
ubforcartprodlem1 = $true,
inference(copy,[status(thm)],[146]) ).
thf(335,plain,
upairinpowunion = $true,
inference(copy,[status(thm)],[145]) ).
thf(336,plain,
upairsubunion = $true,
inference(copy,[status(thm)],[144]) ).
thf(337,plain,
upairset2E = $true,
inference(copy,[status(thm)],[143]) ).
thf(338,plain,
singletoninpowunion = $true,
inference(copy,[status(thm)],[142]) ).
thf(339,plain,
singletoninpowerset = $true,
inference(copy,[status(thm)],[141]) ).
thf(340,plain,
singletonsubset = $true,
inference(copy,[status(thm)],[140]) ).
thf(341,plain,
kpairp = $true,
inference(copy,[status(thm)],[139]) ).
thf(342,plain,
kpairiskpair = $true,
inference(copy,[status(thm)],[138]) ).
thf(343,plain,
setukpairIR = $true,
inference(copy,[status(thm)],[137]) ).
thf(344,plain,
setukpairIL = $true,
inference(copy,[status(thm)],[136]) ).
thf(345,plain,
secondinupair = $true,
inference(copy,[status(thm)],[135]) ).
thf(346,plain,
symdiffIneg2 = $true,
inference(copy,[status(thm)],[134]) ).
thf(347,plain,
symdiffIneg1 = $true,
inference(copy,[status(thm)],[133]) ).
thf(348,plain,
symdiffI2 = $true,
inference(copy,[status(thm)],[132]) ).
thf(349,plain,
symdiffI1 = $true,
inference(copy,[status(thm)],[131]) ).
thf(350,plain,
symdiffE = $true,
inference(copy,[status(thm)],[130]) ).
thf(351,plain,
setminusSubset1 = $true,
inference(copy,[status(thm)],[129]) ).
thf(352,plain,
setminusLsub = $true,
inference(copy,[status(thm)],[128]) ).
thf(353,plain,
setminusIRneg = $true,
inference(copy,[status(thm)],[127]) ).
thf(354,plain,
setminusILneg = $true,
inference(copy,[status(thm)],[126]) ).
thf(355,plain,
setminusELneg = $true,
inference(copy,[status(thm)],[125]) ).
thf(356,plain,
setminusERneg = $true,
inference(copy,[status(thm)],[124]) ).
thf(357,plain,
setminusSubset2 = $true,
inference(copy,[status(thm)],[123]) ).
thf(358,plain,
setminusER = $true,
inference(copy,[status(thm)],[122]) ).
thf(359,plain,
setminusEL = $true,
inference(copy,[status(thm)],[121]) ).
thf(360,plain,
setminusI = $true,
inference(copy,[status(thm)],[120]) ).
thf(361,plain,
bs114d = $true,
inference(copy,[status(thm)],[119]) ).
thf(362,plain,
binintersectSubset1 = $true,
inference(copy,[status(thm)],[118]) ).
thf(363,plain,
binintersectSubset4 = $true,
inference(copy,[status(thm)],[117]) ).
thf(364,plain,
binintersectRsub = $true,
inference(copy,[status(thm)],[116]) ).
thf(365,plain,
disjointsetsI1 = $true,
inference(copy,[status(thm)],[115]) ).
thf(366,plain,
binintersectER = $true,
inference(copy,[status(thm)],[114]) ).
thf(367,plain,
binintersectSubset3 = $true,
inference(copy,[status(thm)],[113]) ).
thf(368,plain,
binintersectSubset2 = $true,
inference(copy,[status(thm)],[112]) ).
thf(369,plain,
binintersectLsub = $true,
inference(copy,[status(thm)],[111]) ).
thf(370,plain,
binintersectEL = $true,
inference(copy,[status(thm)],[110]) ).
thf(371,plain,
binintersectSubset5 = $true,
inference(copy,[status(thm)],[109]) ).
thf(372,plain,
binintersectI = $true,
inference(copy,[status(thm)],[108]) ).
thf(373,plain,
binunionRsub = $true,
inference(copy,[status(thm)],[107]) ).
thf(374,plain,
binunionLsub = $true,
inference(copy,[status(thm)],[106]) ).
thf(375,plain,
binunionE = $true,
inference(copy,[status(thm)],[105]) ).
thf(376,plain,
binunionEcases = $true,
inference(copy,[status(thm)],[104]) ).
thf(377,plain,
binunionIR = $true,
inference(copy,[status(thm)],[103]) ).
thf(378,plain,
upairset2IR = $true,
inference(copy,[status(thm)],[102]) ).
thf(379,plain,
binunionIL = $true,
inference(copy,[status(thm)],[101]) ).
thf(380,plain,
sepSubset = $true,
inference(copy,[status(thm)],[100]) ).
thf(381,plain,
sepInPowerset = $true,
inference(copy,[status(thm)],[99]) ).
thf(382,plain,
powersetsubset = $true,
inference(copy,[status(thm)],[98]) ).
thf(383,plain,
inPowerset = $true,
inference(copy,[status(thm)],[97]) ).
thf(384,plain,
powersetE1 = $true,
inference(copy,[status(thm)],[96]) ).
thf(385,plain,
powersetI1 = $true,
inference(copy,[status(thm)],[95]) ).
thf(386,plain,
subsetemptysetimpeq = $true,
inference(copy,[status(thm)],[94]) ).
thf(387,plain,
setextsub = $true,
inference(copy,[status(thm)],[93]) ).
thf(388,plain,
subset2powerset = $true,
inference(copy,[status(thm)],[92]) ).
thf(389,plain,
setadjoinSub2 = $true,
inference(copy,[status(thm)],[91]) ).
thf(390,plain,
setadjoinSub = $true,
inference(copy,[status(thm)],[90]) ).
thf(391,plain,
subsetTrans = $true,
inference(copy,[status(thm)],[89]) ).
thf(392,plain,
subsetRefl = $true,
inference(copy,[status(thm)],[88]) ).
thf(393,plain,
notequalI2 = $true,
inference(copy,[status(thm)],[87]) ).
thf(394,plain,
notequalI1 = $true,
inference(copy,[status(thm)],[86]) ).
thf(395,plain,
notsubsetI = $true,
inference(copy,[status(thm)],[85]) ).
thf(396,plain,
subsetE2 = $true,
inference(copy,[status(thm)],[84]) ).
thf(397,plain,
subsetE = $true,
inference(copy,[status(thm)],[83]) ).
thf(398,plain,
emptysetsubset = $true,
inference(copy,[status(thm)],[82]) ).
thf(399,plain,
subsetI2 = $true,
inference(copy,[status(thm)],[81]) ).
thf(400,plain,
eqimpsubset1 = $true,
inference(copy,[status(thm)],[80]) ).
thf(401,plain,
eqimpsubset2 = $true,
inference(copy,[status(thm)],[79]) ).
thf(402,plain,
subsetI1 = $true,
inference(copy,[status(thm)],[78]) ).
thf(403,plain,
dsetconstr__Cong = $true,
inference(copy,[status(thm)],[77]) ).
thf(404,plain,
descr__Cong = $true,
inference(copy,[status(thm)],[76]) ).
thf(405,plain,
exuEu = $true,
inference(copy,[status(thm)],[75]) ).
thf(406,plain,
omega__Cong = $true,
inference(copy,[status(thm)],[74]) ).
thf(407,plain,
setunion__Cong = $true,
inference(copy,[status(thm)],[73]) ).
thf(408,plain,
powerset__Cong = $true,
inference(copy,[status(thm)],[72]) ).
thf(409,plain,
setadjoin__Cong = $true,
inference(copy,[status(thm)],[71]) ).
thf(410,plain,
emptyset__Cong = $true,
inference(copy,[status(thm)],[70]) ).
thf(411,plain,
exu__Cong = $true,
inference(copy,[status(thm)],[69]) ).
thf(412,plain,
exuE3u = $true,
inference(copy,[status(thm)],[68]) ).
thf(413,plain,
in__Cong = $true,
inference(copy,[status(thm)],[67]) ).
thf(414,plain,
inCongP = $true,
inference(copy,[status(thm)],[66]) ).
thf(415,plain,
exuI2 = $true,
inference(copy,[status(thm)],[65]) ).
thf(416,plain,
exuI3 = $true,
inference(copy,[status(thm)],[64]) ).
thf(417,plain,
exuI1 = $true,
inference(copy,[status(thm)],[63]) ).
thf(418,plain,
notdallE = $true,
inference(copy,[status(thm)],[62]) ).
thf(419,plain,
notdexE = $true,
inference(copy,[status(thm)],[61]) ).
thf(420,plain,
prop2set2propI = $true,
inference(copy,[status(thm)],[60]) ).
thf(421,plain,
prop2setI = $true,
inference(copy,[status(thm)],[59]) ).
thf(422,plain,
quantDeMorgan4 = $true,
inference(copy,[status(thm)],[58]) ).
thf(423,plain,
quantDeMorgan3 = $true,
inference(copy,[status(thm)],[57]) ).
thf(424,plain,
quantDeMorgan2 = $true,
inference(copy,[status(thm)],[56]) ).
thf(425,plain,
quantDeMorgan1 = $true,
inference(copy,[status(thm)],[55]) ).
thf(426,plain,
vacuousDall = $true,
inference(copy,[status(thm)],[54]) ).
thf(427,plain,
emptyE1 = $true,
inference(copy,[status(thm)],[53]) ).
thf(428,plain,
upairsetIR = $true,
inference(copy,[status(thm)],[52]) ).
thf(429,plain,
upairsetIL = $true,
inference(copy,[status(thm)],[51]) ).
thf(430,plain,
upairsetE = $true,
inference(copy,[status(thm)],[50]) ).
thf(431,plain,
singletonsswitch = $true,
inference(copy,[status(thm)],[49]) ).
thf(432,plain,
eqinunit = $true,
inference(copy,[status(thm)],[48]) ).
thf(433,plain,
notinsingleton = $true,
inference(copy,[status(thm)],[47]) ).
thf(434,plain,
uniqinunit = $true,
inference(copy,[status(thm)],[46]) ).
thf(435,plain,
nonemptyImpWitness = $true,
inference(copy,[status(thm)],[45]) ).
thf(436,plain,
exuE2 = $true,
inference(copy,[status(thm)],[44]) ).
thf(437,plain,
subPowSU = $true,
inference(copy,[status(thm)],[43]) ).
thf(438,plain,
setunionE = $true,
inference(copy,[status(thm)],[42]) ).
thf(439,plain,
setunionI = $true,
inference(copy,[status(thm)],[41]) ).
thf(440,plain,
powersetE = $true,
inference(copy,[status(thm)],[40]) ).
thf(441,plain,
emptyInPowerset = $true,
inference(copy,[status(thm)],[39]) ).
thf(442,plain,
emptyinPowerset = $true,
inference(copy,[status(thm)],[38]) ).
thf(443,plain,
powersetI = $true,
inference(copy,[status(thm)],[37]) ).
thf(444,plain,
setoftrueEq = $true,
inference(copy,[status(thm)],[36]) ).
thf(445,plain,
setadjoinOr = $true,
inference(copy,[status(thm)],[35]) ).
thf(446,plain,
setadjoinE = $true,
inference(copy,[status(thm)],[34]) ).
thf(447,plain,
setadjoinIR = $true,
inference(copy,[status(thm)],[33]) ).
thf(448,plain,
emptyinunitempty = $true,
inference(copy,[status(thm)],[32]) ).
thf(449,plain,
setadjoinIL = $true,
inference(copy,[status(thm)],[31]) ).
thf(450,plain,
nonemptyI1 = $true,
inference(copy,[status(thm)],[30]) ).
thf(451,plain,
nonemptyI = $true,
inference(copy,[status(thm)],[29]) ).
thf(452,plain,
nonemptyE1 = $true,
inference(copy,[status(thm)],[28]) ).
thf(453,plain,
setbeta = $true,
inference(copy,[status(thm)],[27]) ).
thf(454,plain,
noeltsimpempty = $true,
inference(copy,[status(thm)],[26]) ).
thf(455,plain,
emptyI = $true,
inference(copy,[status(thm)],[25]) ).
thf(456,plain,
setext = $true,
inference(copy,[status(thm)],[24]) ).
thf(457,plain,
exuE3e = $true,
inference(copy,[status(thm)],[23]) ).
thf(458,plain,
notinemptyset = $true,
inference(copy,[status(thm)],[22]) ).
thf(459,plain,
emptysetimpfalse = $true,
inference(copy,[status(thm)],[21]) ).
thf(460,plain,
emptysetE = $true,
inference(copy,[status(thm)],[20]) ).
thf(461,plain,
prop2setE = $true,
inference(copy,[status(thm)],[19]) ).
thf(462,plain,
exuE1 = $true,
inference(copy,[status(thm)],[18]) ).
thf(463,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[17]) ).
thf(464,plain,
dsetconstrEL = $true,
inference(copy,[status(thm)],[16]) ).
thf(465,plain,
dsetconstrI = $true,
inference(copy,[status(thm)],[15]) ).
thf(466,plain,
descrp = $true,
inference(copy,[status(thm)],[14]) ).
thf(467,plain,
wellorderingAx = $true,
inference(copy,[status(thm)],[13]) ).
thf(468,plain,
foundationAx = $true,
inference(copy,[status(thm)],[12]) ).
thf(469,plain,
replAx = $true,
inference(copy,[status(thm)],[11]) ).
thf(470,plain,
omegaIndAx = $true,
inference(copy,[status(thm)],[10]) ).
thf(471,plain,
omegaSAx = $true,
inference(copy,[status(thm)],[9]) ).
thf(472,plain,
omega0Ax = $true,
inference(copy,[status(thm)],[8]) ).
thf(473,plain,
setunionAx = $true,
inference(copy,[status(thm)],[7]) ).
thf(474,plain,
powersetAx = $true,
inference(copy,[status(thm)],[6]) ).
thf(475,plain,
setadjoinAx = $true,
inference(copy,[status(thm)],[5]) ).
thf(476,plain,
emptysetAx = $true,
inference(copy,[status(thm)],[4]) ).
thf(477,plain,
setextAx = $true,
inference(copy,[status(thm)],[3]) ).
thf(478,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY2 @ sK1_A )
& ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
& ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(479,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)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(480,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)],[336,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(481,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)],[263,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(482,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)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(483,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)],[287,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(484,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)],[290,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(485,plain,
( ( ! [SX0: $i] : ( subset @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[327,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(486,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)],[248,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(487,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)],[265,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(489,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)],[282,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(490,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)],[311,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(491,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(492,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)],[260,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(493,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(494,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)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(495,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)],[267,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(496,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)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(497,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(498,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(499,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(500,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(501,plain,
( ( omega = omega )
= $true ),
inference(unfold_def,[status(thm)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(502,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)],[300,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(503,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)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(504,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)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(505,plain,
( ( emptyset = emptyset )
= $true ),
inference(unfold_def,[status(thm)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(506,plain,
( ( ! [SX0: $i] : ( in @ SX0 @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(507,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(508,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)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(510,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)],[268,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(511,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(512,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(513,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( kfst @ ( kpair @ SX0 @ SX1 ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[316,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(514,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)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(515,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(516,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(517,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(518,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)],[299,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(519,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(520,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(521,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(522,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(523,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)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(524,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(525,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)],[288,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(526,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(527,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( kpair @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(528,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(529,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)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(530,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)],[266,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(531,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(532,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(533,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(534,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[376,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(536,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(538,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( setminus @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(539,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(540,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(541,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(543,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(544,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( binintersect @ SX0 @ ( binunion @ SX1 @ SX2 ) )
= ( binunion @ ( binintersect @ SX0 @ SX1 ) @ ( binintersect @ SX0 @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(545,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(546,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(547,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(548,plain,
( ( ! [SX0: $i,SX1: $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)],[261,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(549,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(550,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(552,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(553,plain,
( ( ! [SX0: $i] :
( ( setunion @ ( setadjoin @ SX0 @ emptyset ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[325,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(554,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(555,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $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)],[281,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(557,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[274,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(560,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[243,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(561,plain,
( ( ! [SX0: $i > $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)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(562,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( 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)],[244,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i,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)],[269,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(564,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(565,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $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)],[259,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(569,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(570,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $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)],[296,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(572,plain,
( ( ! [SX0: $i > $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)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(575,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(576,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(578,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(579,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(581,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( 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)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(583,plain,
( ( ! [SX0: $i,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)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(585,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(587,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(588,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i,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)],[275,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(591,plain,
( ( ~ ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK1_A )
| ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(593,plain,
( ( ! [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : $true )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[444,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $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)],[258,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(597,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(600,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(601,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(603,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i > $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)],[324,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i,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)],[283,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(607,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $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)],[252,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( subset
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i,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)],[293,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i,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)],[308,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[314,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i > $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)],[321,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(628,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(632,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $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)],[257,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(634,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(635,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(636,plain,
( ( ! [SX0: $i > $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)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(637,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( 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)],[273,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(641,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(642,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(643,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(644,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(645,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[270,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(646,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( 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)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(647,plain,
( ( ! [SX0: $i,SX1: $i,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)],[291,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(648,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(649,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(650,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binunion @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(651,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(652,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,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)],[310,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(654,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(656,plain,
( ( ! [SX0: $i] : ( subset @ emptyset @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(658,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i,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)],[276,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i,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)],[292,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(661,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(662,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(663,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(664,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(666,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(667,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(669,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( kpair @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(671,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(673,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[460,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( 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)],[289,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(678,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(679,plain,
( ( ! [SX0: $i > $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)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(680,plain,
( ( ! [SX0: $i > $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)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( in
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i,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)],[264,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(691,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[392,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(692,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(695,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(696,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $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)],[279,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(698,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(699,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( 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)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(702,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ksnd @ ( kpair @ SX0 @ SX1 ) )
= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[305,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ 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,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( 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)],[246,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(707,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(711,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(713,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(715,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementTI1,complementT_lem,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(716,plain,
! [SV1: $i] :
( ( ! [SY3: $i > $o,SY4: $i] :
( ~ ( in @ SY4 @ SV1 )
| ~ ( SY3 @ SY4 )
| ( ( dsetconstr @ SV1
@ ^ [SX3: $i] : ( SY3 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(717,plain,
! [SV2: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ~ ( in @ SY7 @ SV2 )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ SY6 )
| ( subset @ ( setadjoin @ SY7 @ ( setadjoin @ SY8 @ emptyset ) ) @ ( binunion @ SV2 @ SY6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(718,plain,
! [SV3: $i] :
( ( ! [SY9: $i,SY10: $i > $i] :
( ~ ! [SY11: $i] :
( ~ ( in @ SY11 @ SV3 )
| ( in @ ( SY10 @ SY11 ) @ SY9 ) )
| ! [SY12: $i] :
( ~ ( in @ SY12 @ SV3 )
| ( ( ap @ SV3 @ SY9
@ ( lam @ SV3 @ SY9
@ ^ [SX4: $i] : ( SY10 @ SX4 ) )
@ SY12 )
= ( SY10 @ SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(719,plain,
! [SV4: $i > $i > $o] :
( ( ! [SY14: $i] :
( ~ ! [SY15: $i] :
( ~ ( in @ SY15 @ SY14 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( SV4 @ SY15 @ SY16 )
| ~ ! [SY17: $i] :
( ~ ( SV4 @ SY15 @ SY17 )
| ( SY16 = SY17 ) ) ) )
| ~ ! [SY18: $i] :
~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SY18 )
| ~ ! [SY20: $i] :
~ ~ ( ~ ( in @ SY20 @ SY14 )
| ~ ( SV4 @ SY20 @ SY19 ) ) )
| ~ ( ~ ~ ! [SY21: $i] :
~ ~ ( ~ ( in @ SY21 @ SY14 )
| ~ ( SV4 @ SY21 @ SY19 ) )
| ( in @ SY19 @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(720,plain,
! [SV5: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( func @ SV5 @ SY22 @ SY23 )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ SV5 )
| ( in @ ( ap @ SV5 @ SY22 @ SY23 @ SY24 ) @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(721,plain,
! [SV6: $i] :
( ( ! [SY25: $i,SY26: $i > $i > $o,SY27: $i,SY28: $i] :
( ~ ( in @ ( kpair @ SY27 @ SY28 )
@ ( dpsetconstr @ SV6 @ SY25
@ ^ [SX5: $i,SX6: $i] : ( SY26 @ SX5 @ SX6 ) ) )
| ( SY26 @ SY27 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(722,plain,
! [SV7: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV7 @ emptyset ) ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(723,plain,
! [SV8: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ ( powerset @ SV8 ) )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ ( powerset @ SV8 ) )
| ( in @ ( setminus @ SY31 @ SY32 ) @ ( powerset @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(724,plain,
! [SV9: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( func @ SV9 @ SY33 @ SY34 )
| ( ( lam @ SV9 @ SY33
@ ^ [SY35: $i] : ( ap @ SV9 @ SY33 @ SY34 @ SY35 ) )
= SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(725,plain,
! [SV10: $i] :
( ( ! [SY36: $i] :
( ( SV10 != SY36 )
| ( ( powerset @ SV10 )
= ( powerset @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(726,plain,
! [SV11: $i] :
( ( ! [SY37: $i,SY38: $i > $i] :
( ~ ! [SY39: $i] :
( ~ ( in @ SY39 @ SV11 )
| ( in @ ( SY38 @ SY39 ) @ SY37 ) )
| ( func @ SV11 @ SY37
@ ( lam @ SV11 @ SY37
@ ^ [SX3: $i] : ( SY38 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(727,plain,
! [SV12: $i] :
( ( ! [SY41: $i] :
( ( SV12 != SY41 )
| ( ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SY41 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(728,plain,
! [SV13: $i] :
( ( ~ ! [SY42: $i] :
~ ( in @ SY42 @ SV13 )
| ( SV13 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(729,plain,
! [SV14: $i] :
( ( ! [SY43: $o,SY44: $i] :
( ~ ( in @ SY44 @ SV14 )
| ! [SY45: $i] :
( ~ ( in @ SY45 @ SV14 )
| ~ ~ SY43
| ( ( dsetconstr @ SV14
@ ^ [SX4: $i] :
( ~ ( ~ SY43
| ( SX4 != SY44 ) )
| ~ ( ~ ~ SY43
| ( SX4 != SY45 ) ) ) )
= ( setadjoin @ SY45 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(730,plain,
! [SV15: $i] :
( ( in @ emptyset @ ( powerset @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(731,plain,
! [SV16: $i > $o] :
( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ( SV16 @ SY47 )
| ~ ! [SY48: $i] :
( ~ ( SV16 @ SY48 )
| ( SY47 = SY48 ) ) )
| ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(732,plain,
! [SV17: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( func @ SV17 @ SY51 @ SY52 )
| ! [SY53: $i] :
( ~ ( in @ SY53 @ SV17 )
| ( ( ap @ SV17 @ SY51 @ SY52 @ SY53 )
= ( ap @ SV17 @ SY51 @ SY52 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(733,plain,
! [SV18: $i] :
( ( ~ ~ ! [SY54: $i] :
~ ( in @ SY54 @ SV18 )
| ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(734,plain,
! [SV19: $i] :
( ( ~ ( singleton @ SV19 )
| ! [SY57: $i] :
( ~ ( in @ SY57 @ SV19 )
| ( ( setunion @ SV19 )
= SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(735,plain,
! [SV20: $i] :
( ( ! [SY58: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV20
@ ^ [SX2: $i] : ( SY58 @ SX2 ) ) )
| ! [SY60: $i] :
( ~ ( in @ SY60 @ SV20 )
| ! [SY61: $i] :
( ~ ( in @ SY61 @ SV20 )
| ~ ( SY58 @ SY60 )
| ~ ( SY58 @ SY61 )
| ( SY60 = SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(736,plain,
! [SV21: $i] :
( ( ~ ( in @ SV21 @ omega )
| ( in @ ( setadjoin @ SV21 @ SV21 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(737,plain,
! [SV22: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( in @ SY63 @ SV22 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY62 )
| ( ( kpair @ SY63 @ SX3 )
= ( kpair @ SY63 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(738,plain,
! [SV23: $i] :
( ( ~ ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ SY65 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY66 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ~ ~ ( ~ ( in @ SY68 @ SV23 )
| ~ ( in @ SY69 @ SV23 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY65 )
| ~ ( ~ ( ~ ( in @ SY68 @ SX4 )
| ( in @ SY69 @ SX4 ) )
| ~ ( ~ ( in @ SY69 @ SX4 )
| ( in @ SY68 @ SX4 ) ) ) )
| ( SY68 = SY69 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY65 )
| ~ ( in @ SX3 @ SY65 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY75: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY75 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY75 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY65 )
| ~ ( in @ SX4 @ SY75 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY75 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY65 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(739,plain,
! [SV24: $i] :
( ( ! [SY83: $i] :
( ~ ( in @ SY83 @ ( setunion @ SV24 ) )
| ! [SY84: $o] :
( ~ ! [SY85: $i] :
( ~ ( in @ SY83 @ SY85 )
| ~ ( in @ SY85 @ SV24 )
| SY84 )
| SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(740,plain,
! [SV25: $i] :
( ( in @ SV25 @ ( powerset @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(741,plain,
! [SV26: $i] :
( ( ! [SY86: $i] :
( ( SV26 != SY86 )
| ( subset @ SY86 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(742,plain,
! [SV27: $i > $o] :
( ( ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( SV27 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV27 @ SY88 )
| ( SY87 = SY88 ) ) )
| ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(743,plain,
! [SV28: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( in @ SY91 @ ( setadjoin @ SV28 @ SY90 ) )
| ( SY91 = SV28 )
| ( in @ SY91 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(744,plain,
! [SV29: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ~ ( in @ SY93 @ ( funcSet @ SV29 @ SY92 ) )
| ! [SY94: $i] :
( ~ ( in @ SY94 @ SV29 )
| ( ( ap @ SV29 @ SY92 @ SY93 @ SY94 )
= ( ap @ SV29 @ SY92 @ SY93 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(745,plain,
! [SV30: $i] :
( ( ! [SY95: $i > $o,SY96: $i] :
( ~ ( in @ SY96 @ SV30 )
| ~ ( SY95 @ SY96 )
| ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV30 )
| ~ ( SY95 @ SY97 )
| ( SY97 = SY96 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SX3: $i] : ( SY95 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(746,plain,
! [SV31: $i] :
( ( ~ ( iskpair @ SV31 )
| ( ( kpair @ ( kfst @ SV31 ) @ ( ksnd @ SV31 ) )
= SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(747,plain,
! [SV32: $i] :
( ( ! [SY99: $i] :
( ( kfst @ ( kpair @ SV32 @ SY99 ) )
= SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(748,plain,
! [SV33: $i] :
( ( ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ ( setunion @ SV33 ) )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY100 @ SY101 )
| ~ ( in @ SY101 @ SV33 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY100 @ SY102 )
| ~ ( in @ SY102 @ SV33 ) )
| ( in @ SY100 @ ( setunion @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(749,plain,
! [SV34: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( in @ SY104 @ SV34 )
| ~ ( in @ SY104 @ SY103 )
| ~ ( in @ SY104 @ ( symdiff @ SV34 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(750,plain,
! [SV35: $i] :
( ( ! [SY105: $i] :
( ( SV35 != SY105 )
| ( ( setadjoin @ SV35 @ ( setadjoin @ SY105 @ emptyset ) )
= ( setadjoin @ SV35 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(751,plain,
! [SV36: $i] :
( ( ~ ~ ! [SY106: $i] :
~ ( in @ SY106 @ SV36 )
| ( SV36 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(752,plain,
! [SV37: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( in @ SY108 @ SV37 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY107 )
| ( ( kfst @ ( kpair @ SY108 @ SX3 ) )
= SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(753,plain,
! [SV38: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( in @ SY111 @ SV38 )
| ~ ~ ( in @ SY111 @ SY110 )
| ( in @ SY111 @ ( setminus @ SV38 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(754,plain,
! [SV39: $i] :
( ( ! [SY112: $i,SY113: $i] :
( ~ ( in @ SY113 @ SV39 )
| ~ ~ ( in @ SY113 @ SY112 )
| ( SV39 != SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(755,plain,
! [SV40: $i] :
( ( ! [SY114: $i] :
( ( ( setminus @ SV40 @ SY114 )
!= emptyset )
| ( subset @ SV40 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(756,plain,
! [SV41: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( in @ SY116 @ ( setadjoin @ SV41 @ ( setadjoin @ SY115 @ emptyset ) ) )
| ( SY116 = SV41 )
| ( SY116 = SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(757,plain,
! [SV42: $i > $o] :
( ( ! [SY117: $i > $o] :
( ~ ! [SY118: $i,SY119: $i] :
( ( SY118 != SY119 )
| ~ ( ~ ( ~ ( SV42 @ SY118 )
| ( SY117 @ SY119 ) )
| ~ ( ~ ( SY117 @ SY119 )
| ( SV42 @ SY118 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY117 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY117 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY117 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY117 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(758,plain,
! [SV43: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( subset @ SV43 @ SY128 )
| ~ ~ ( in @ SY129 @ SY128 )
| ~ ( in @ SY129 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(759,plain,
! [SV44: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( func @ SV44 @ SY130 @ SY131 )
| ! [SY132: $i] :
( ~ ( in @ SY132 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY130
@ ^ [SX4: $i] : ( in @ ( kpair @ SY132 @ SX4 ) @ SY131 ) ) )
@ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(760,plain,
! [SV45: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ~ ( in @ SY135 @ SV45 )
| ~ ~ ( in @ SY135 @ SY134 )
| ~ ( in @ SY135 @ ( symdiff @ SV45 @ SY134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(761,plain,
! [SV46: $i] :
( ( ! [SY136: $i] : ( iskpair @ ( kpair @ SV46 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(762,plain,
! [SV47: $i] :
( ( ! [SY137: $i] :
( ~ ! [SY138: $i] :
( ~ ( in @ SY138 @ SY137 )
| ( in @ SY138 @ SV47 ) )
| ( in @ SY137 @ ( powerset @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(763,plain,
! [SV48: $i] :
( ( ! [SY139: $i > $o] :
( ~ ~ ! [SY140: $i] :
~ ~ ( ~ ( in @ SY140 @ SV48 )
| ~ ~ ( SY139 @ SY140 ) )
| ~ ! [SY141: $i] :
( ~ ( in @ SY141 @ SV48 )
| ( SY139 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(764,plain,
! [SV49: $i] :
( ( ! [SY142: $i,SY143: $i > $i] :
( ~ ! [SY144: $i] :
( ~ ( in @ SY144 @ SV49 )
| ( in @ ( SY143 @ SY144 ) @ SY142 ) )
| ! [SY145: $i] :
( ~ ( in @ SY145 @ SV49 )
| ( ( ap @ SV49 @ SY142
@ ( lam @ SV49 @ SY142
@ ^ [SX4: $i] : ( SY143 @ SX4 ) )
@ SY145 )
= ( SY143 @ SY145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(765,plain,
! [SV50: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ( func @ SV50 @ SY147 @ SY148 )
| ( in @ SY148 @ ( funcSet @ SV50 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(766,plain,
! [SV51: $i > $o] :
( ( ~ ~ ! [SY149: $i] :
~ ~ ( ~ ( SV51 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( SV51 @ SY150 )
| ( SY149 = SY150 ) ) )
| ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(767,plain,
! [SV52: $i] :
( ( ! [SY153: $i] : ( subset @ ( binintersect @ SV52 @ SY153 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(768,plain,
! [SV53: $i] :
( ( ! [SY154: $i,SY155: $i,SY156: $o] :
( ~ ( in @ SY155 @ ( binunion @ SV53 @ SY154 ) )
| ~ ( ~ ( in @ SY155 @ SV53 )
| SY156 )
| ~ ( ~ ( in @ SY155 @ SY154 )
| SY156 )
| SY156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(769,plain,
! [SV54: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ~ ( in @ SY158 @ ( setminus @ SV54 @ SY157 ) )
| ~ ( in @ SY158 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(770,plain,
! [SV55: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ~ ( subset @ SV55 @ SY159 )
| ~ ( in @ SY160 @ SV55 )
| ( in @ SY160 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(771,plain,
! [SV56: $i] :
( ( ! [SY161: $i] :
( ( SV56 != SY161 )
| ! [SY162: $i,SY163: $i] :
( ( SY162 != SY163 )
| ( ( setadjoin @ SV56 @ SY162 )
= ( setadjoin @ SY161 @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(772,plain,
! [SV57: $i] :
( ( ! [SY164: $i] : ( subset @ ( setminus @ SV57 @ SY164 ) @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(773,plain,
! [SV58: $i] :
( ( ! [SY165: $i,SY166: $i] :
( ~ ( in @ SY166 @ ( symdiff @ SV58 @ SY165 ) )
| ! [SY167: $o] :
( ~ ( ~ ( in @ SY166 @ SV58 )
| ~ ~ ( in @ SY166 @ SY165 )
| SY167 )
| ~ ( ~ ~ ( in @ SY166 @ SV58 )
| ~ ( in @ SY166 @ SY165 )
| SY167 )
| SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(774,plain,
! [SV59: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( in @ SY169 @ ( cartprod @ SV59 @ SY168 ) )
| ( iskpair @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(775,plain,
! [SV60: $i] :
( ( ! [SY170: $i] :
( ( ( binintersect @ SV60 @ SY170 )
!= SY170 )
| ( subset @ SY170 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(776,plain,
! [SV61: $i] :
( ( ! [SY171: $i] :
( ~ ! [SY172: $i] :
( ~ ( in @ SY172 @ SV61 )
| ( in @ SY172 @ SY171 ) )
| ~ ! [SY173: $i] :
( ~ ( in @ SY173 @ SY171 )
| ( in @ SY173 @ SV61 ) )
| ( SV61 = SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(777,plain,
! [SV62: $i] :
( ( ! [SY174: $o,SY175: $i] :
( ~ ( in @ SY175 @ SV62 )
| ! [SY176: $i] :
( ~ ( in @ SY176 @ SV62 )
| ~ SY174
| ( ( if @ SV62 @ SY174 @ SY175 @ SY176 )
= SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(778,plain,
! [SV63: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ( binintersect @ SV63 @ ( binunion @ SY177 @ SY178 ) )
= ( binunion @ ( binintersect @ SV63 @ SY177 ) @ ( binintersect @ SV63 @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(779,plain,
! [SV64: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( ( setadjoin @ SV64 @ ( setadjoin @ SY179 @ emptyset ) )
!= ( setadjoin @ SY180 @ emptyset ) )
| ( SV64 = SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(780,plain,
! [SV65: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( in @ SY182 @ SV65 )
| ( in @ ( setadjoin @ SY182 @ emptyset ) @ ( powerset @ ( binunion @ SV65 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(781,plain,
! [SV66: $i] :
( ( ! [SY183: $i] :
( ~ ~ ( subset @ SV66 @ SY183 )
| ( SV66 != SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(782,plain,
! [SV67: $i] :
( ( ! [SY184: $o,SY185: $i] :
( ~ ( in @ SY185 @ SV67 )
| ! [SY186: $i] :
( ~ ( in @ SY186 @ SV67 )
| ~ ~ SY184
| ( in @ SY186
@ ( dsetconstr @ SV67
@ ^ [SX4: $i] :
( ~ ( ~ SY184
| ( SX4 != SY185 ) )
| ~ ( ~ ~ SY184
| ( SX4 != SY186 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(783,plain,
! [SV68: $i] :
( ( ! [SY188: $i > $o] :
( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SV68 )
| ~ ( SY188 @ SY189 ) )
| ~ ~ ! [SY190: $i] :
~ ~ ( ~ ( in @ SY190 @ SV68 )
| ~ ( SY188 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(784,plain,
! [SV69: $i] :
( ( ! [SY191: $i > $o] :
( ~ ~ ~ ! [SY192: $i] :
~ ~ ( ~ ( in @ SY192 @ SV69 )
| ~ ( SY191 @ SY192 ) )
| ! [SY193: $i] :
( ~ ( in @ SY193 @ SV69 )
| ~ ( SY191 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(785,plain,
! [SV70: $i] :
( ( ! [SY194: $i,SY195: $i] :
( ~ ( in @ SY194 @ ( powerset @ SV70 ) )
| ~ ( in @ SY195 @ SY194 )
| ( in @ SY195 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(786,plain,
! [SV71: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ~ ( in @ SY197 @ SV71 )
| ( in @ SY197 @ ( binunion @ SV71 @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(787,plain,
! [SV72: $i] :
( ( ( setunion @ ( setadjoin @ SV72 @ emptyset ) )
= SV72 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(788,plain,
! [SV73: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( in @ SY199 @ SV73 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY198 )
| ( ( ksnd @ ( kpair @ SY199 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(789,plain,
! [SV74: $i] :
( ( ! [SY201: $i] :
( ( SV74 != SY201 )
| ! [SY202: $i,SY203: $i] :
( ( SY202 != SY203 )
| ~ ( ~ ( ~ ( in @ SY202 @ SV74 )
| ( in @ SY203 @ SY201 ) )
| ~ ( ~ ( in @ SY203 @ SY201 )
| ( in @ SY202 @ SV74 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(790,plain,
! [SV75: $i] :
( ( ! [SY204: $i,SY205: $i > $i] :
( ~ ! [SY206: $i] :
( ~ ( in @ SY206 @ SV75 )
| ( in @ ( SY205 @ SY206 ) @ SY204 ) )
| ( in
@ ( lam @ SV75 @ SY204
@ ^ [SX3: $i] : ( SY205 @ SX3 ) )
@ ( funcSet @ SV75 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(791,plain,
! [SV76: $i] :
( ( ! [SY208: $i > $o] :
( ~ ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SV76 )
| ( SY208 @ SY209 ) )
| ~ ! [SY210: $i] :
~ ~ ( ~ ( in @ SY210 @ SV76 )
| ~ ~ ( SY208 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(792,plain,
! [SV77: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ( func @ SV77 @ SY211 @ SY212 )
| ! [SY213: $i] :
( ~ ( func @ SV77 @ SY211 @ SY213 )
| ~ ! [SY214: $i] :
( ~ ( in @ SY214 @ SV77 )
| ( ( ap @ SV77 @ SY211 @ SY212 @ SY214 )
= ( ap @ SV77 @ SY211 @ SY213 @ SY214 ) ) )
| ! [SY215: $i] :
( ~ ( in @ SY215 @ SV77 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY211 )
| ~ ( in @ ( kpair @ SY215 @ SX5 ) @ SY213 )
| ( in @ ( kpair @ SY215 @ SX5 ) @ SY212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(793,plain,
! [SV78: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( in @ ( setadjoin @ SY218 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SY217 @ emptyset ) ) @ emptyset ) ) )
| ( SV78 = SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(794,plain,
! [SV79: $i] :
( ( ! [SY219: $i] :
( ~ ( in @ SY219 @ ( powerset @ SV79 ) )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ ( powerset @ SV79 ) )
| ! [SY221: $i] :
( ~ ( in @ SY221 @ SV79 )
| ~ ( in @ SY219 @ ( powerset @ SY220 ) )
| ~ ( in @ SY221 @ SY219 )
| ( in @ SY221 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(795,plain,
! [SV80: $i > $o] :
( ( ~ ~ ! [SY222: $i] :
~ ~ ( ~ ( SV80 @ SY222 )
| ~ ! [SY223: $i] :
( ~ ( SV80 @ SY223 )
| ( SY222 = SY223 ) ) )
| ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(796,plain,
! [SV81: $i] :
( ( ! [SY226: $i] :
( ~ ( in @ SY226 @ ( powerset @ SV81 ) )
| ! [SY227: $i] :
( ~ ( in @ SY227 @ ( powerset @ SV81 ) )
| ~ ! [SY228: $i] :
( ~ ( in @ SY228 @ SV81 )
| ~ ( in @ SY228 @ SY226 )
| ( in @ SY228 @ SY227 ) )
| ( in @ SY226 @ ( powerset @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(797,plain,
! [SV82: $i] :
( ( ! [SY229: $i,SY230: $i] :
( ~ ( in @ SY230 @ ( funcSet @ SV82 @ SY229 ) )
| ! [SY231: $i] :
( ~ ( in @ SY231 @ ( funcSet @ SV82 @ SY229 ) )
| ~ ! [SY232: $i] :
( ~ ( in @ SY232 @ SV82 )
| ( ( ap @ SV82 @ SY229 @ SY230 @ SY232 )
= ( ap @ SV82 @ SY229 @ SY231 @ SY232 ) ) )
| ( SY230 = SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(798,plain,
! [SV83: $i] :
( ( ~ ! [SY233: $i] :
~ ( in @ SY233 @ SV83 )
| ( SV83 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(799,plain,
! [SV84: $i] :
( ( ! [SY234: $i] :
( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SY234 @ emptyset ) )
| ( SV84 = SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(800,plain,
! [SV85: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( subset @ SY236 @ ( cartprod @ SV85 @ SY235 ) )
| ! [SY237: $i] :
( ~ ( subset @ SY237 @ ( cartprod @ SV85 @ SY235 ) )
| ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV85 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY235 )
| ~ ( in @ ( kpair @ SY238 @ SX5 ) @ SY236 )
| ( in @ ( kpair @ SY238 @ SX5 ) @ SY237 ) ) )
| ~ ! [SY240: $i] :
( ~ ( in @ SY240 @ SV85 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY235 )
| ~ ( in @ ( kpair @ SY240 @ SX5 ) @ SY237 )
| ( in @ ( kpair @ SY240 @ SX5 ) @ SY236 ) ) )
| ( SY236 = SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(801,plain,
! [SV86: $i] :
( ( ! [SY242: $o,SY243: $i] :
( ~ ( in @ SY243 @ SV86 )
| ! [SY244: $i] :
( ~ ( in @ SY244 @ SV86 )
| ~ SY242
| ( in @ SY243
@ ( dsetconstr @ SV86
@ ^ [SX4: $i] :
( ~ ( ~ SY242
| ( SX4 != SY243 ) )
| ~ ( ~ ~ SY242
| ( SX4 != SY244 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(802,plain,
! [SV87: $i] :
( ( ! [SY246: $i > $o,SY247: $i] :
( ~ ( in @ SY247
@ ( dsetconstr @ SV87
@ ^ [SX3: $i] : ( SY246 @ SX3 ) ) )
| ( SY246 @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(803,plain,
! [SV88: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ( ( kpair @ SV88 @ SY249 )
!= ( kpair @ SY250 @ SY251 ) )
| ( SY249 = SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(804,plain,
! [SV89: $i] :
( ( ~ ( ( SV89 != emptyset ) )
| ~ ! [SY252: $i] :
~ ~ ( ~ ( in @ SY252 @ SV89 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(805,plain,
! [SV90: $i] :
( ( ! [SY253: $i,SY254: $i > $i > $o,SY255: $i] :
( ~ ( in @ SY255 @ SV90 )
| ! [SY256: $i] :
( ~ ( in @ SY256 @ SY253 )
| ~ ( SY254 @ SY255 @ SY256 )
| ( in @ ( kpair @ SY255 @ SY256 )
@ ( dpsetconstr @ SV90 @ SY253
@ ^ [SX5: $i,SX6: $i] : ( SY254 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(806,plain,
! [SV91: $i > $o] :
( ( ~ ~ ! [SY259: $i] :
~ ~ ( ~ ( SV91 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV91 @ SY260 )
| ( SY259 = SY260 ) ) )
| ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(807,plain,
! [SV92: $i] :
( ( ! [SY263: $i] :
( ~ ! [SY264: $i] :
( ~ ( in @ SY264 @ SV92 )
| ( in @ SY264 @ SY263 ) )
| ( subset @ SV92 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(808,plain,
! [SV93: $i] :
( ( ! [SY265: $i] :
( ~ ( subset @ SV93 @ SY265 )
| ( subset @ ( powerset @ SV93 ) @ ( powerset @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(809,plain,
! [SV94: $i] :
( ( ~ ( iskpair @ SV94 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV94 )
@ ^ [SY266: $i] :
( SV94
= ( kpair @ ( kfst @ SV94 ) @ SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(810,plain,
! [SV95: $i] :
( ( ! [SY267: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV95
@ ^ [SX2: $i] : ( SY267 @ SX2 ) ) )
| ~ ! [SY269: $i] :
~ ~ ( ~ ( in @ SY269 @ SV95 )
| ~ ( SY267 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(811,plain,
! [SV96: $i] :
( ( ! [SY270: $i > $o] :
( ~ ~ ~ ! [SY271: $i] :
~ ~ ( ~ ( in @ SY271 @ SV96 )
| ~ ( SY270 @ SY271 ) )
| ! [SY272: $i] :
( ~ ( in @ SY272 @ SV96 )
| ~ ( SY270 @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(812,plain,
! [SV97: $i] :
( ( ! [SY273: $i] : ( in @ SY273 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV97 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV97 @ ( setadjoin @ SY273 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(813,plain,
! [SV98: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( in @ SY275 @ SV98 )
| ! [SY276: $i] :
( ~ ( in @ SY276 @ SY274 )
| ( in @ ( kpair @ SY275 @ SY276 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SY274 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(814,plain,
! [SV99: $i] :
( ( ! [SY277: $i] :
~ ( ~ ( ~ ( in @ SY277 @ ( powerset @ SV99 ) )
| ! [SY278: $i] :
( ~ ( in @ SY278 @ SY277 )
| ( in @ SY278 @ SV99 ) ) )
| ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SY277 )
| ( in @ SY279 @ SV99 ) )
| ( in @ SY277 @ ( powerset @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(815,plain,
! [SV100: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( in @ SY281 @ ( binintersect @ SV100 @ SY280 ) )
| ( in @ SY281 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(816,plain,
! [SV101: $i] :
( ( ! [SY282: $i,SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ ( setadjoin @ SV101 @ SY282 ) )
| ( SY283 = SV101 )
| ( in @ SY283 @ SY282 ) )
| ~ ( ~ ( ( SY283 = SV101 )
| ( in @ SY283 @ SY282 ) )
| ( in @ SY283 @ ( setadjoin @ SV101 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(817,plain,
! [SV102: $i] :
( ( ! [SY284: $i] :
( ~ ( in @ SV102 @ ( setadjoin @ SY284 @ emptyset ) )
| ( in @ SY284 @ ( setadjoin @ SV102 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(818,plain,
! [SV103: $i > $o] :
( ( ! [SY285: $i] :
( ~ ( in @ SY285 @ emptyset )
| ( SV103 @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(819,plain,
! [SV104: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ~ ( in @ SY287 @ SV104 )
| ! [SY288: $i] :
( ~ ( in @ SY288 @ SY286 )
| ( in @ ( setadjoin @ SY287 @ ( setadjoin @ SY288 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SY286 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(820,plain,
! [SV105: $i] :
( ( ! [SY289: $i] :
( ( SV105 != SY289 )
| ! [SY290: $i,SY291: $i] :
( ( SY290 != SY291 )
| ~ ( in @ SY290 @ SV105 )
| ( in @ SY291 @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(821,plain,
! [SV106: $i] :
( ( ! [SY292: $i] : ( in @ SY292 @ ( setadjoin @ SV106 @ ( setadjoin @ SY292 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(822,plain,
! [SV107: $i] :
( ( ! [SY293: $i] :
( ( SV107 != SY293 )
| ( subset @ SV107 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(823,plain,
! [SV108: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ~ ( func @ SV108 @ SY294 @ SY295 )
| ! [SY296: $i] :
( ~ ( in @ SY296 @ SV108 )
| ! [SY297: $i] :
( ~ ( in @ SY297 @ SY294 )
| ~ ( in @ ( kpair @ SY296 @ SY297 ) @ SY295 )
| ( ( ap @ SV108 @ SY294 @ SY295 @ SY296 )
= SY297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(824,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK1_A )
| ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(825,plain,
! [SV109: $i] :
( ( ! [SY298: $i] :
( ~ ! [SY299: $i] :
~ ( ~ ( ~ ( in @ SY299 @ SV109 )
| ( in @ SY299 @ SY298 ) )
| ~ ( ~ ( in @ SY299 @ SY298 )
| ( in @ SY299 @ SV109 ) ) )
| ( SV109 = SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(826,plain,
! [SV110: $i] :
( ( ( dsetconstr @ SV110
@ ^ [SX1: $i] : $true )
= SV110 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(827,plain,
! [SV111: $i] :
( ( ! [SY301: $i] : ( in @ SY301 @ ( setadjoin @ SV111 @ ( setadjoin @ SY301 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(828,plain,
! [SV112: $i] :
( ( ! [SY302: $i > $o,SY303: $i] :
( ~ ( in @ SY303 @ SV112 )
| ~ ( ~ ( ~ ( in @ SY303
@ ( dsetconstr @ SV112
@ ^ [SX3: $i] : ( SY302 @ SX3 ) ) )
| ( SY302 @ SY303 ) )
| ~ ( ~ ( SY302 @ SY303 )
| ( in @ SY303
@ ( dsetconstr @ SV112
@ ^ [SX3: $i] : ( SY302 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(829,plain,
! [SV113: $i] :
( ( ! [SY306: $o,SY307: $i] :
( ~ ( in @ SY307 @ SV113 )
| ! [SY308: $i] :
( ~ ( in @ SY308 @ SV113 )
| ~ SY306
| ( ( dsetconstr @ SV113
@ ^ [SX4: $i] :
( ~ ( ~ SY306
| ( SX4 != SY307 ) )
| ~ ( ~ ~ SY306
| ( SX4 != SY308 ) ) ) )
= ( setadjoin @ SY307 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(830,plain,
! [SV114: $i] :
( ( ~ ( ( SV114 != emptyset ) )
| ~ ! [SY310: $i] :
~ ( in @ SY310 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(831,plain,
! [SV115: $i] :
( ( ! [SY311: $i,SY312: $i,SY313: $i] :
( ~ ( in @ ( kpair @ SY312 @ SY313 ) @ ( cartprod @ SV115 @ SY311 ) )
| ( in @ SY313 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(832,plain,
! [SV116: $i] :
( ( ! [SY314: $i > $o,SY315: $i] :
( ~ ( in @ SY315
@ ( dsetconstr @ SV116
@ ^ [SX3: $i] : ( SY314 @ SX3 ) ) )
| ( in @ SY315 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(833,plain,
! [SV117: $i] :
( ( ~ ( iskpair @ SV117 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV117 )
@ ^ [SY317: $i] : ( in @ ( setadjoin @ SY317 @ emptyset ) @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(834,plain,
! [SV118: $i] :
( ( ! [SY318: $i] :
( ~ ( in @ SY318 @ SV118 )
| ( subset @ ( setadjoin @ SY318 @ emptyset ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(835,plain,
! [SV119: $i] :
( ( ! [SY319: $i] :
( ~ ( subset @ SY319 @ SV119 )
| ( ( binintersect @ SV119 @ SY319 )
= SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(836,plain,
! [SV120: $i] :
( ( ! [SY320: $i,SY321: $i] :
( ~ ( in @ SY321 @ SY320 )
| ( in @ SY321 @ ( setadjoin @ SV120 @ SY320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(837,plain,
! [SV121: $i] :
( ( ! [SY322: $i > $o] :
( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SV121 )
| ! [SY324: $i] :
( ~ ( in @ SY324 @ SV121 )
| ~ ( SY322 @ SY323 )
| ~ ( SY322 @ SY324 )
| ( SY323 = SY324 ) ) )
| ~ ~ ! [SY325: $i] :
~ ~ ( ~ ( in @ SY325 @ SV121 )
| ~ ( SY322 @ SY325 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SX2: $i] : ( SY322 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(838,plain,
! [SV122: $i] :
( ( ! [SY327: $o,SY328: $i] :
( ~ ( in @ SY328 @ SV122 )
| ! [SY329: $i] :
( ~ ( in @ SY329 @ SV122 )
| ~ ~ SY327
| ( ( if @ SV122 @ SY327 @ SY328 @ SY329 )
= SY329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(839,plain,
! [SV123: $i] :
( ( ! [SY330: $i,SY331: $i > $i] :
( ~ ! [SY332: $i] :
( ~ ( in @ SY332 @ SV123 )
| ( in @ ( SY331 @ SY332 ) @ SY330 ) )
| ( func @ SV123 @ SY330
@ ( dpsetconstr @ SV123 @ SY330
@ ^ [SX3: $i,SX4: $i] :
( ( SY331 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(840,plain,
! [SV124: $o] :
( ( ! [SY335: $i] :
( ~ ( in @ SY335 @ ( prop2set @ SV124 ) )
| SV124 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[607]) ).
thf(841,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[607]) ).
thf(842,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[607]) ).
thf(843,plain,
! [SV125: $i] :
( ( ! [SY336: $o,SY337: $i] :
( ~ ( in @ SY337 @ SV125 )
| ! [SY338: $i] :
( ~ ( in @ SY338 @ SV125 )
| ( in @ ( if @ SV125 @ SY336 @ SY337 @ SY338 ) @ ( setadjoin @ SY337 @ ( setadjoin @ SY338 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(844,plain,
! [SV126: $i] :
( ( ! [SY339: $i] :
( ~ ( subset @ SV126 @ SY339 )
| ( ( binintersect @ SV126 @ SY339 )
= SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(845,plain,
! [SV127: $i] :
( ( ! [SY340: $i] : ( subset @ SY340 @ ( binunion @ SV127 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(846,plain,
! [SV128: $i] :
( ( ! [SY341: $i > $o] :
( subset
@ ( dsetconstr @ SV128
@ ^ [SX2: $i] : ( SY341 @ SX2 ) )
@ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(847,plain,
! [SV129: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ~ ( in @ SY344 @ SV129 )
| ~ ( in @ SY344 @ SY343 )
| ( in @ SY344 @ ( binintersect @ SV129 @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(848,plain,
! [SV130: $i] :
( ( ! [SY345: $i,SY346: $i > $i > $o,SY347: $i] :
( ~ ( in @ SY347 @ SV130 )
| ! [SY348: $i] :
( ~ ( in @ SY348 @ SY345 )
| ~ ( in @ ( kpair @ SY347 @ SY348 )
@ ( dpsetconstr @ SV130 @ SY345
@ ^ [SX5: $i,SX6: $i] : ( SY346 @ SX5 @ SX6 ) ) )
| ( SY346 @ SY347 @ SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(849,plain,
! [SV131: $i] :
( ( ! [SY351: $i] :
( ( ( binintersect @ SV131 @ SY351 )
!= SV131 )
| ( subset @ SV131 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(850,plain,
! [SV132: $i] :
( ( ! [SY352: $i] : ( subset @ SV132 @ ( binunion @ SV132 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(851,plain,
! [SV133: $i] :
( ( ! [SY353: $o,SY354: $i] :
( ~ ( in @ SY354 @ SV133 )
| ! [SY355: $i] :
( ~ ( in @ SY355 @ SV133 )
| ( in @ ( if @ SV133 @ SY353 @ SY354 @ SY355 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(852,plain,
! [SV134: $i] :
( ( ! [SY356: $i] :
( ~ ( in @ SY356 @ ( powerset @ SV134 ) )
| ( subset @ SY356 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(853,plain,
! [SV135: $i] :
( ( ! [SY357: $i,SY358: $i] :
( ~ ~ ( in @ SY358 @ SV135 )
| ~ ( in @ SY358 @ SY357 )
| ( in @ SY358 @ ( symdiff @ SV135 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(854,plain,
! [SV136: $i] :
( ( ! [SY359: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV136 @ ( setadjoin @ SY359 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(855,plain,
! [SV137: $i] :
( ( ! [SY360: $i,SY361: $i,SY362: $i] :
( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SY360 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY361 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY361 @ ( setadjoin @ SY362 @ emptyset ) ) @ emptyset ) ) )
| ( SY360 = SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(856,plain,
! [SV138: $i] :
( ( ! [SY363: $i,SY364: $i,SY365: $i] :
( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SY363 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY364 @ ( setadjoin @ SY365 @ emptyset ) ) @ emptyset ) ) )
| ( SV138 = SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(857,plain,
! [SV139: $i] :
( ( ! [SY366: $i > $o] :
( ~ ! [SY367: $i] :
( ~ ( in @ SY367 @ SV139 )
| ! [SY368: $i] :
( ~ ( in @ SY368 @ SV139 )
| ~ ( SY366 @ SY367 )
| ~ ( SY366 @ SY368 )
| ( SY367 = SY368 ) ) )
| ~ ~ ! [SY369: $i] :
~ ~ ( ~ ( in @ SY369 @ SV139 )
| ~ ( SY366 @ SY369 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SX2: $i] : ( SY366 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(858,plain,
! [SV140: $i] :
( ( ! [SY371: $i] : ( in @ SY371 @ ( setadjoin @ SV140 @ ( setadjoin @ SY371 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(859,plain,
! [SV141: $i] :
( ( ! [SY372: $i] :
( ~ ( in @ SY372 @ SV141 )
| ( in @ ( setadjoin @ SY372 @ emptyset ) @ ( powerset @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(860,plain,
! [SV142: $i] :
( ( ! [SY373: $i] :
( ~ ( subset @ SV142 @ SY373 )
| ( in @ SV142 @ ( powerset @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(861,plain,
! [SV143: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ( in @ SY375 @ SV143 )
| ! [SY376: $i] :
( ~ ( in @ SY376 @ SY374 )
| ( in @ ( kpair @ SY375 @ SY376 ) @ ( cartprod @ SV143 @ SY374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(862,plain,
! [SV144: $i] :
( ( ! [SY377: $i] :
( ~ ( in @ SY377 @ ( powerset @ SV144 ) )
| ( in @ ( powerset @ SY377 ) @ ( powerset @ ( powerset @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(863,plain,
! [SV145: $i > $o] :
( ( ~ ~ ! [SY378: $i] :
~ ~ ( ~ ( SV145 @ SY378 )
| ~ ! [SY379: $i] :
( ~ ( SV145 @ SY379 )
| ( SY378 = SY379 ) ) )
| ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(864,plain,
! [SV146: $i] :
( ( ! [SY381: $i] : ( subset @ SY381 @ ( setadjoin @ SV146 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(865,plain,
! [SV147: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ~ ( in @ SY383 @ ( binunion @ SV147 @ SY382 ) )
| ( in @ SY383 @ SV147 )
| ( in @ SY383 @ SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(866,plain,
! [SV148: $i] :
( ( ! [SY384: $i] : ( in @ SV148 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV148 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV148 @ ( setadjoin @ SY384 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(867,plain,
! [SV149: $o] :
( ( ~ SV149
| ( set2prop @ ( prop2set @ SV149 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[632]) ).
thf(868,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[632]) ).
thf(869,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[632]) ).
thf(870,plain,
! [SV150: $i] :
( ( ! [SY385: $o,SY386: $i] :
( ~ ( in @ SY386 @ SV150 )
| ! [SY387: $i] :
( ~ ( in @ SY387 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SX4: $i] :
( ~ ( ~ SY385
| ( SX4 != SY386 ) )
| ~ ( ~ ~ SY385
| ( SX4 != SY387 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(871,plain,
! [SV151: $o] :
( ( ~ SV151
| ( in @ emptyset @ ( prop2set @ SV151 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[634]) ).
thf(872,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[634]) ).
thf(873,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[634]) ).
thf(874,plain,
! [SV152: $i] :
( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ ( powerset @ SV152 ) )
| ! [SY390: $i] :
( ~ ( in @ SY390 @ ( powerset @ SV152 ) )
| ~ ! [SY391: $i] :
( ~ ( in @ SY391 @ SV152 )
| ~ ( in @ SY391 @ SY389 )
| ( in @ SY391 @ SY390 ) )
| ( subset @ SY389 @ SY390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(875,plain,
! [SV153: $i > $o] :
( ( ~ ~ ! [SY392: $i] :
~ ! [SY393: $i] :
~ ( ~ ( ~ ( SV153 @ SY393 )
| ( SY393 = SY392 ) )
| ~ ( ( SY393 != SY392 )
| ( SV153 @ SY393 ) ) )
| ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(876,plain,
! [SV154: $i] :
( ( ! [SY396: $i] :
( ( SV154 != SY396 )
| ( ( setunion @ SV154 )
= ( setunion @ SY396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(877,plain,
! [SV155: $i] :
( ( ! [SY397: $i] :
( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV155 )
| ( in @ SY398 @ SY397 ) )
| ( subset @ SV155 @ SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(878,plain,
! [SV156: $i] :
( ( ! [SY399: $i,SY400: $i] :
( ~ ( in @ SY400 @ ( funcSet @ SV156 @ SY399 ) )
| ! [SY401: $i] :
( ~ ( in @ SY401 @ SV156 )
| ! [SY402: $i] :
( ~ ( in @ SY402 @ SY399 )
| ~ ( in @ ( kpair @ SY401 @ SY402 ) @ SY400 )
| ( ( ap @ SV156 @ SY399 @ SY400 @ SY401 )
= SY402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(879,plain,
! [SV157: $i] :
( ( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY404 @ ( funcSet @ SV157 @ SY403 ) )
| ! [SY405: $i] :
( ~ ( in @ SY405 @ SV157 )
| ( in @ ( ap @ SV157 @ SY403 @ SY404 @ SY405 ) @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(880,plain,
! [SV158: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ~ ~ ( in @ SY407 @ ( setminus @ SV158 @ SY406 ) )
| ~ ( in @ SY407 @ SV158 )
| ( in @ SY407 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(881,plain,
! [SV159: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( in @ SY409 @ ( cartprod @ SV159 @ SY408 ) )
| ( in @ ( ksnd @ SY409 ) @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(882,plain,
! [SV160: $i] :
( ( ~ ( in @ SV160 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(883,plain,
! [SV161: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( in @ SY411 @ ( binintersect @ SV161 @ SY410 ) )
| ( in @ SY411 @ SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(884,plain,
! [SV162: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( func @ SV162 @ SY412 @ SY413 )
| ! [SY414: $i] :
( ~ ( func @ SV162 @ SY412 @ SY414 )
| ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV162 )
| ( ( ap @ SV162 @ SY412 @ SY413 @ SY415 )
= ( ap @ SV162 @ SY412 @ SY414 @ SY415 ) ) )
| ( SY413 = SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(885,plain,
! [SV163: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV163 )
| ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) )
| ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(886,plain,
! [SV164: $i] :
( ( ! [SY418: $i,SY419: $i > $i > $o,SY420: $i,SY421: $i] :
( ~ ( in @ ( kpair @ SY420 @ SY421 )
@ ( dpsetconstr @ SV164 @ SY418
@ ^ [SX5: $i,SX6: $i] : ( SY419 @ SX5 @ SX6 ) ) )
| ( in @ SY421 @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(887,plain,
! [SV165: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( func @ SV165 @ SY424 @ SY425 )
| ! [SY426: $i] :
( ~ ( in @ SY426 @ SV165 )
| ( in @ ( kpair @ SY426 @ ( ap @ SV165 @ SY424 @ SY425 @ SY426 ) ) @ SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(888,plain,
! [SV166: $i] :
( ( ! [SY427: $i,SY428: $i] :
( ~ ( in @ SY428 @ ( setadjoin @ SV166 @ SY427 ) )
| ! [SY429: $o] :
( ~ ( ( SY428 != SV166 )
| SY429 )
| ~ ( ~ ( in @ SY428 @ SY427 )
| SY429 )
| SY429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(889,plain,
! [SV167: $i] :
( ( ! [SY430: $i] :
( ~ ( in @ SY430 @ ( powerset @ SV167 ) )
| ! [SY431: $i] :
( ~ ( in @ SY431 @ ( powerset @ SV167 ) )
| ( in @ ( binunion @ SY430 @ SY431 ) @ ( powerset @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(890,plain,
! [SV168: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( in @ SY433 @ SV168 )
| ! [SY434: $i] :
( ~ ( in @ SY434 @ SY432 )
| ( in @ ( setadjoin @ ( setadjoin @ SY433 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY433 @ ( setadjoin @ SY434 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SY432 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(891,plain,
! [SV169: $i] :
( ( ! [SY435: $i,SY436: $i] :
( ~ ( subset @ SY436 @ SV169 )
| ~ ( subset @ SY436 @ SY435 )
| ( subset @ SY436 @ ( binintersect @ SV169 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(892,plain,
! [SV170: $i] :
( ( ! [SY437: $i,SY438: $i,SY439: $i] :
( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SY437 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY438 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY438 @ ( setadjoin @ SY439 @ emptyset ) ) @ emptyset ) ) )
| ( SY438 != SY439 )
| ( SY437 = SY439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(893,plain,
! [SV171: $i] :
( ( ! [SY440: $i,SY441: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV171 @ SY440
@ ^ [SX3: $i,SX4: $i] : ( SY441 @ SX3 @ SX4 ) )
@ ( cartprod @ SV171 @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(894,plain,
! [SV172: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( in @ SY445 @ ( cartprod @ SV172 @ SY444 ) )
| ( in @ ( kfst @ SY445 ) @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(895,plain,
! [SV173: $i] :
( ( subset @ emptyset @ SV173 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(896,plain,
! [SV174: $i] :
( ( ! [SY446: $i] :
( ~ ( subset @ SV174 @ SY446 )
| ~ ( subset @ SY446 @ SV174 )
| ( SV174 = SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(897,plain,
! [SV175: $i > $o] :
( ( ~ ~ ! [SY447: $i] :
~ ~ ( ~ ( SV175 @ SY447 )
| ~ ! [SY448: $i] :
( ~ ( SV175 @ SY448 )
| ( SY447 = SY448 ) ) )
| ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(898,plain,
! [SV176: $i] :
( ( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY452 @ ( funcSet @ SV176 @ SY451 ) )
| ! [SY453: $i] :
( ~ ( in @ SY453 @ SV176 )
| ( in @ ( kpair @ SY453 @ ( ap @ SV176 @ SY451 @ SY452 @ SY453 ) ) @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(899,plain,
! [SV177: $i] :
( ( ! [SY454: $i,SY455: $i > $i > $o,SY456: $i,SY457: $i] :
( ~ ( in @ ( kpair @ SY456 @ SY457 )
@ ( dpsetconstr @ SV177 @ SY454
@ ^ [SX5: $i,SX6: $i] : ( SY455 @ SX5 @ SX6 ) ) )
| ( in @ SY456 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(900,plain,
! [SV178: $i] :
( ( ! [SY460: $i] :
( ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SV178 )
| ~ ( in @ SY461 @ SY460 ) )
| ( ( binintersect @ SV178 @ SY460 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(901,plain,
! [SV179: $i] :
( ( ! [SY462: $i,SY463: $i] :
( ~ ( subset @ SY463 @ ( cartprod @ SV179 @ SY462 ) )
| ! [SY464: $i > $o] :
( ~ ! [SY465: $i] :
( ~ ( in @ SY465 @ SV179 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY462 )
| ~ ( in @ ( kpair @ SY465 @ SX5 ) @ SY463 )
| ( SY464 @ ( kpair @ SY465 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY463 )
| ( SY464 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(902,plain,
! [SV180: $i] :
( ( in @ emptyset @ ( powerset @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(903,plain,
! [SV181: $i] :
( ( ~ ( in @ SV181 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(904,plain,
! [SV182: $i] :
( ( ! [SY468: $i,SY469: $i] :
( ~ ~ ( in @ SY469 @ ( setminus @ SV182 @ SY468 ) )
| ~ ~ ( in @ SY469 @ SY468 )
| ~ ( in @ SY469 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(905,plain,
! [SV183: $i] :
( ( ! [SY470: $i,SY471: $i] :
( ~ ( in @ SY471 @ ( funcSet @ SV183 @ SY470 ) )
| ( func @ SV183 @ SY470 @ SY471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(906,plain,
! [SV184: $i] :
( ( ~ ( singleton @ SV184 )
| ( in @ ( setunion @ SV184 ) @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(907,plain,
! [SV185: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ~ ( in @ SY473 @ ( setminus @ SV185 @ SY472 ) )
| ( in @ SY473 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(908,plain,
! [SV186: $i] :
( ( ! [SY474: $i] :
( ( SV186 != SY474 )
| ( in @ SV186 @ ( setadjoin @ SY474 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(909,plain,
! [SV187: $i] :
( ( ! [SY475: $i,SY476: $i] :
( ~ ( in @ SY476 @ ( cartprod @ SV187 @ SY475 ) )
| ~ ! [SY477: $i] :
~ ~ ( ~ ( in @ SY477 @ SV187 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY475 )
| ( SY476
!= ( kpair @ SY477 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(910,plain,
! [SV188: $i] :
( ( ! [SY479: $i] :
( ~ ( in @ SY479 @ ( powerset @ SV188 ) )
| ! [SY480: $i] :
( ~ ( in @ SY480 @ ( powerset @ SV188 ) )
| ( in @ ( binintersect @ SY479 @ SY480 ) @ ( powerset @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(911,plain,
! [SV189: $i] :
( ( ! [SY481: $i] : ( subset @ ( binintersect @ SV189 @ SY481 ) @ SY481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(912,plain,
! [SV190: $i] :
( ( ~ ( in @ SV190 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(913,plain,
! [SV191: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ~ ( in @ SY484 @ SV191 )
| ~ ~ ( in @ SY484 @ SY483 )
| ~ ( subset @ SV191 @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(914,plain,
! [SV192: $i] :
( ( ! [SY485: $i,SY486: $i] :
( ~ ( in @ SY486 @ SV192 )
| ! [SY487: $i] :
( ~ ( in @ SY487 @ SY485 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY486 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY486 @ ( setadjoin @ SY487 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SY485 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(915,plain,
! [SV193: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ~ ( func @ SV193 @ SY488 @ SY489 )
| ! [SY490: $i] :
( ~ ( in @ SY490 @ SV193 )
| ( singleton
@ ( dsetconstr @ SY488
@ ^ [SX4: $i] : ( in @ ( kpair @ SY490 @ SX4 ) @ SY489 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(916,plain,
! [SV194: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ~ ( subset @ SV194 @ SY493 )
| ( subset @ SV194 @ ( setadjoin @ SY492 @ SY493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(917,plain,
! [SV195: $i] :
( ( ! [SY494: $i,SY495: $i] :
( ~ ( in @ SY495 @ ( funcSet @ SV195 @ SY494 ) )
| ( ( lam @ SV195 @ SY494
@ ^ [SY496: $i] : ( ap @ SV195 @ SY494 @ SY495 @ SY496 ) )
= SY495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(918,plain,
! [SV196: $i > $o] :
( ( ~ ~ ! [SY497: $i] :
~ ( SV196 @ SY497 )
| ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(919,plain,
! [SV197: $i > $o] :
( ( ! [SY502: $i > $o] :
( ~ ! [SY503: $i,SY504: $i] :
( ( SY503 != SY504 )
| ~ ( ~ ( ~ ( SV197 @ SY503 )
| ( SY502 @ SY504 ) )
| ~ ( ~ ( SY502 @ SY504 )
| ( SV197 @ SY503 ) ) ) )
| ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY502 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY502 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SX2: $i] : ( SY502 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(920,plain,
! [SV198: $i] :
( ( ! [SY511: $i > $o] :
( in
@ ( dsetconstr @ SV198
@ ^ [SX2: $i] : ( SY511 @ SX2 ) )
@ ( powerset @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(921,plain,
! [SV199: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ( in @ SY514 @ SY513 )
| ~ ( in @ SY514 @ ( setminus @ SV199 @ SY513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(922,plain,
! [SV200: $i] :
( ( ! [SY515: $i] :
( ~ ( in @ SY515 @ ( setunion @ SV200 ) )
| ~ ! [SY516: $i] :
~ ~ ( ~ ( in @ SY516 @ SV200 )
| ~ ( in @ SY515 @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(923,plain,
! [SV201: $i] :
( ( ! [SY517: $i,SY518: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV201 @ SY517
@ ^ [SX3: $i,SX4: $i] : ( SY518 @ SX3 @ SX4 ) )
@ ( cartprod @ SV201 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(924,plain,
! [SV202: $i] :
( ( ! [SY521: $i,SY522: $i > $i] :
( ~ ! [SY523: $i] :
( ~ ( in @ SY523 @ SV202 )
| ( in @ ( SY522 @ SY523 ) @ SY521 ) )
| ( ( lam @ SV202 @ SY521
@ ^ [SX3: $i] : ( SY522 @ SX3 ) )
= ( lam @ SV202 @ SY521
@ ^ [SX3: $i] : ( SY522 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(925,plain,
! [SV203: $i] :
( ( ! [SY526: $i,SY527: $i,SY528: $i] :
( ( ( kpair @ SV203 @ SY526 )
!= ( kpair @ SY527 @ SY528 ) )
| ( SV203 = SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(926,plain,
! [SV204: $i] :
( ( ! [SY529: $i] :
( ~ ( in @ SV204 @ ( setadjoin @ SY529 @ emptyset ) )
| ( SV204 = SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(927,plain,
! [SV205: $i] :
( ( ! [SY530: $i,SY531: $i] :
( ~ ( in @ SY531 @ SV205 )
| ~ ~ ( in @ SY531 @ SY530 )
| ( in @ SY531 @ ( symdiff @ SV205 @ SY530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(928,plain,
! [SV206: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( subset @ SV206 @ SY532 )
| ~ ( subset @ SY532 @ SY533 )
| ( subset @ SV206 @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(929,plain,
! [SV207: $i] :
( ( ! [SY534: $i,SY535: $i] :
( ~ ( in @ SY535 @ ( setadjoin @ SV207 @ ( setadjoin @ SY534 @ emptyset ) ) )
| ( SY535 = SV207 )
| ( SY535 = SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(930,plain,
! [SV208: $i] :
( ( subset @ SV208 @ SV208 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(931,plain,
! [SV209: $i] :
( ( subset @ SV209 @ ( setunion @ ( setadjoin @ SV209 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(932,plain,
! [SV210: $i] :
( ( ! [SY536: $i] :
( ~ ( ( SV210 != SY536 ) )
| ~ ( in @ SY536 @ ( setadjoin @ SV210 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(933,plain,
! [SV211: $i] :
( ( ! [SY537: $i,SY538: $i] :
( ~ ( in @ SY538 @ ( cartprod @ SV211 @ SY537 ) )
| ( ( kpair @ ( kfst @ SY538 ) @ ( ksnd @ SY538 ) )
= SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(934,plain,
! [SV212: $i] :
( ( ! [SY539: $i] :
( ~ ( subset @ SV212 @ SY539 )
| ( ( setminus @ SV212 @ SY539 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(935,plain,
! [SV213: $i] :
( ( ! [SY540: $i,SY541: $i] :
( ~ ( subset @ SY541 @ ( cartprod @ SV213 @ SY540 ) )
| ! [SY542: $i > $o] :
( ~ ! [SY543: $i] :
( ~ ( in @ SY543 @ SV213 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY540 )
| ~ ( in @ ( kpair @ SY543 @ SX5 ) @ SY541 )
| ( SY542 @ ( kpair @ SY543 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY541 )
| ( SY542 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(936,plain,
! [SV214: $i] :
( ( ! [SY546: $i,SY547: $i] :
( ~ ( in @ SY547 @ SY546 )
| ( in @ SY547 @ ( binunion @ SV214 @ SY546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(937,plain,
! [SV215: $i] :
( ( ! [SY548: $i] :
( ~ ( in @ SY548 @ ( powerset @ SV215 ) )
| ( in @ ( setminus @ SV215 @ SY548 ) @ ( powerset @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(938,plain,
! [SV216: $i] :
( ( ! [SY549: $i] :
( ~ ( in @ SY549 @ ( powerset @ SV216 ) )
| ! [SY550: $i] :
( ~ ( in @ SY550 @ SV216 )
| ~ ( in @ SY550 @ SY549 )
| ~ ( in @ SY550 @ ( setminus @ SV216 @ SY549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(939,plain,
! [SV217: $i] :
( ( ! [SY551: $i] : ( in @ SV217 @ ( setadjoin @ SV217 @ SY551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(940,plain,
! [SV218: $i] :
( ( ! [SY552: $i] :
( ( SV218 != SY552 )
| ! [SY553: $i > $o,SY554: $i > $o] :
( ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV218 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY552 )
| ( SY555 != SX5 )
| ~ ( ~ ( ~ ( SY553 @ SY555 )
| ( SY554 @ SX5 ) )
| ~ ( ~ ( SY554 @ SX5 )
| ( SY553 @ SY555 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SX4: $i] : ( SY553 @ SX4 ) )
= ( dsetconstr @ SY552
@ ^ [SX4: $i] : ( SY554 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(941,plain,
! [SV219: $i] :
( ( ! [SY559: $i] :
( ( ksnd @ ( kpair @ SV219 @ SY559 ) )
= SY559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(942,plain,
! [SV220: $i] :
( ( ! [SY560: $i] :
( ~ ( in @ SY560 @ SV220 )
| ( in @ SY560 @ ( powerset @ ( setunion @ SV220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(943,plain,
! [SV221: $i] :
( ( ! [SY561: $i] : ( in @ SV221 @ ( setadjoin @ SV221 @ ( setadjoin @ SY561 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(944,plain,
! [SV222: $i] :
( ( ! [SY562: $i] :
( ~ ( in @ SY562 @ ( powerset @ SV222 ) )
| ! [SY563: $i] :
( ~ ( in @ SY563 @ ( powerset @ SV222 ) )
| ~ ! [SY564: $i] :
( ~ ( in @ SY564 @ SV222 )
| ~ ( in @ SY564 @ SY562 )
| ( in @ SY564 @ SY563 ) )
| ~ ! [SY565: $i] :
( ~ ( in @ SY565 @ SV222 )
| ~ ( in @ SY565 @ SY563 )
| ( in @ SY565 @ SY562 ) )
| ( SY562 = SY563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(945,plain,
! [SV223: $i] :
( ( ! [SY566: $i] :
( ~ ( subset @ SY566 @ SV223 )
| ( in @ SY566 @ ( powerset @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(946,plain,
! [SV224: $i] :
( ( ! [SY567: $i > $o] :
( ~ ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SV224 )
| ( SY567 @ SY568 ) )
| ~ ! [SY569: $i] :
~ ~ ( ~ ( in @ SY569 @ SV224 )
| ~ ~ ( SY567 @ SY569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(947,plain,
! [SV225: $i] :
( ( ! [SY570: $i > $o,SY571: $i] :
( ~ ( in @ SY571 @ SV225 )
| ~ ( SY570 @ SY571 )
| ( in @ SY571
@ ( dsetconstr @ SV225
@ ^ [SX3: $i] : ( SY570 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(948,plain,
! [SV226: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( in @ SY573 @ SY574 )
| ~ ( in @ SY574 @ SV226 )
| ( in @ SY573 @ ( setunion @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(949,plain,
! [SV227: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( subset @ SY576 @ ( cartprod @ SV227 @ SY575 ) )
| ! [SY577: $i] :
( ~ ( subset @ SY577 @ ( cartprod @ SV227 @ SY575 ) )
| ~ ! [SY578: $i] :
( ~ ( in @ SY578 @ SV227 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY575 )
| ~ ( in @ ( kpair @ SY578 @ SX5 ) @ SY576 )
| ( in @ ( kpair @ SY578 @ SX5 ) @ SY577 ) ) )
| ( subset @ SY576 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(950,plain,
! [SV228: $i] :
( ( ~ ( in @ SV228 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(951,plain,
! [SV229: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ~ ~ ( in @ SY581 @ SV229 )
| ~ ( in @ SY581 @ ( setminus @ SV229 @ SY580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(952,plain,
! [SV230: $i] :
( ( ! [SY582: $i,SY583: $i,SY584: $i] :
( ~ ( in @ ( kpair @ SY583 @ SY584 ) @ ( cartprod @ SV230 @ SY582 ) )
| ( in @ SY583 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(953,plain,
! [SV231: $i] :
( ( ! [SY585: $i > $o] :
( ~ ~ ! [SY586: $i] :
~ ~ ( ~ ( in @ SY586 @ SV231 )
| ~ ( SY585 @ SY586 ) )
| ( ( dsetconstr @ SV231
@ ^ [SX2: $i] : ( SY585 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(954,plain,
! [SV232: $i] :
( ( ~ ( subset @ SV232 @ emptyset )
| ( SV232 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(955,plain,
! [SV233: $i > $o,SV1: $i] :
( ( ! [SY588: $i] :
( ~ ( in @ SY588 @ SV1 )
| ~ ( SV233 @ SY588 )
| ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(956,plain,
! [SV234: $i,SV2: $i] :
( ( ! [SY590: $i] :
( ~ ( in @ SY590 @ SV2 )
| ! [SY591: $i] :
( ~ ( in @ SY591 @ SV234 )
| ( subset @ ( setadjoin @ SY590 @ ( setadjoin @ SY591 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(957,plain,
! [SV235: $i,SV3: $i] :
( ( ! [SY592: $i > $i] :
( ~ ! [SY593: $i] :
( ~ ( in @ SY593 @ SV3 )
| ( in @ ( SY592 @ SY593 ) @ SV235 ) )
| ! [SY594: $i] :
( ~ ( in @ SY594 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SX4: $i] : ( SY592 @ SX4 ) )
@ SY594 )
= ( SY592 @ SY594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(958,plain,
! [SV4: $i > $i > $o,SV236: $i] :
( ( ~ ! [SY596: $i] :
( ~ ( in @ SY596 @ SV236 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( SV4 @ SY596 @ SY16 )
| ~ ! [SY17: $i] :
( ~ ( SV4 @ SY596 @ SY17 )
| ( SY16 = SY17 ) ) ) )
| ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(959,plain,
! [SV237: $i,SV5: $i] :
( ( ! [SY603: $i] :
( ~ ( func @ SV5 @ SV237 @ SY603 )
| ! [SY604: $i] :
( ~ ( in @ SY604 @ SV5 )
| ( in @ ( ap @ SV5 @ SV237 @ SY603 @ SY604 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(960,plain,
! [SV238: $i,SV6: $i] :
( ( ! [SY605: $i > $i > $o,SY606: $i,SY607: $i] :
( ~ ( in @ ( kpair @ SY606 @ SY607 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SX5: $i,SX6: $i] : ( SY605 @ SX5 @ SX6 ) ) )
| ( SY605 @ SY606 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(961,plain,
! [SV8: $i,SV239: $i] :
( ( ~ ( in @ SV239 @ ( powerset @ SV8 ) )
| ! [SY610: $i] :
( ~ ( in @ SY610 @ ( powerset @ SV8 ) )
| ( in @ ( setminus @ SV239 @ SY610 ) @ ( powerset @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(962,plain,
! [SV240: $i,SV9: $i] :
( ( ! [SY611: $i] :
( ~ ( func @ SV9 @ SV240 @ SY611 )
| ( ( lam @ SV9 @ SV240
@ ^ [SY612: $i] : ( ap @ SV9 @ SV240 @ SY611 @ SY612 ) )
= SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(963,plain,
! [SV241: $i,SV10: $i] :
( ( ( SV10 != SV241 )
| ( ( powerset @ SV10 )
= ( powerset @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(964,plain,
! [SV242: $i,SV11: $i] :
( ( ! [SY613: $i > $i] :
( ~ ! [SY614: $i] :
( ~ ( in @ SY614 @ SV11 )
| ( in @ ( SY613 @ SY614 ) @ SV242 ) )
| ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SX3: $i] : ( SY613 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(965,plain,
! [SV243: $i,SV12: $i] :
( ( ( SV12 != SV243 )
| ( ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV243 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(966,plain,
! [SV13: $i] :
( ( ( ~ ! [SY42: $i] :
~ ( in @ SY42 @ SV13 ) )
= $true )
| ( ( SV13 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(967,plain,
! [SV244: $o,SV14: $i] :
( ( ! [SY616: $i] :
( ~ ( in @ SY616 @ SV14 )
| ! [SY617: $i] :
( ~ ( in @ SY617 @ SV14 )
| ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY618: $i] :
( ~ ( ~ SV244
| ( SY618 != SY616 ) )
| ~ ( ~ ~ SV244
| ( SY618 != SY617 ) ) ) )
= ( setadjoin @ SY617 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(968,plain,
! [SV14: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV14 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV14 )
| ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(969,plain,
! [SV14: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV14 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV14 )
| ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(970,plain,
! [SV16: $i > $o] :
( ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ( SV16 @ SY47 )
| ~ ! [SY48: $i] :
( ~ ( SV16 @ SY48 )
| ( SY47 = SY48 ) ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(971,plain,
! [SV245: $i,SV17: $i] :
( ( ! [SY619: $i] :
( ~ ( func @ SV17 @ SV245 @ SY619 )
| ! [SY620: $i] :
( ~ ( in @ SY620 @ SV17 )
| ( ( ap @ SV17 @ SV245 @ SY619 @ SY620 )
= ( ap @ SV17 @ SV245 @ SY619 @ SY620 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(972,plain,
! [SV18: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( in @ SY54 @ SV18 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(973,plain,
! [SV19: $i] :
( ( ( ~ ( singleton @ SV19 ) )
= $true )
| ( ( ! [SY57: $i] :
( ~ ( in @ SY57 @ SV19 )
| ( ( setunion @ SV19 )
= SY57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(974,plain,
! [SV246: $i > $o,SV20: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
| ! [SY622: $i] :
( ~ ( in @ SY622 @ SV20 )
| ! [SY623: $i] :
( ~ ( in @ SY623 @ SV20 )
| ~ ( SV246 @ SY622 )
| ~ ( SV246 @ SY623 )
| ( SY622 = SY623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(975,plain,
! [SV21: $i] :
( ( ( ~ ( in @ SV21 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV21 @ SV21 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(976,plain,
! [SV247: $i,SV22: $i] :
( ( ! [SY624: $i] :
( ~ ( in @ SY624 @ SV22 )
| ! [SY625: $i] :
( ~ ( in @ SY625 @ SV247 )
| ( ( kpair @ SY624 @ SY625 )
= ( kpair @ SY624 @ SY625 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(977,plain,
! [SV23: $i] :
( ( ! [SY65: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY66: $i] :
( ~ ( in @ SY66 @ SY65 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY66 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY68: $i,SY69: $i] :
( ~ ~ ( ~ ( in @ SY68 @ SV23 )
| ~ ( in @ SY69 @ SV23 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY65 )
| ~ ( ~ ( ~ ( in @ SY68 @ SX4 )
| ( in @ SY69 @ SX4 ) )
| ~ ( ~ ( in @ SY69 @ SX4 )
| ( in @ SY68 @ SX4 ) ) ) )
| ( SY68 = SY69 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY65 )
| ~ ( in @ SX3 @ SY65 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY75: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY75 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY75 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY65 )
| ~ ( in @ SX4 @ SY75 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY75 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY65 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(978,plain,
! [SV24: $i,SV248: $i] :
( ( ~ ( in @ SV248 @ ( setunion @ SV24 ) )
| ! [SY626: $o] :
( ~ ! [SY627: $i] :
( ~ ( in @ SV248 @ SY627 )
| ~ ( in @ SY627 @ SV24 )
| SY626 )
| SY626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(979,plain,
! [SV249: $i,SV26: $i] :
( ( ( SV26 != SV249 )
| ( subset @ SV249 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(980,plain,
! [SV27: $i > $o] :
( ( ( ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( SV27 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV27 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(981,plain,
! [SV250: $i,SV28: $i] :
( ( ! [SY628: $i] :
( ~ ( in @ SY628 @ ( setadjoin @ SV28 @ SV250 ) )
| ( SY628 = SV28 )
| ( in @ SY628 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(982,plain,
! [SV251: $i,SV29: $i] :
( ( ! [SY629: $i] :
( ~ ( in @ SY629 @ ( funcSet @ SV29 @ SV251 ) )
| ! [SY630: $i] :
( ~ ( in @ SY630 @ SV29 )
| ( ( ap @ SV29 @ SV251 @ SY629 @ SY630 )
= ( ap @ SV29 @ SV251 @ SY629 @ SY630 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(983,plain,
! [SV252: $i > $o,SV30: $i] :
( ( ! [SY631: $i] :
( ~ ( in @ SY631 @ SV30 )
| ~ ( SV252 @ SY631 )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV30 )
| ~ ( SV252 @ SY632 )
| ( SY632 = SY631 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(984,plain,
! [SV31: $i] :
( ( ( ~ ( iskpair @ SV31 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV31 ) @ ( ksnd @ SV31 ) )
= SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(985,plain,
! [SV253: $i,SV32: $i] :
( ( ( kfst @ ( kpair @ SV32 @ SV253 ) )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(986,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ( ~ ( ~ ( in @ SV254 @ ( setunion @ SV33 ) )
| ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
| ~ ( ~ ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) )
| ( in @ SV254 @ ( setunion @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(987,plain,
! [SV255: $i,SV34: $i] :
( ( ! [SY636: $i] :
( ~ ( in @ SY636 @ SV34 )
| ~ ( in @ SY636 @ SV255 )
| ~ ( in @ SY636 @ ( symdiff @ SV34 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(988,plain,
! [SV256: $i,SV35: $i] :
( ( ( SV35 != SV256 )
| ( ( setadjoin @ SV35 @ ( setadjoin @ SV256 @ emptyset ) )
= ( setadjoin @ SV35 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(989,plain,
! [SV36: $i] :
( ( ( ~ ~ ! [SY106: $i] :
~ ( in @ SY106 @ SV36 ) )
= $true )
| ( ( SV36 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(990,plain,
! [SV257: $i,SV37: $i] :
( ( ! [SY637: $i] :
( ~ ( in @ SY637 @ SV37 )
| ! [SY638: $i] :
( ~ ( in @ SY638 @ SV257 )
| ( ( kfst @ ( kpair @ SY637 @ SY638 ) )
= SY637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(991,plain,
! [SV258: $i,SV38: $i] :
( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV38 )
| ~ ~ ( in @ SY639 @ SV258 )
| ( in @ SY639 @ ( setminus @ SV38 @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(992,plain,
! [SV259: $i,SV39: $i] :
( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ SV39 )
| ~ ~ ( in @ SY640 @ SV259 )
| ( SV39 != SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(993,plain,
! [SV260: $i,SV40: $i] :
( ( ( ( setminus @ SV40 @ SV260 )
!= emptyset )
| ( subset @ SV40 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(994,plain,
! [SV261: $i,SV41: $i] :
( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ ( setadjoin @ SV41 @ ( setadjoin @ SV261 @ emptyset ) ) )
| ( SY641 = SV41 )
| ( SY641 = SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(995,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642 != SY643 )
| ~ ( ~ ( ~ ( SV42 @ SY642 )
| ( SV262 @ SY643 ) )
| ~ ( ~ ( SV262 @ SY643 )
| ( SV42 @ SY642 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(996,plain,
! [SV263: $i,SV43: $i] :
( ( ! [SY652: $i] :
( ~ ( subset @ SV43 @ SV263 )
| ~ ~ ( in @ SY652 @ SV263 )
| ~ ( in @ SY652 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(997,plain,
! [SV264: $i,SV44: $i] :
( ( ! [SY653: $i] :
( ~ ( func @ SV44 @ SV264 @ SY653 )
| ! [SY654: $i] :
( ~ ( in @ SY654 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SX4: $i] : ( in @ ( kpair @ SY654 @ SX4 ) @ SY653 ) ) )
@ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(998,plain,
! [SV265: $i,SV45: $i] :
( ( ! [SY656: $i] :
( ~ ~ ( in @ SY656 @ SV45 )
| ~ ~ ( in @ SY656 @ SV265 )
| ~ ( in @ SY656 @ ( symdiff @ SV45 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(999,plain,
! [SV266: $i,SV46: $i] :
( ( iskpair @ ( kpair @ SV46 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1000,plain,
! [SV47: $i,SV267: $i] :
( ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV267 )
| ( in @ SY657 @ SV47 ) )
| ( in @ SV267 @ ( powerset @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1001,plain,
! [SV268: $i > $o,SV48: $i] :
( ( ~ ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ SY658 @ SV48 )
| ~ ~ ( SV268 @ SY658 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1002,plain,
! [SV269: $i,SV49: $i] :
( ( ! [SY660: $i > $i] :
( ~ ! [SY661: $i] :
( ~ ( in @ SY661 @ SV49 )
| ( in @ ( SY660 @ SY661 ) @ SV269 ) )
| ! [SY662: $i] :
( ~ ( in @ SY662 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SX4: $i] : ( SY660 @ SX4 ) )
@ SY662 )
= ( SY660 @ SY662 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1003,plain,
! [SV270: $i,SV50: $i] :
( ( ! [SY664: $i] :
( ~ ( func @ SV50 @ SV270 @ SY664 )
| ( in @ SY664 @ ( funcSet @ SV50 @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1004,plain,
! [SV51: $i > $o] :
( ( ( ~ ~ ! [SY149: $i] :
~ ~ ( ~ ( SV51 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( SV51 @ SY150 )
| ( SY149 = SY150 ) ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(1005,plain,
! [SV271: $i,SV52: $i] :
( ( subset @ ( binintersect @ SV52 @ SV271 ) @ SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1006,plain,
! [SV272: $i,SV53: $i] :
( ( ! [SY665: $i,SY666: $o] :
( ~ ( in @ SY665 @ ( binunion @ SV53 @ SV272 ) )
| ~ ( ~ ( in @ SY665 @ SV53 )
| SY666 )
| ~ ( ~ ( in @ SY665 @ SV272 )
| SY666 )
| SY666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1007,plain,
! [SV273: $i,SV54: $i] :
( ( ! [SY667: $i] :
( ~ ( in @ SY667 @ ( setminus @ SV54 @ SV273 ) )
| ~ ( in @ SY667 @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1008,plain,
! [SV274: $i,SV55: $i] :
( ( ! [SY668: $i] :
( ~ ( subset @ SV55 @ SV274 )
| ~ ( in @ SY668 @ SV55 )
| ( in @ SY668 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1009,plain,
! [SV275: $i,SV56: $i] :
( ( ( SV56 != SV275 )
| ! [SY669: $i,SY670: $i] :
( ( SY669 != SY670 )
| ( ( setadjoin @ SV56 @ SY669 )
= ( setadjoin @ SV275 @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1010,plain,
! [SV276: $i,SV57: $i] :
( ( subset @ ( setminus @ SV57 @ SV276 ) @ SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1011,plain,
! [SV277: $i,SV58: $i] :
( ( ! [SY671: $i] :
( ~ ( in @ SY671 @ ( symdiff @ SV58 @ SV277 ) )
| ! [SY672: $o] :
( ~ ( ~ ( in @ SY671 @ SV58 )
| ~ ~ ( in @ SY671 @ SV277 )
| SY672 )
| ~ ( ~ ~ ( in @ SY671 @ SV58 )
| ~ ( in @ SY671 @ SV277 )
| SY672 )
| SY672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1012,plain,
! [SV278: $i,SV59: $i] :
( ( ! [SY673: $i] :
( ~ ( in @ SY673 @ ( cartprod @ SV59 @ SV278 ) )
| ( iskpair @ SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1013,plain,
! [SV279: $i,SV60: $i] :
( ( ( ( binintersect @ SV60 @ SV279 )
!= SV279 )
| ( subset @ SV279 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1014,plain,
! [SV280: $i,SV61: $i] :
( ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV61 )
| ( in @ SY674 @ SV280 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1015,plain,
! [SV281: $o,SV62: $i] :
( ( ! [SY676: $i] :
( ~ ( in @ SY676 @ SV62 )
| ! [SY677: $i] :
( ~ ( in @ SY677 @ SV62 )
| ~ SV281
| ( ( if @ SV62 @ SV281 @ SY676 @ SY677 )
= SY676 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[777]) ).
thf(1016,plain,
! [SV62: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV62 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV62 )
| ~ $true
| ( ( if @ SV62 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[777]) ).
thf(1017,plain,
! [SV62: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV62 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV62 )
| ~ $false
| ( ( if @ SV62 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[777]) ).
thf(1018,plain,
! [SV282: $i,SV63: $i] :
( ( ! [SY678: $i] :
( ( binintersect @ SV63 @ ( binunion @ SV282 @ SY678 ) )
= ( binunion @ ( binintersect @ SV63 @ SV282 ) @ ( binintersect @ SV63 @ SY678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1019,plain,
! [SV283: $i,SV64: $i] :
( ( ! [SY679: $i] :
( ( ( setadjoin @ SV64 @ ( setadjoin @ SV283 @ emptyset ) )
!= ( setadjoin @ SY679 @ emptyset ) )
| ( SV64 = SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1020,plain,
! [SV284: $i,SV65: $i] :
( ( ! [SY680: $i] :
( ~ ( in @ SY680 @ SV65 )
| ( in @ ( setadjoin @ SY680 @ emptyset ) @ ( powerset @ ( binunion @ SV65 @ SV284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1021,plain,
! [SV285: $i,SV66: $i] :
( ( ~ ~ ( subset @ SV66 @ SV285 )
| ( SV66 != SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1022,plain,
! [SV286: $o,SV67: $i] :
( ( ! [SY681: $i] :
( ~ ( in @ SY681 @ SV67 )
| ! [SY682: $i] :
( ~ ( in @ SY682 @ SV67 )
| ~ ~ SV286
| ( in @ SY682
@ ( dsetconstr @ SV67
@ ^ [SY683: $i] :
( ~ ( ~ SV286
| ( SY683 != SY681 ) )
| ~ ( ~ ~ SV286
| ( SY683 != SY682 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[782]) ).
thf(1023,plain,
! [SV67: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV67 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV67 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV67
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[782]) ).
thf(1024,plain,
! [SV67: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV67 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV67 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV67
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[782]) ).
thf(1025,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SV68 )
| ~ ( SV287 @ SY684 ) )
| ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1026,plain,
! [SV288: $i > $o,SV69: $i] :
( ( ~ ~ ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV69 )
| ~ ( SV288 @ SY686 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1027,plain,
! [SV70: $i,SV289: $i] :
( ( ! [SY688: $i] :
( ~ ( in @ SV289 @ ( powerset @ SV70 ) )
| ~ ( in @ SY688 @ SV289 )
| ( in @ SY688 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1028,plain,
! [SV290: $i,SV71: $i] :
( ( ! [SY689: $i] :
( ~ ( in @ SY689 @ SV71 )
| ( in @ SY689 @ ( binunion @ SV71 @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1029,plain,
! [SV291: $i,SV73: $i] :
( ( ! [SY690: $i] :
( ~ ( in @ SY690 @ SV73 )
| ! [SY691: $i] :
( ~ ( in @ SY691 @ SV291 )
| ( ( ksnd @ ( kpair @ SY690 @ SY691 ) )
= SY691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1030,plain,
! [SV292: $i,SV74: $i] :
( ( ( SV74 != SV292 )
| ! [SY692: $i,SY693: $i] :
( ( SY692 != SY693 )
| ~ ( ~ ( ~ ( in @ SY692 @ SV74 )
| ( in @ SY693 @ SV292 ) )
| ~ ( ~ ( in @ SY693 @ SV292 )
| ( in @ SY692 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1031,plain,
! [SV293: $i,SV75: $i] :
( ( ! [SY694: $i > $i] :
( ~ ! [SY695: $i] :
( ~ ( in @ SY695 @ SV75 )
| ( in @ ( SY694 @ SY695 ) @ SV293 ) )
| ( in
@ ( lam @ SV75 @ SV293
@ ^ [SX3: $i] : ( SY694 @ SX3 ) )
@ ( funcSet @ SV75 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1032,plain,
! [SV294: $i > $o,SV76: $i] :
( ( ~ ~ ! [SY697: $i] :
( ~ ( in @ SY697 @ SV76 )
| ( SV294 @ SY697 ) )
| ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1033,plain,
! [SV295: $i,SV77: $i] :
( ( ! [SY699: $i] :
( ~ ( func @ SV77 @ SV295 @ SY699 )
| ! [SY700: $i] :
( ~ ( func @ SV77 @ SV295 @ SY700 )
| ~ ! [SY701: $i] :
( ~ ( in @ SY701 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SY699 @ SY701 )
= ( ap @ SV77 @ SV295 @ SY700 @ SY701 ) ) )
| ! [SY702: $i] :
( ~ ( in @ SY702 @ SV77 )
| ! [SY703: $i] :
( ~ ( in @ SY703 @ SV295 )
| ~ ( in @ ( kpair @ SY702 @ SY703 ) @ SY700 )
| ( in @ ( kpair @ SY702 @ SY703 ) @ SY699 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1034,plain,
! [SV296: $i,SV78: $i] :
( ( ! [SY704: $i] :
( ~ ( in @ ( setadjoin @ SY704 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV296 @ emptyset ) ) @ emptyset ) ) )
| ( SV78 = SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1035,plain,
! [SV79: $i,SV297: $i] :
( ( ~ ( in @ SV297 @ ( powerset @ SV79 ) )
| ! [SY705: $i] :
( ~ ( in @ SY705 @ ( powerset @ SV79 ) )
| ! [SY706: $i] :
( ~ ( in @ SY706 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SY705 ) )
| ~ ( in @ SY706 @ SV297 )
| ( in @ SY706 @ SY705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1036,plain,
! [SV80: $i > $o] :
( ( ( ~ ~ ! [SY222: $i] :
~ ~ ( ~ ( SV80 @ SY222 )
| ~ ! [SY223: $i] :
( ~ ( SV80 @ SY223 )
| ( SY222 = SY223 ) ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(1037,plain,
! [SV81: $i,SV298: $i] :
( ( ~ ( in @ SV298 @ ( powerset @ SV81 ) )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ ( powerset @ SV81 ) )
| ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV81 )
| ~ ( in @ SY708 @ SV298 )
| ( in @ SY708 @ SY707 ) )
| ( in @ SV298 @ ( powerset @ SY707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1038,plain,
! [SV299: $i,SV82: $i] :
( ( ! [SY709: $i] :
( ~ ( in @ SY709 @ ( funcSet @ SV82 @ SV299 ) )
| ! [SY710: $i] :
( ~ ( in @ SY710 @ ( funcSet @ SV82 @ SV299 ) )
| ~ ! [SY711: $i] :
( ~ ( in @ SY711 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SY709 @ SY711 )
= ( ap @ SV82 @ SV299 @ SY710 @ SY711 ) ) )
| ( SY709 = SY710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1039,plain,
! [SV83: $i] :
( ( ( ~ ! [SY233: $i] :
~ ( in @ SY233 @ SV83 ) )
= $true )
| ( ( SV83 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(1040,plain,
! [SV300: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SV300 @ emptyset ) )
| ( SV84 = SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1041,plain,
! [SV301: $i,SV85: $i] :
( ( ! [SY712: $i] :
( ~ ( subset @ SY712 @ ( cartprod @ SV85 @ SV301 ) )
| ! [SY713: $i] :
( ~ ( subset @ SY713 @ ( cartprod @ SV85 @ SV301 ) )
| ~ ! [SY714: $i] :
( ~ ( in @ SY714 @ SV85 )
| ! [SY715: $i] :
( ~ ( in @ SY715 @ SV301 )
| ~ ( in @ ( kpair @ SY714 @ SY715 ) @ SY712 )
| ( in @ ( kpair @ SY714 @ SY715 ) @ SY713 ) ) )
| ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ SV85 )
| ! [SY717: $i] :
( ~ ( in @ SY717 @ SV301 )
| ~ ( in @ ( kpair @ SY716 @ SY717 ) @ SY713 )
| ( in @ ( kpair @ SY716 @ SY717 ) @ SY712 ) ) )
| ( SY712 = SY713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1042,plain,
! [SV302: $o,SV86: $i] :
( ( ! [SY718: $i] :
( ~ ( in @ SY718 @ SV86 )
| ! [SY719: $i] :
( ~ ( in @ SY719 @ SV86 )
| ~ SV302
| ( in @ SY718
@ ( dsetconstr @ SV86
@ ^ [SY720: $i] :
( ~ ( ~ SV302
| ( SY720 != SY718 ) )
| ~ ( ~ ~ SV302
| ( SY720 != SY719 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[801]) ).
thf(1043,plain,
! [SV86: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV86 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV86 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV86
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[801]) ).
thf(1044,plain,
! [SV86: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV86 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV86 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV86
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[801]) ).
thf(1045,plain,
! [SV303: $i > $o,SV87: $i] :
( ( ! [SY721: $i] :
( ~ ( in @ SY721
@ ( dsetconstr @ SV87
@ ^ [SY722: $i] : ( SV303 @ SY722 ) ) )
| ( SV303 @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1046,plain,
! [SV304: $i,SV88: $i] :
( ( ! [SY723: $i,SY724: $i] :
( ( ( kpair @ SV88 @ SV304 )
!= ( kpair @ SY723 @ SY724 ) )
| ( SV304 = SY724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1047,plain,
! [SV89: $i] :
( ( ( ~ ( ( SV89 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( in @ SY252 @ SV89 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(1048,plain,
! [SV305: $i,SV90: $i] :
( ( ! [SY725: $i > $i > $o,SY726: $i] :
( ~ ( in @ SY726 @ SV90 )
| ! [SY727: $i] :
( ~ ( in @ SY727 @ SV305 )
| ~ ( SY725 @ SY726 @ SY727 )
| ( in @ ( kpair @ SY726 @ SY727 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SX5: $i,SX6: $i] : ( SY725 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1049,plain,
! [SV91: $i > $o] :
( ( ( ~ ~ ! [SY259: $i] :
~ ~ ( ~ ( SV91 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV91 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(1050,plain,
! [SV306: $i,SV92: $i] :
( ( ~ ! [SY730: $i] :
( ~ ( in @ SY730 @ SV92 )
| ( in @ SY730 @ SV306 ) )
| ( subset @ SV92 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1051,plain,
! [SV307: $i,SV93: $i] :
( ( ~ ( subset @ SV93 @ SV307 )
| ( subset @ ( powerset @ SV93 ) @ ( powerset @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1052,plain,
! [SV94: $i] :
( ( ( ~ ( iskpair @ SV94 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV94 )
@ ^ [SY266: $i] :
( SV94
= ( kpair @ ( kfst @ SV94 ) @ SY266 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(1053,plain,
! [SV308: $i > $o,SV95: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
| ~ ! [SY732: $i] :
~ ~ ( ~ ( in @ SY732 @ SV95 )
| ~ ( SV308 @ SY732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1054,plain,
! [SV309: $i > $o,SV96: $i] :
( ( ~ ~ ~ ! [SY733: $i] :
~ ~ ( ~ ( in @ SY733 @ SV96 )
| ~ ( SV309 @ SY733 ) )
| ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1055,plain,
! [SV97: $i,SV310: $i] :
( ( in @ SV310 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV97 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV97 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1056,plain,
! [SV311: $i,SV98: $i] :
( ( ! [SY735: $i] :
( ~ ( in @ SY735 @ SV98 )
| ! [SY736: $i] :
( ~ ( in @ SY736 @ SV311 )
| ( in @ ( kpair @ SY735 @ SY736 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1057,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ( ~ ( ~ ( in @ SV312 @ ( powerset @ SV99 ) )
| ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) )
| ~ ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) )
| ( in @ SV312 @ ( powerset @ SV99 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1058,plain,
! [SV313: $i,SV100: $i] :
( ( ! [SY739: $i] :
( ~ ( in @ SY739 @ ( binintersect @ SV100 @ SV313 ) )
| ( in @ SY739 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1059,plain,
! [SV314: $i,SV101: $i] :
( ( ! [SY740: $i] :
~ ( ~ ( ~ ( in @ SY740 @ ( setadjoin @ SV101 @ SV314 ) )
| ( SY740 = SV101 )
| ( in @ SY740 @ SV314 ) )
| ~ ( ~ ( ( SY740 = SV101 )
| ( in @ SY740 @ SV314 ) )
| ( in @ SY740 @ ( setadjoin @ SV101 @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1060,plain,
! [SV315: $i,SV102: $i] :
( ( ~ ( in @ SV102 @ ( setadjoin @ SV315 @ emptyset ) )
| ( in @ SV315 @ ( setadjoin @ SV102 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1061,plain,
! [SV103: $i > $o,SV316: $i] :
( ( ~ ( in @ SV316 @ emptyset )
| ( SV103 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1062,plain,
! [SV317: $i,SV104: $i] :
( ( ! [SY741: $i] :
( ~ ( in @ SY741 @ SV104 )
| ! [SY742: $i] :
( ~ ( in @ SY742 @ SV317 )
| ( in @ ( setadjoin @ SY741 @ ( setadjoin @ SY742 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1063,plain,
! [SV318: $i,SV105: $i] :
( ( ( SV105 != SV318 )
| ! [SY743: $i,SY744: $i] :
( ( SY743 != SY744 )
| ~ ( in @ SY743 @ SV105 )
| ( in @ SY744 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1064,plain,
! [SV106: $i,SV319: $i] :
( ( in @ SV319 @ ( setadjoin @ SV106 @ ( setadjoin @ SV319 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1065,plain,
! [SV320: $i,SV107: $i] :
( ( ( SV107 != SV320 )
| ( subset @ SV107 @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1066,plain,
! [SV321: $i,SV108: $i] :
( ( ! [SY745: $i] :
( ~ ( func @ SV108 @ SV321 @ SY745 )
| ! [SY746: $i] :
( ~ ( in @ SY746 @ SV108 )
| ! [SY747: $i] :
( ~ ( in @ SY747 @ SV321 )
| ~ ( in @ ( kpair @ SY746 @ SY747 ) @ SY745 )
| ( ( ap @ SV108 @ SV321 @ SY745 @ SY746 )
= SY747 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1067,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(1068,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY2 @ sK1_A )
| ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[824]) ).
thf(1069,plain,
! [SV322: $i,SV109: $i] :
( ( ~ ! [SY748: $i] :
~ ( ~ ( ~ ( in @ SY748 @ SV109 )
| ( in @ SY748 @ SV322 ) )
| ~ ( ~ ( in @ SY748 @ SV322 )
| ( in @ SY748 @ SV109 ) ) )
| ( SV109 = SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1070,plain,
! [SV111: $i,SV323: $i] :
( ( in @ SV323 @ ( setadjoin @ SV111 @ ( setadjoin @ SV323 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1071,plain,
! [SV324: $i > $o,SV112: $i] :
( ( ! [SY749: $i] :
( ~ ( in @ SY749 @ SV112 )
| ~ ( ~ ( ~ ( in @ SY749
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SY749 ) )
| ~ ( ~ ( SV324 @ SY749 )
| ( in @ SY749
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1072,plain,
! [SV325: $o,SV113: $i] :
( ( ! [SY752: $i] :
( ~ ( in @ SY752 @ SV113 )
| ! [SY753: $i] :
( ~ ( in @ SY753 @ SV113 )
| ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY754: $i] :
( ~ ( ~ SV325
| ( SY754 != SY752 ) )
| ~ ( ~ ~ SV325
| ( SY754 != SY753 ) ) ) )
= ( setadjoin @ SY752 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[829]) ).
thf(1073,plain,
! [SV113: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV113 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV113 )
| ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[829]) ).
thf(1074,plain,
! [SV113: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV113 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV113 )
| ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[829]) ).
thf(1075,plain,
! [SV114: $i] :
( ( ( ~ ( ( SV114 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY310: $i] :
~ ( in @ SY310 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(1076,plain,
! [SV326: $i,SV115: $i] :
( ( ! [SY755: $i,SY756: $i] :
( ~ ( in @ ( kpair @ SY755 @ SY756 ) @ ( cartprod @ SV115 @ SV326 ) )
| ( in @ SY756 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1077,plain,
! [SV327: $i > $o,SV116: $i] :
( ( ! [SY757: $i] :
( ~ ( in @ SY757
@ ( dsetconstr @ SV116
@ ^ [SY758: $i] : ( SV327 @ SY758 ) ) )
| ( in @ SY757 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1078,plain,
! [SV117: $i] :
( ( ( ~ ( iskpair @ SV117 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV117 )
@ ^ [SY317: $i] : ( in @ ( setadjoin @ SY317 @ emptyset ) @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(1079,plain,
! [SV118: $i,SV328: $i] :
( ( ~ ( in @ SV328 @ SV118 )
| ( subset @ ( setadjoin @ SV328 @ emptyset ) @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1080,plain,
! [SV119: $i,SV329: $i] :
( ( ~ ( subset @ SV329 @ SV119 )
| ( ( binintersect @ SV119 @ SV329 )
= SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1081,plain,
! [SV120: $i,SV330: $i] :
( ( ! [SY759: $i] :
( ~ ( in @ SY759 @ SV330 )
| ( in @ SY759 @ ( setadjoin @ SV120 @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1082,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ~ ! [SY760: $i] :
( ~ ( in @ SY760 @ SV121 )
| ! [SY761: $i] :
( ~ ( in @ SY761 @ SV121 )
| ~ ( SV331 @ SY760 )
| ~ ( SV331 @ SY761 )
| ( SY760 = SY761 ) ) )
| ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1083,plain,
! [SV332: $o,SV122: $i] :
( ( ! [SY764: $i] :
( ~ ( in @ SY764 @ SV122 )
| ! [SY765: $i] :
( ~ ( in @ SY765 @ SV122 )
| ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SY764 @ SY765 )
= SY765 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[838]) ).
thf(1084,plain,
! [SV122: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV122 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV122 )
| ~ ~ $true
| ( ( if @ SV122 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[838]) ).
thf(1085,plain,
! [SV122: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV122 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV122 )
| ~ ~ $false
| ( ( if @ SV122 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[838]) ).
thf(1086,plain,
! [SV333: $i,SV123: $i] :
( ( ! [SY766: $i > $i] :
( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ SV123 )
| ( in @ ( SY766 @ SY767 ) @ SV333 ) )
| ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SX3: $i,SX4: $i] :
( ( SY766 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1087,plain,
! [SV124: $o,SV334: $i] :
( ( ~ ( in @ SV334 @ ( prop2set @ SV124 ) )
| SV124 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1088,plain,
! [SV335: $i] :
( ( ~ ( in @ SV335 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1089,plain,
! [SV336: $i] :
( ( ~ ( in @ SV336 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1090,plain,
! [SV337: $o,SV125: $i] :
( ( ! [SY770: $i] :
( ~ ( in @ SY770 @ SV125 )
| ! [SY771: $i] :
( ~ ( in @ SY771 @ SV125 )
| ( in @ ( if @ SV125 @ SV337 @ SY770 @ SY771 ) @ ( setadjoin @ SY770 @ ( setadjoin @ SY771 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[843]) ).
thf(1091,plain,
! [SV125: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV125 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV125 )
| ( in @ ( if @ SV125 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[843]) ).
thf(1092,plain,
! [SV125: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV125 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV125 )
| ( in @ ( if @ SV125 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[843]) ).
thf(1093,plain,
! [SV338: $i,SV126: $i] :
( ( ~ ( subset @ SV126 @ SV338 )
| ( ( binintersect @ SV126 @ SV338 )
= SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1094,plain,
! [SV127: $i,SV339: $i] :
( ( subset @ SV339 @ ( binunion @ SV127 @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1095,plain,
! [SV340: $i > $o,SV128: $i] :
( ( subset
@ ( dsetconstr @ SV128
@ ^ [SY772: $i] : ( SV340 @ SY772 ) )
@ SV128 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1096,plain,
! [SV341: $i,SV129: $i] :
( ( ! [SY773: $i] :
( ~ ( in @ SY773 @ SV129 )
| ~ ( in @ SY773 @ SV341 )
| ( in @ SY773 @ ( binintersect @ SV129 @ SV341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1097,plain,
! [SV342: $i,SV130: $i] :
( ( ! [SY774: $i > $i > $o,SY775: $i] :
( ~ ( in @ SY775 @ SV130 )
| ! [SY776: $i] :
( ~ ( in @ SY776 @ SV342 )
| ~ ( in @ ( kpair @ SY775 @ SY776 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SX5: $i,SX6: $i] : ( SY774 @ SX5 @ SX6 ) ) )
| ( SY774 @ SY775 @ SY776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1098,plain,
! [SV343: $i,SV131: $i] :
( ( ( ( binintersect @ SV131 @ SV343 )
!= SV131 )
| ( subset @ SV131 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1099,plain,
! [SV344: $i,SV132: $i] :
( ( subset @ SV132 @ ( binunion @ SV132 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1100,plain,
! [SV345: $o,SV133: $i] :
( ( ! [SY779: $i] :
( ~ ( in @ SY779 @ SV133 )
| ! [SY780: $i] :
( ~ ( in @ SY780 @ SV133 )
| ( in @ ( if @ SV133 @ SV345 @ SY779 @ SY780 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[851]) ).
thf(1101,plain,
! [SV133: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV133 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV133 )
| ( in @ ( if @ SV133 @ $true @ SX0 @ SX1 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[851]) ).
thf(1102,plain,
! [SV133: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV133 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV133 )
| ( in @ ( if @ SV133 @ $false @ SX0 @ SX1 ) @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[851]) ).
thf(1103,plain,
! [SV134: $i,SV346: $i] :
( ( ~ ( in @ SV346 @ ( powerset @ SV134 ) )
| ( subset @ SV346 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1104,plain,
! [SV347: $i,SV135: $i] :
( ( ! [SY781: $i] :
( ~ ~ ( in @ SY781 @ SV135 )
| ~ ( in @ SY781 @ SV347 )
| ( in @ SY781 @ ( symdiff @ SV135 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1105,plain,
! [SV348: $i,SV136: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV136 @ ( setadjoin @ SV348 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1106,plain,
! [SV349: $i,SV137: $i] :
( ( ! [SY782: $i,SY783: $i] :
( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SV349 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY782 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY782 @ ( setadjoin @ SY783 @ emptyset ) ) @ emptyset ) ) )
| ( SV349 = SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1107,plain,
! [SV350: $i,SV138: $i] :
( ( ! [SY784: $i,SY785: $i] :
( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY784 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY784 @ ( setadjoin @ SY785 @ emptyset ) ) @ emptyset ) ) )
| ( SV138 = SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1108,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ~ ! [SY786: $i] :
( ~ ( in @ SY786 @ SV139 )
| ! [SY787: $i] :
( ~ ( in @ SY787 @ SV139 )
| ~ ( SV351 @ SY786 )
| ~ ( SV351 @ SY787 )
| ( SY786 = SY787 ) ) )
| ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1109,plain,
! [SV140: $i,SV352: $i] :
( ( in @ SV352 @ ( setadjoin @ SV140 @ ( setadjoin @ SV352 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1110,plain,
! [SV141: $i,SV353: $i] :
( ( ~ ( in @ SV353 @ SV141 )
| ( in @ ( setadjoin @ SV353 @ emptyset ) @ ( powerset @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1111,plain,
! [SV354: $i,SV142: $i] :
( ( ~ ( subset @ SV142 @ SV354 )
| ( in @ SV142 @ ( powerset @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1112,plain,
! [SV355: $i,SV143: $i] :
( ( ! [SY790: $i] :
( ~ ( in @ SY790 @ SV143 )
| ! [SY791: $i] :
( ~ ( in @ SY791 @ SV355 )
| ( in @ ( kpair @ SY790 @ SY791 ) @ ( cartprod @ SV143 @ SV355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1113,plain,
! [SV144: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ ( powerset @ SV144 ) )
| ( in @ ( powerset @ SV356 ) @ ( powerset @ ( powerset @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1114,plain,
! [SV145: $i > $o] :
( ( ( ~ ~ ! [SY378: $i] :
~ ~ ( ~ ( SV145 @ SY378 )
| ~ ! [SY379: $i] :
( ~ ( SV145 @ SY379 )
| ( SY378 = SY379 ) ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(1115,plain,
! [SV146: $i,SV357: $i] :
( ( subset @ SV357 @ ( setadjoin @ SV146 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1116,plain,
! [SV358: $i,SV147: $i] :
( ( ! [SY792: $i] :
( ~ ( in @ SY792 @ ( binunion @ SV147 @ SV358 ) )
| ( in @ SY792 @ SV147 )
| ( in @ SY792 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1117,plain,
! [SV359: $i,SV148: $i] :
( ( in @ SV148 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV148 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV148 @ ( setadjoin @ SV359 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1118,plain,
! [SV149: $o] :
( ( ( ~ SV149 ) = $true )
| ( ( set2prop @ ( prop2set @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(1119,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(1120,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1121,plain,
! [SV360: $o,SV150: $i] :
( ( ! [SY793: $i] :
( ~ ( in @ SY793 @ SV150 )
| ! [SY794: $i] :
( ~ ( in @ SY794 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY795: $i] :
( ~ ( ~ SV360
| ( SY795 != SY793 ) )
| ~ ( ~ ~ SV360
| ( SY795 != SY794 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[870]) ).
thf(1122,plain,
! [SV150: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV150 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[870]) ).
thf(1123,plain,
! [SV150: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV150 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[870]) ).
thf(1124,plain,
! [SV151: $o] :
( ( ( ~ SV151 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1125,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1126,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1127,plain,
! [SV152: $i,SV361: $i] :
( ( ~ ( in @ SV361 @ ( powerset @ SV152 ) )
| ! [SY796: $i] :
( ~ ( in @ SY796 @ ( powerset @ SV152 ) )
| ~ ! [SY797: $i] :
( ~ ( in @ SY797 @ SV152 )
| ~ ( in @ SY797 @ SV361 )
| ( in @ SY797 @ SY796 ) )
| ( subset @ SV361 @ SY796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1128,plain,
! [SV153: $i > $o] :
( ( ( ~ ~ ! [SY392: $i] :
~ ! [SY393: $i] :
~ ( ~ ( ~ ( SV153 @ SY393 )
| ( SY393 = SY392 ) )
| ~ ( ( SY393 != SY392 )
| ( SV153 @ SY393 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1129,plain,
! [SV362: $i,SV154: $i] :
( ( ( SV154 != SV362 )
| ( ( setunion @ SV154 )
= ( setunion @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1130,plain,
! [SV363: $i,SV155: $i] :
( ( ~ ! [SY798: $i] :
( ~ ( in @ SY798 @ SV155 )
| ( in @ SY798 @ SV363 ) )
| ( subset @ SV155 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1131,plain,
! [SV364: $i,SV156: $i] :
( ( ! [SY799: $i] :
( ~ ( in @ SY799 @ ( funcSet @ SV156 @ SV364 ) )
| ! [SY800: $i] :
( ~ ( in @ SY800 @ SV156 )
| ! [SY801: $i] :
( ~ ( in @ SY801 @ SV364 )
| ~ ( in @ ( kpair @ SY800 @ SY801 ) @ SY799 )
| ( ( ap @ SV156 @ SV364 @ SY799 @ SY800 )
= SY801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1132,plain,
! [SV365: $i,SV157: $i] :
( ( ! [SY802: $i] :
( ~ ( in @ SY802 @ ( funcSet @ SV157 @ SV365 ) )
| ! [SY803: $i] :
( ~ ( in @ SY803 @ SV157 )
| ( in @ ( ap @ SV157 @ SV365 @ SY802 @ SY803 ) @ SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1133,plain,
! [SV366: $i,SV158: $i] :
( ( ! [SY804: $i] :
( ~ ~ ( in @ SY804 @ ( setminus @ SV158 @ SV366 ) )
| ~ ( in @ SY804 @ SV158 )
| ( in @ SY804 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1134,plain,
! [SV367: $i,SV159: $i] :
( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ ( cartprod @ SV159 @ SV367 ) )
| ( in @ ( ksnd @ SY805 ) @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1135,plain,
! [SV160: $i] :
( ( in @ SV160 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1136,plain,
! [SV368: $i,SV161: $i] :
( ( ! [SY806: $i] :
( ~ ( in @ SY806 @ ( binintersect @ SV161 @ SV368 ) )
| ( in @ SY806 @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1137,plain,
! [SV369: $i,SV162: $i] :
( ( ! [SY807: $i] :
( ~ ( func @ SV162 @ SV369 @ SY807 )
| ! [SY808: $i] :
( ~ ( func @ SV162 @ SV369 @ SY808 )
| ~ ! [SY809: $i] :
( ~ ( in @ SY809 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SY807 @ SY809 )
= ( ap @ SV162 @ SV369 @ SY808 @ SY809 ) ) )
| ( SY807 = SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1138,plain,
! [SV163: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV163 )
| ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) ) )
= $true )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(1139,plain,
! [SV370: $i,SV164: $i] :
( ( ! [SY810: $i > $i > $o,SY811: $i,SY812: $i] :
( ~ ( in @ ( kpair @ SY811 @ SY812 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SX5: $i,SX6: $i] : ( SY810 @ SX5 @ SX6 ) ) )
| ( in @ SY812 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1140,plain,
! [SV371: $i,SV165: $i] :
( ( ! [SY815: $i] :
( ~ ( func @ SV165 @ SV371 @ SY815 )
| ! [SY816: $i] :
( ~ ( in @ SY816 @ SV165 )
| ( in @ ( kpair @ SY816 @ ( ap @ SV165 @ SV371 @ SY815 @ SY816 ) ) @ SY815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1141,plain,
! [SV372: $i,SV166: $i] :
( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ ( setadjoin @ SV166 @ SV372 ) )
| ! [SY818: $o] :
( ~ ( ( SY817 != SV166 )
| SY818 )
| ~ ( ~ ( in @ SY817 @ SV372 )
| SY818 )
| SY818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1142,plain,
! [SV167: $i,SV373: $i] :
( ( ~ ( in @ SV373 @ ( powerset @ SV167 ) )
| ! [SY819: $i] :
( ~ ( in @ SY819 @ ( powerset @ SV167 ) )
| ( in @ ( binunion @ SV373 @ SY819 ) @ ( powerset @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1143,plain,
! [SV374: $i,SV168: $i] :
( ( ! [SY820: $i] :
( ~ ( in @ SY820 @ SV168 )
| ! [SY821: $i] :
( ~ ( in @ SY821 @ SV374 )
| ( in @ ( setadjoin @ ( setadjoin @ SY820 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY820 @ ( setadjoin @ SY821 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1144,plain,
! [SV375: $i,SV169: $i] :
( ( ! [SY822: $i] :
( ~ ( subset @ SY822 @ SV169 )
| ~ ( subset @ SY822 @ SV375 )
| ( subset @ SY822 @ ( binintersect @ SV169 @ SV375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1145,plain,
! [SV376: $i,SV170: $i] :
( ( ! [SY823: $i,SY824: $i] :
( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY823 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY823 @ ( setadjoin @ SY824 @ emptyset ) ) @ emptyset ) ) )
| ( SY823 != SY824 )
| ( SV376 = SY824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1146,plain,
! [SV377: $i,SV171: $i] :
( ( ! [SY825: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV171 @ SV377
@ ^ [SX3: $i,SX4: $i] : ( SY825 @ SX3 @ SX4 ) )
@ ( cartprod @ SV171 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1147,plain,
! [SV378: $i,SV172: $i] :
( ( ! [SY828: $i] :
( ~ ( in @ SY828 @ ( cartprod @ SV172 @ SV378 ) )
| ( in @ ( kfst @ SY828 ) @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1148,plain,
! [SV379: $i,SV174: $i] :
( ( ~ ( subset @ SV174 @ SV379 )
| ~ ( subset @ SV379 @ SV174 )
| ( SV174 = SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1149,plain,
! [SV175: $i > $o] :
( ( ( ~ ~ ! [SY447: $i] :
~ ~ ( ~ ( SV175 @ SY447 )
| ~ ! [SY448: $i] :
( ~ ( SV175 @ SY448 )
| ( SY447 = SY448 ) ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1150,plain,
! [SV380: $i,SV176: $i] :
( ( ! [SY829: $i] :
( ~ ( in @ SY829 @ ( funcSet @ SV176 @ SV380 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SV176 )
| ( in @ ( kpair @ SY830 @ ( ap @ SV176 @ SV380 @ SY829 @ SY830 ) ) @ SY829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1151,plain,
! [SV381: $i,SV177: $i] :
( ( ! [SY831: $i > $i > $o,SY832: $i,SY833: $i] :
( ~ ( in @ ( kpair @ SY832 @ SY833 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SX5: $i,SX6: $i] : ( SY831 @ SX5 @ SX6 ) ) )
| ( in @ SY832 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1152,plain,
! [SV382: $i,SV178: $i] :
( ( ~ ~ ~ ! [SY836: $i] :
~ ~ ( ~ ( in @ SY836 @ SV178 )
| ~ ( in @ SY836 @ SV382 ) )
| ( ( binintersect @ SV178 @ SV382 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1153,plain,
! [SV383: $i,SV179: $i] :
( ( ! [SY837: $i] :
( ~ ( subset @ SY837 @ ( cartprod @ SV179 @ SV383 ) )
| ! [SY838: $i > $o] :
( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV179 )
| ! [SY840: $i] :
( ~ ( in @ SY840 @ SV383 )
| ~ ( in @ ( kpair @ SY839 @ SY840 ) @ SY837 )
| ( SY838 @ ( kpair @ SY839 @ SY840 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY837 )
| ( SY838 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1154,plain,
! [SV181: $i] :
( ( in @ SV181 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1155,plain,
! [SV384: $i,SV182: $i] :
( ( ! [SY842: $i] :
( ~ ~ ( in @ SY842 @ ( setminus @ SV182 @ SV384 ) )
| ~ ~ ( in @ SY842 @ SV384 )
| ~ ( in @ SY842 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1156,plain,
! [SV385: $i,SV183: $i] :
( ( ! [SY843: $i] :
( ~ ( in @ SY843 @ ( funcSet @ SV183 @ SV385 ) )
| ( func @ SV183 @ SV385 @ SY843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1157,plain,
! [SV184: $i] :
( ( ( ~ ( singleton @ SV184 ) )
= $true )
| ( ( in @ ( setunion @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1158,plain,
! [SV386: $i,SV185: $i] :
( ( ! [SY844: $i] :
( ~ ( in @ SY844 @ ( setminus @ SV185 @ SV386 ) )
| ( in @ SY844 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1159,plain,
! [SV387: $i,SV186: $i] :
( ( ( SV186 != SV387 )
| ( in @ SV186 @ ( setadjoin @ SV387 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1160,plain,
! [SV388: $i,SV187: $i] :
( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ ( cartprod @ SV187 @ SV388 ) )
| ~ ! [SY846: $i] :
~ ~ ( ~ ( in @ SY846 @ SV187 )
| ~ ~ ! [SY847: $i] :
~ ~ ( ~ ( in @ SY847 @ SV388 )
| ( SY845
!= ( kpair @ SY846 @ SY847 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1161,plain,
! [SV188: $i,SV389: $i] :
( ( ~ ( in @ SV389 @ ( powerset @ SV188 ) )
| ! [SY848: $i] :
( ~ ( in @ SY848 @ ( powerset @ SV188 ) )
| ( in @ ( binintersect @ SV389 @ SY848 ) @ ( powerset @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1162,plain,
! [SV390: $i,SV189: $i] :
( ( subset @ ( binintersect @ SV189 @ SV390 ) @ SV390 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1163,plain,
! [SV190: $i] :
( ( ( ~ ( in @ SV190 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1164,plain,
! [SV391: $i,SV191: $i] :
( ( ! [SY849: $i] :
( ~ ( in @ SY849 @ SV191 )
| ~ ~ ( in @ SY849 @ SV391 )
| ~ ( subset @ SV191 @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1165,plain,
! [SV392: $i,SV192: $i] :
( ( ! [SY850: $i] :
( ~ ( in @ SY850 @ SV192 )
| ! [SY851: $i] :
( ~ ( in @ SY851 @ SV392 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY850 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY850 @ ( setadjoin @ SY851 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1166,plain,
! [SV393: $i,SV193: $i] :
( ( ! [SY852: $i] :
( ~ ( func @ SV193 @ SV393 @ SY852 )
| ! [SY853: $i] :
( ~ ( in @ SY853 @ SV193 )
| ( singleton
@ ( dsetconstr @ SV393
@ ^ [SX4: $i] : ( in @ ( kpair @ SY853 @ SX4 ) @ SY852 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1167,plain,
! [SV394: $i,SV194: $i] :
( ( ! [SY855: $i] :
( ~ ( subset @ SV194 @ SY855 )
| ( subset @ SV194 @ ( setadjoin @ SV394 @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1168,plain,
! [SV395: $i,SV195: $i] :
( ( ! [SY856: $i] :
( ~ ( in @ SY856 @ ( funcSet @ SV195 @ SV395 ) )
| ( ( lam @ SV195 @ SV395
@ ^ [SY857: $i] : ( ap @ SV195 @ SV395 @ SY856 @ SY857 ) )
= SY856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1169,plain,
! [SV196: $i > $o] :
( ( ( ~ ~ ! [SY497: $i] :
~ ( SV196 @ SY497 ) )
= $true )
| ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1170,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ~ ! [SY858: $i,SY859: $i] :
( ( SY858 != SY859 )
| ~ ( ~ ( ~ ( SV197 @ SY858 )
| ( SV396 @ SY859 ) )
| ~ ( ~ ( SV396 @ SY859 )
| ( SV197 @ SY858 ) ) ) )
| ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1171,plain,
! [SV397: $i > $o,SV198: $i] :
( ( in
@ ( dsetconstr @ SV198
@ ^ [SY866: $i] : ( SV397 @ SY866 ) )
@ ( powerset @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1172,plain,
! [SV199: $i,SV398: $i] :
( ( ! [SY867: $i] :
( ~ ( in @ SY867 @ SV398 )
| ~ ( in @ SY867 @ ( setminus @ SV199 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1173,plain,
! [SV200: $i,SV399: $i] :
( ( ~ ( in @ SV399 @ ( setunion @ SV200 ) )
| ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ SY868 @ SV200 )
| ~ ( in @ SV399 @ SY868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1174,plain,
! [SV400: $i,SV201: $i] :
( ( ! [SY869: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV201 @ SV400
@ ^ [SX3: $i,SX4: $i] : ( SY869 @ SX3 @ SX4 ) )
@ ( cartprod @ SV201 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1175,plain,
! [SV401: $i,SV202: $i] :
( ( ! [SY872: $i > $i] :
( ~ ! [SY873: $i] :
( ~ ( in @ SY873 @ SV202 )
| ( in @ ( SY872 @ SY873 ) @ SV401 ) )
| ( ( lam @ SV202 @ SV401
@ ^ [SX3: $i] : ( SY872 @ SX3 ) )
= ( lam @ SV202 @ SV401
@ ^ [SX3: $i] : ( SY872 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1176,plain,
! [SV402: $i,SV203: $i] :
( ( ! [SY876: $i,SY877: $i] :
( ( ( kpair @ SV203 @ SV402 )
!= ( kpair @ SY876 @ SY877 ) )
| ( SV203 = SY876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1177,plain,
! [SV403: $i,SV204: $i] :
( ( ~ ( in @ SV204 @ ( setadjoin @ SV403 @ emptyset ) )
| ( SV204 = SV403 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1178,plain,
! [SV404: $i,SV205: $i] :
( ( ! [SY878: $i] :
( ~ ( in @ SY878 @ SV205 )
| ~ ~ ( in @ SY878 @ SV404 )
| ( in @ SY878 @ ( symdiff @ SV205 @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1179,plain,
! [SV405: $i,SV206: $i] :
( ( ! [SY879: $i] :
( ~ ( subset @ SV206 @ SV405 )
| ~ ( subset @ SV405 @ SY879 )
| ( subset @ SV206 @ SY879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1180,plain,
! [SV406: $i,SV207: $i] :
( ( ! [SY880: $i] :
( ~ ( in @ SY880 @ ( setadjoin @ SV207 @ ( setadjoin @ SV406 @ emptyset ) ) )
| ( SY880 = SV207 )
| ( SY880 = SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1181,plain,
! [SV407: $i,SV210: $i] :
( ( ~ ( ( SV210 != SV407 ) )
| ~ ( in @ SV407 @ ( setadjoin @ SV210 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1182,plain,
! [SV408: $i,SV211: $i] :
( ( ! [SY881: $i] :
( ~ ( in @ SY881 @ ( cartprod @ SV211 @ SV408 ) )
| ( ( kpair @ ( kfst @ SY881 ) @ ( ksnd @ SY881 ) )
= SY881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1183,plain,
! [SV409: $i,SV212: $i] :
( ( ~ ( subset @ SV212 @ SV409 )
| ( ( setminus @ SV212 @ SV409 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1184,plain,
! [SV410: $i,SV213: $i] :
( ( ! [SY882: $i] :
( ~ ( subset @ SY882 @ ( cartprod @ SV213 @ SV410 ) )
| ! [SY883: $i > $o] :
( ~ ! [SY884: $i] :
( ~ ( in @ SY884 @ SV213 )
| ! [SY885: $i] :
( ~ ( in @ SY885 @ SV410 )
| ~ ( in @ ( kpair @ SY884 @ SY885 ) @ SY882 )
| ( SY883 @ ( kpair @ SY884 @ SY885 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY882 )
| ( SY883 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1185,plain,
! [SV214: $i,SV411: $i] :
( ( ! [SY887: $i] :
( ~ ( in @ SY887 @ SV411 )
| ( in @ SY887 @ ( binunion @ SV214 @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1186,plain,
! [SV215: $i,SV412: $i] :
( ( ~ ( in @ SV412 @ ( powerset @ SV215 ) )
| ( in @ ( setminus @ SV215 @ SV412 ) @ ( powerset @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1187,plain,
! [SV216: $i,SV413: $i] :
( ( ~ ( in @ SV413 @ ( powerset @ SV216 ) )
| ! [SY888: $i] :
( ~ ( in @ SY888 @ SV216 )
| ~ ( in @ SY888 @ SV413 )
| ~ ( in @ SY888 @ ( setminus @ SV216 @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1188,plain,
! [SV414: $i,SV217: $i] :
( ( in @ SV217 @ ( setadjoin @ SV217 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1189,plain,
! [SV415: $i,SV218: $i] :
( ( ( SV218 != SV415 )
| ! [SY889: $i > $o,SY890: $i > $o] :
( ~ ! [SY891: $i] :
( ~ ( in @ SY891 @ SV218 )
| ! [SY892: $i] :
( ~ ( in @ SY892 @ SV415 )
| ( SY891 != SY892 )
| ~ ( ~ ( ~ ( SY889 @ SY891 )
| ( SY890 @ SY892 ) )
| ~ ( ~ ( SY890 @ SY892 )
| ( SY889 @ SY891 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SX4: $i] : ( SY889 @ SX4 ) )
= ( dsetconstr @ SV415
@ ^ [SX4: $i] : ( SY890 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1190,plain,
! [SV416: $i,SV219: $i] :
( ( ( ksnd @ ( kpair @ SV219 @ SV416 ) )
= SV416 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1191,plain,
! [SV220: $i,SV417: $i] :
( ( ~ ( in @ SV417 @ SV220 )
| ( in @ SV417 @ ( powerset @ ( setunion @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1192,plain,
! [SV418: $i,SV221: $i] :
( ( in @ SV221 @ ( setadjoin @ SV221 @ ( setadjoin @ SV418 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1193,plain,
! [SV222: $i,SV419: $i] :
( ( ~ ( in @ SV419 @ ( powerset @ SV222 ) )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ ( powerset @ SV222 ) )
| ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV222 )
| ~ ( in @ SY896 @ SV419 )
| ( in @ SY896 @ SY895 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV222 )
| ~ ( in @ SY897 @ SY895 )
| ( in @ SY897 @ SV419 ) )
| ( SV419 = SY895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1194,plain,
! [SV223: $i,SV420: $i] :
( ( ~ ( subset @ SV420 @ SV223 )
| ( in @ SV420 @ ( powerset @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1195,plain,
! [SV421: $i > $o,SV224: $i] :
( ( ~ ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV224 )
| ( SV421 @ SY898 ) )
| ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1196,plain,
! [SV422: $i > $o,SV225: $i] :
( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV225 )
| ~ ( SV422 @ SY900 )
| ( in @ SY900
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1197,plain,
! [SV226: $i,SV423: $i] :
( ( ! [SY902: $i] :
( ~ ( in @ SV423 @ SY902 )
| ~ ( in @ SY902 @ SV226 )
| ( in @ SV423 @ ( setunion @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1198,plain,
! [SV424: $i,SV227: $i] :
( ( ! [SY903: $i] :
( ~ ( subset @ SY903 @ ( cartprod @ SV227 @ SV424 ) )
| ! [SY904: $i] :
( ~ ( subset @ SY904 @ ( cartprod @ SV227 @ SV424 ) )
| ~ ! [SY905: $i] :
( ~ ( in @ SY905 @ SV227 )
| ! [SY906: $i] :
( ~ ( in @ SY906 @ SV424 )
| ~ ( in @ ( kpair @ SY905 @ SY906 ) @ SY903 )
| ( in @ ( kpair @ SY905 @ SY906 ) @ SY904 ) ) )
| ( subset @ SY903 @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1199,plain,
! [SV228: $i] :
( ( ( ~ ( in @ SV228 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1200,plain,
! [SV425: $i,SV229: $i] :
( ( ! [SY907: $i] :
( ~ ~ ( in @ SY907 @ SV229 )
| ~ ( in @ SY907 @ ( setminus @ SV229 @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1201,plain,
! [SV426: $i,SV230: $i] :
( ( ! [SY908: $i,SY909: $i] :
( ~ ( in @ ( kpair @ SY908 @ SY909 ) @ ( cartprod @ SV230 @ SV426 ) )
| ( in @ SY908 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1202,plain,
! [SV427: $i > $o,SV231: $i] :
( ( ~ ~ ! [SY910: $i] :
~ ~ ( ~ ( in @ SY910 @ SV231 )
| ~ ( SV427 @ SY910 ) )
| ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1203,plain,
! [SV232: $i] :
( ( ( ~ ( subset @ SV232 @ emptyset ) )
= $true )
| ( ( SV232 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1204,plain,
! [SV233: $i > $o,SV1: $i,SV428: $i] :
( ( ~ ( in @ SV428 @ SV1 )
| ~ ( SV233 @ SV428 )
| ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1205,plain,
! [SV234: $i,SV2: $i,SV429: $i] :
( ( ~ ( in @ SV429 @ SV2 )
| ! [SY913: $i] :
( ~ ( in @ SY913 @ SV234 )
| ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SY913 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1206,plain,
! [SV235: $i,SV430: $i > $i,SV3: $i] :
( ( ~ ! [SY914: $i] :
( ~ ( in @ SY914 @ SV3 )
| ( in @ ( SV430 @ SY914 ) @ SV235 ) )
| ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1207,plain,
! [SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ! [SY596: $i] :
( ~ ( in @ SY596 @ SV236 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( SV4 @ SY596 @ SY16 )
| ~ ! [SY17: $i] :
( ~ ( SV4 @ SY596 @ SY17 )
| ( SY16 = SY17 ) ) ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1208,plain,
! [SV431: $i,SV237: $i,SV5: $i] :
( ( ~ ( func @ SV5 @ SV237 @ SV431 )
| ! [SY917: $i] :
( ~ ( in @ SY917 @ SV5 )
| ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SY917 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1209,plain,
! [SV432: $i > $i > $o,SV238: $i,SV6: $i] :
( ( ! [SY918: $i,SY919: $i] :
( ~ ( in @ ( kpair @ SY918 @ SY919 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SY920: $i,SY921: $i] : ( SV432 @ SY920 @ SY921 ) ) )
| ( SV432 @ SY918 @ SY919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1210,plain,
! [SV8: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( ! [SY610: $i] :
( ~ ( in @ SY610 @ ( powerset @ SV8 ) )
| ( in @ ( setminus @ SV239 @ SY610 ) @ ( powerset @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1211,plain,
! [SV433: $i,SV240: $i,SV9: $i] :
( ( ~ ( func @ SV9 @ SV240 @ SV433 )
| ( ( lam @ SV9 @ SV240
@ ^ [SY922: $i] : ( ap @ SV9 @ SV240 @ SV433 @ SY922 ) )
= SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1212,plain,
! [SV241: $i,SV10: $i] :
( ( ( SV10 != SV241 )
= $true )
| ( ( ( powerset @ SV10 )
= ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1213,plain,
! [SV242: $i,SV434: $i > $i,SV11: $i] :
( ( ~ ! [SY923: $i] :
( ~ ( in @ SY923 @ SV11 )
| ( in @ ( SV434 @ SY923 ) @ SV242 ) )
| ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1214,plain,
! [SV243: $i,SV12: $i] :
( ( ( SV12 != SV243 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV243 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1215,plain,
! [SV13: $i] :
( ( ( ! [SY42: $i] :
~ ( in @ SY42 @ SV13 ) )
= $false )
| ( ( SV13 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1216,plain,
! [SV244: $o,SV14: $i,SV435: $i] :
( ( ~ ( in @ SV435 @ SV14 )
| ! [SY925: $i] :
( ~ ( in @ SY925 @ SV14 )
| ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY926: $i] :
( ~ ( ~ SV244
| ( SY926 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY926 != SY925 ) ) ) )
= ( setadjoin @ SY925 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1217,plain,
! [SV14: $i,SV436: $i] :
( ( ~ ( in @ SV436 @ SV14 )
| ! [SY927: $i] :
( ~ ( in @ SY927 @ SV14 )
| ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY928: $i] :
( ~ ( ~ $true
| ( SY928 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY928 != SY927 ) ) ) )
= ( setadjoin @ SY927 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1218,plain,
! [SV14: $i,SV437: $i] :
( ( ~ ( in @ SV437 @ SV14 )
| ! [SY929: $i] :
( ~ ( in @ SY929 @ SV14 )
| ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY930: $i] :
( ~ ( ~ $false
| ( SY930 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY930 != SY929 ) ) ) )
= ( setadjoin @ SY929 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1219,plain,
! [SV16: $i > $o] :
( ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ( SV16 @ SY47 )
| ~ ! [SY48: $i] :
( ~ ( SV16 @ SY48 )
| ( SY47 = SY48 ) ) ) )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1220,plain,
! [SV438: $i,SV245: $i,SV17: $i] :
( ( ~ ( func @ SV17 @ SV245 @ SV438 )
| ! [SY931: $i] :
( ~ ( in @ SY931 @ SV17 )
| ( ( ap @ SV17 @ SV245 @ SV438 @ SY931 )
= ( ap @ SV17 @ SV245 @ SV438 @ SY931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1221,plain,
! [SV18: $i] :
( ( ( ~ ! [SY54: $i] :
~ ( in @ SY54 @ SV18 ) )
= $false )
| ( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1222,plain,
! [SV19: $i] :
( ( ( singleton @ SV19 )
= $false )
| ( ( ! [SY57: $i] :
( ~ ( in @ SY57 @ SV19 )
| ( ( setunion @ SV19 )
= SY57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1223,plain,
! [SV246: $i > $o,SV20: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) ) )
= $true )
| ( ( ! [SY622: $i] :
( ~ ( in @ SY622 @ SV20 )
| ! [SY623: $i] :
( ~ ( in @ SY623 @ SV20 )
| ~ ( SV246 @ SY622 )
| ~ ( SV246 @ SY623 )
| ( SY622 = SY623 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1224,plain,
! [SV21: $i] :
( ( ( in @ SV21 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV21 @ SV21 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1225,plain,
! [SV247: $i,SV22: $i,SV439: $i] :
( ( ~ ( in @ SV439 @ SV22 )
| ! [SY932: $i] :
( ~ ( in @ SY932 @ SV247 )
| ( ( kpair @ SV439 @ SY932 )
= ( kpair @ SV439 @ SY932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1226,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
| ~ ! [SY942: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY942 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY942 ) )
| ~ ! [SY945: $i] :
~ ~ ! [SY946: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY945 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY946 @ SY942 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY945 )
| ~ ( in @ SX5 @ SY942 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY945 ) )
| ( in @ SY946 @ SY948 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[977]) ).
thf(1227,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( setunion @ SV24 ) ) )
= $true )
| ( ( ! [SY626: $o] :
( ~ ! [SY627: $i] :
( ~ ( in @ SV248 @ SY627 )
| ~ ( in @ SY627 @ SV24 )
| SY626 )
| SY626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1228,plain,
! [SV249: $i,SV26: $i] :
( ( ( SV26 != SV249 )
= $true )
| ( ( subset @ SV249 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1229,plain,
! [SV27: $i > $o] :
( ( ( ~ ! [SY87: $i] :
~ ~ ( ~ ( SV27 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV27 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1230,plain,
! [SV250: $i,SV28: $i,SV440: $i] :
( ( ~ ( in @ SV440 @ ( setadjoin @ SV28 @ SV250 ) )
| ( SV440 = SV28 )
| ( in @ SV440 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1231,plain,
! [SV251: $i,SV29: $i,SV441: $i] :
( ( ~ ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) )
| ! [SY950: $i] :
( ~ ( in @ SY950 @ SV29 )
| ( ( ap @ SV29 @ SV251 @ SV441 @ SY950 )
= ( ap @ SV29 @ SV251 @ SV441 @ SY950 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1232,plain,
! [SV252: $i > $o,SV30: $i,SV442: $i] :
( ( ~ ( in @ SV442 @ SV30 )
| ~ ( SV252 @ SV442 )
| ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1233,plain,
! [SV31: $i] :
( ( ( iskpair @ SV31 )
= $false )
| ( ( ( kpair @ ( kfst @ SV31 ) @ ( ksnd @ SV31 ) )
= SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1234,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ( ~ ( in @ SV254 @ ( setunion @ SV33 ) )
| ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
| ~ ( ~ ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) )
| ( in @ SV254 @ ( setunion @ SV33 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1235,plain,
! [SV255: $i,SV34: $i,SV443: $i] :
( ( ~ ( in @ SV443 @ SV34 )
| ~ ( in @ SV443 @ SV255 )
| ~ ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1236,plain,
! [SV256: $i,SV35: $i] :
( ( ( SV35 != SV256 )
= $true )
| ( ( ( setadjoin @ SV35 @ ( setadjoin @ SV256 @ emptyset ) )
= ( setadjoin @ SV35 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1237,plain,
! [SV36: $i] :
( ( ( ~ ! [SY106: $i] :
~ ( in @ SY106 @ SV36 ) )
= $false )
| ( ( SV36 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1238,plain,
! [SV257: $i,SV37: $i,SV444: $i] :
( ( ~ ( in @ SV444 @ SV37 )
| ! [SY953: $i] :
( ~ ( in @ SY953 @ SV257 )
| ( ( kfst @ ( kpair @ SV444 @ SY953 ) )
= SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1239,plain,
! [SV258: $i,SV38: $i,SV445: $i] :
( ( ~ ( in @ SV445 @ SV38 )
| ~ ~ ( in @ SV445 @ SV258 )
| ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1240,plain,
! [SV259: $i,SV39: $i,SV446: $i] :
( ( ~ ( in @ SV446 @ SV39 )
| ~ ~ ( in @ SV446 @ SV259 )
| ( SV39 != SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1241,plain,
! [SV260: $i,SV40: $i] :
( ( ( ( setminus @ SV40 @ SV260 )
!= emptyset )
= $true )
| ( ( subset @ SV40 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1242,plain,
! [SV261: $i,SV41: $i,SV447: $i] :
( ( ~ ( in @ SV447 @ ( setadjoin @ SV41 @ ( setadjoin @ SV261 @ emptyset ) ) )
| ( SV447 = SV41 )
| ( SV447 = SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1243,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY642: $i,SY643: $i] :
( ( SY642 != SY643 )
| ~ ( ~ ( ~ ( SV42 @ SY642 )
| ( SV262 @ SY643 ) )
| ~ ( ~ ( SV262 @ SY643 )
| ( SV42 @ SY642 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1244,plain,
! [SV448: $i,SV263: $i,SV43: $i] :
( ( ~ ( subset @ SV43 @ SV263 )
| ~ ~ ( in @ SV448 @ SV263 )
| ~ ( in @ SV448 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1245,plain,
! [SV449: $i,SV264: $i,SV44: $i] :
( ( ~ ( func @ SV44 @ SV264 @ SV449 )
| ! [SY954: $i] :
( ~ ( in @ SY954 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY955: $i] : ( in @ ( kpair @ SY954 @ SY955 ) @ SV449 ) ) )
@ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1246,plain,
! [SV265: $i,SV45: $i,SV450: $i] :
( ( ~ ~ ( in @ SV450 @ SV45 )
| ~ ~ ( in @ SV450 @ SV265 )
| ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1247,plain,
! [SV47: $i,SV267: $i] :
( ( ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV267 )
| ( in @ SY657 @ SV47 ) ) )
= $true )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1248,plain,
! [SV268: $i > $o,SV48: $i] :
( ( ( ~ ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ SY658 @ SV48 )
| ~ ~ ( SV268 @ SY658 ) ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1249,plain,
! [SV269: $i,SV451: $i > $i,SV49: $i] :
( ( ~ ! [SY956: $i] :
( ~ ( in @ SY956 @ SV49 )
| ( in @ ( SV451 @ SY956 ) @ SV269 ) )
| ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1250,plain,
! [SV452: $i,SV270: $i,SV50: $i] :
( ( ~ ( func @ SV50 @ SV270 @ SV452 )
| ( in @ SV452 @ ( funcSet @ SV50 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1251,plain,
! [SV51: $i > $o] :
( ( ( ~ ! [SY149: $i] :
~ ~ ( ~ ( SV51 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( SV51 @ SY150 )
| ( SY149 = SY150 ) ) ) )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1252,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ! [SY959: $o] :
( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
| ~ ( ~ ( in @ SV453 @ SV53 )
| SY959 )
| ~ ( ~ ( in @ SV453 @ SV272 )
| SY959 )
| SY959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1253,plain,
! [SV273: $i,SV54: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ ( setminus @ SV54 @ SV273 ) )
| ~ ( in @ SV454 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1254,plain,
! [SV455: $i,SV274: $i,SV55: $i] :
( ( ~ ( subset @ SV55 @ SV274 )
| ~ ( in @ SV455 @ SV55 )
| ( in @ SV455 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1255,plain,
! [SV275: $i,SV56: $i] :
( ( ( SV56 != SV275 )
= $true )
| ( ( ! [SY669: $i,SY670: $i] :
( ( SY669 != SY670 )
| ( ( setadjoin @ SV56 @ SY669 )
= ( setadjoin @ SV275 @ SY670 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1256,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ~ ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
| ! [SY960: $o] :
( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SY960 )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SY960 )
| SY960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1257,plain,
! [SV278: $i,SV59: $i,SV457: $i] :
( ( ~ ( in @ SV457 @ ( cartprod @ SV59 @ SV278 ) )
| ( iskpair @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1258,plain,
! [SV279: $i,SV60: $i] :
( ( ( ( binintersect @ SV60 @ SV279 )
!= SV279 )
= $true )
| ( ( subset @ SV279 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1259,plain,
! [SV280: $i,SV61: $i] :
( ( ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV61 )
| ( in @ SY674 @ SV280 ) ) )
= $true )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1260,plain,
! [SV281: $o,SV62: $i,SV458: $i] :
( ( ~ ( in @ SV458 @ SV62 )
| ! [SY961: $i] :
( ~ ( in @ SY961 @ SV62 )
| ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SY961 )
= SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1261,plain,
! [SV62: $i,SV459: $i] :
( ( ~ ( in @ SV459 @ SV62 )
| ! [SY962: $i] :
( ~ ( in @ SY962 @ SV62 )
| ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SY962 )
= SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1262,plain,
! [SV62: $i,SV460: $i] :
( ( ~ ( in @ SV460 @ SV62 )
| ! [SY963: $i] :
( ~ ( in @ SY963 @ SV62 )
| ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SY963 )
= SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1263,plain,
! [SV461: $i,SV282: $i,SV63: $i] :
( ( ( binintersect @ SV63 @ ( binunion @ SV282 @ SV461 ) )
= ( binunion @ ( binintersect @ SV63 @ SV282 ) @ ( binintersect @ SV63 @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1264,plain,
! [SV462: $i,SV283: $i,SV64: $i] :
( ( ( ( setadjoin @ SV64 @ ( setadjoin @ SV283 @ emptyset ) )
!= ( setadjoin @ SV462 @ emptyset ) )
| ( SV64 = SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1265,plain,
! [SV284: $i,SV65: $i,SV463: $i] :
( ( ~ ( in @ SV463 @ SV65 )
| ( in @ ( setadjoin @ SV463 @ emptyset ) @ ( powerset @ ( binunion @ SV65 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1266,plain,
! [SV285: $i,SV66: $i] :
( ( ( ~ ~ ( subset @ SV66 @ SV285 ) )
= $true )
| ( ( SV66 != SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1267,plain,
! [SV286: $o,SV67: $i,SV464: $i] :
( ( ~ ( in @ SV464 @ SV67 )
| ! [SY964: $i] :
( ~ ( in @ SY964 @ SV67 )
| ~ ~ SV286
| ( in @ SY964
@ ( dsetconstr @ SV67
@ ^ [SY965: $i] :
( ~ ( ~ SV286
| ( SY965 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY965 != SY964 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1268,plain,
! [SV67: $i,SV465: $i] :
( ( ~ ( in @ SV465 @ SV67 )
| ! [SY966: $i] :
( ~ ( in @ SY966 @ SV67 )
| ~ ~ $true
| ( in @ SY966
@ ( dsetconstr @ SV67
@ ^ [SY967: $i] :
( ~ ( ~ $true
| ( SY967 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY967 != SY966 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1269,plain,
! [SV67: $i,SV466: $i] :
( ( ~ ( in @ SV466 @ SV67 )
| ! [SY968: $i] :
( ~ ( in @ SY968 @ SV67 )
| ~ ~ $false
| ( in @ SY968
@ ( dsetconstr @ SV67
@ ^ [SY969: $i] :
( ~ ( ~ $false
| ( SY969 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY969 != SY968 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1270,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SV68 )
| ~ ( SV287 @ SY684 ) ) )
= $true )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1271,plain,
! [SV288: $i > $o,SV69: $i] :
( ( ( ~ ~ ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV69 )
| ~ ( SV288 @ SY686 ) ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1272,plain,
! [SV467: $i,SV70: $i,SV289: $i] :
( ( ~ ( in @ SV289 @ ( powerset @ SV70 ) )
| ~ ( in @ SV467 @ SV289 )
| ( in @ SV467 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1273,plain,
! [SV290: $i,SV71: $i,SV468: $i] :
( ( ~ ( in @ SV468 @ SV71 )
| ( in @ SV468 @ ( binunion @ SV71 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1274,plain,
! [SV291: $i,SV73: $i,SV469: $i] :
( ( ~ ( in @ SV469 @ SV73 )
| ! [SY970: $i] :
( ~ ( in @ SY970 @ SV291 )
| ( ( ksnd @ ( kpair @ SV469 @ SY970 ) )
= SY970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1275,plain,
! [SV292: $i,SV74: $i] :
( ( ( SV74 != SV292 )
= $true )
| ( ( ! [SY692: $i,SY693: $i] :
( ( SY692 != SY693 )
| ~ ( ~ ( ~ ( in @ SY692 @ SV74 )
| ( in @ SY693 @ SV292 ) )
| ~ ( ~ ( in @ SY693 @ SV292 )
| ( in @ SY692 @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1276,plain,
! [SV293: $i,SV470: $i > $i,SV75: $i] :
( ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SV75 )
| ( in @ ( SV470 @ SY971 ) @ SV293 ) )
| ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1277,plain,
! [SV294: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY697: $i] :
( ~ ( in @ SY697 @ SV76 )
| ( SV294 @ SY697 ) ) )
= $true )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1278,plain,
! [SV471: $i,SV295: $i,SV77: $i] :
( ( ~ ( func @ SV77 @ SV295 @ SV471 )
| ! [SY973: $i] :
( ~ ( func @ SV77 @ SV295 @ SY973 )
| ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY974 )
= ( ap @ SV77 @ SV295 @ SY973 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV77 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV295 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SY973 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV471 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1279,plain,
! [SV296: $i,SV78: $i,SV472: $i] :
( ( ~ ( in @ ( setadjoin @ SV472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV296 @ emptyset ) ) @ emptyset ) ) )
| ( SV78 = SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1280,plain,
! [SV79: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ ( powerset @ SV79 ) )
| ! [SY706: $i] :
( ~ ( in @ SY706 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SY705 ) )
| ~ ( in @ SY706 @ SV297 )
| ( in @ SY706 @ SY705 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1281,plain,
! [SV80: $i > $o] :
( ( ( ~ ! [SY222: $i] :
~ ~ ( ~ ( SV80 @ SY222 )
| ~ ! [SY223: $i] :
( ~ ( SV80 @ SY223 )
| ( SY222 = SY223 ) ) ) )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1282,plain,
! [SV81: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ ( powerset @ SV81 ) )
| ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV81 )
| ~ ( in @ SY708 @ SV298 )
| ( in @ SY708 @ SY707 ) )
| ( in @ SV298 @ ( powerset @ SY707 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1283,plain,
! [SV299: $i,SV82: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
| ! [SY977: $i] :
( ~ ( in @ SY977 @ ( funcSet @ SV82 @ SV299 ) )
| ~ ! [SY978: $i] :
( ~ ( in @ SY978 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY978 )
= ( ap @ SV82 @ SV299 @ SY977 @ SY978 ) ) )
| ( SV473 = SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1284,plain,
! [SV83: $i] :
( ( ( ! [SY233: $i] :
~ ( in @ SY233 @ SV83 ) )
= $false )
| ( ( SV83 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1285,plain,
! [SV300: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SV300 @ emptyset ) )
= $true )
| ( ( SV84 = SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1286,plain,
! [SV301: $i,SV85: $i,SV474: $i] :
( ( ~ ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
| ! [SY979: $i] :
( ~ ( subset @ SY979 @ ( cartprod @ SV85 @ SV301 ) )
| ~ ! [SY980: $i] :
( ~ ( in @ SY980 @ SV85 )
| ! [SY981: $i] :
( ~ ( in @ SY981 @ SV301 )
| ~ ( in @ ( kpair @ SY980 @ SY981 ) @ SV474 )
| ( in @ ( kpair @ SY980 @ SY981 ) @ SY979 ) ) )
| ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV85 )
| ! [SY983: $i] :
( ~ ( in @ SY983 @ SV301 )
| ~ ( in @ ( kpair @ SY982 @ SY983 ) @ SY979 )
| ( in @ ( kpair @ SY982 @ SY983 ) @ SV474 ) ) )
| ( SV474 = SY979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1287,plain,
! [SV302: $o,SV86: $i,SV475: $i] :
( ( ~ ( in @ SV475 @ SV86 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV86 )
| ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY985: $i] :
( ~ ( ~ SV302
| ( SY985 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY985 != SY984 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1288,plain,
! [SV86: $i,SV476: $i] :
( ( ~ ( in @ SV476 @ SV86 )
| ! [SY986: $i] :
( ~ ( in @ SY986 @ SV86 )
| ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY987: $i] :
( ~ ( ~ $true
| ( SY987 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY987 != SY986 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1289,plain,
! [SV86: $i,SV477: $i] :
( ( ~ ( in @ SV477 @ SV86 )
| ! [SY988: $i] :
( ~ ( in @ SY988 @ SV86 )
| ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY989: $i] :
( ~ ( ~ $false
| ( SY989 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY989 != SY988 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1290,plain,
! [SV303: $i > $o,SV87: $i,SV478: $i] :
( ( ~ ( in @ SV478
@ ( dsetconstr @ SV87
@ ^ [SY722: $i] : ( SV303 @ SY722 ) ) )
| ( SV303 @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1291,plain,
! [SV479: $i,SV304: $i,SV88: $i] :
( ( ! [SY991: $i] :
( ( ( kpair @ SV88 @ SV304 )
!= ( kpair @ SV479 @ SY991 ) )
| ( SV304 = SY991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1292,plain,
! [SV89: $i] :
( ( ( SV89 != emptyset )
= $false )
| ( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( in @ SY252 @ SV89 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1293,plain,
! [SV480: $i > $i > $o,SV305: $i,SV90: $i] :
( ( ! [SY992: $i] :
( ~ ( in @ SY992 @ SV90 )
| ! [SY993: $i] :
( ~ ( in @ SY993 @ SV305 )
| ~ ( SV480 @ SY992 @ SY993 )
| ( in @ ( kpair @ SY992 @ SY993 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1294,plain,
! [SV91: $i > $o] :
( ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV91 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV91 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1295,plain,
! [SV306: $i,SV92: $i] :
( ( ( ~ ! [SY730: $i] :
( ~ ( in @ SY730 @ SV92 )
| ( in @ SY730 @ SV306 ) ) )
= $true )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1296,plain,
! [SV307: $i,SV93: $i] :
( ( ( ~ ( subset @ SV93 @ SV307 ) )
= $true )
| ( ( subset @ ( powerset @ SV93 ) @ ( powerset @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1297,plain,
! [SV94: $i] :
( ( ( iskpair @ SV94 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV94 )
@ ^ [SY266: $i] :
( SV94
= ( kpair @ ( kfst @ SV94 ) @ SY266 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1298,plain,
! [SV308: $i > $o,SV95: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY732: $i] :
~ ~ ( ~ ( in @ SY732 @ SV95 )
| ~ ( SV308 @ SY732 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1299,plain,
! [SV309: $i > $o,SV96: $i] :
( ( ( ~ ~ ~ ! [SY733: $i] :
~ ~ ( ~ ( in @ SY733 @ SV96 )
| ~ ( SV309 @ SY733 ) ) )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1300,plain,
! [SV311: $i,SV98: $i,SV481: $i] :
( ( ~ ( in @ SV481 @ SV98 )
| ! [SY996: $i] :
( ~ ( in @ SY996 @ SV311 )
| ( in @ ( kpair @ SV481 @ SY996 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1301,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ( ~ ( in @ SV312 @ ( powerset @ SV99 ) )
| ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) )
| ~ ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) )
| ( in @ SV312 @ ( powerset @ SV99 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1302,plain,
! [SV313: $i,SV100: $i,SV482: $i] :
( ( ~ ( in @ SV482 @ ( binintersect @ SV100 @ SV313 ) )
| ( in @ SV482 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1303,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( ~ ( ~ ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
| ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ~ ( ~ ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1304,plain,
! [SV315: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ ( setadjoin @ SV315 @ emptyset ) ) )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV102 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1305,plain,
! [SV103: $i > $o,SV316: $i] :
( ( ( ~ ( in @ SV316 @ emptyset ) )
= $true )
| ( ( SV103 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1306,plain,
! [SV317: $i,SV104: $i,SV484: $i] :
( ( ~ ( in @ SV484 @ SV104 )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV317 )
| ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SY997 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1307,plain,
! [SV318: $i,SV105: $i] :
( ( ( SV105 != SV318 )
= $true )
| ( ( ! [SY743: $i,SY744: $i] :
( ( SY743 != SY744 )
| ~ ( in @ SY743 @ SV105 )
| ( in @ SY744 @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1308,plain,
! [SV320: $i,SV107: $i] :
( ( ( SV107 != SV320 )
= $true )
| ( ( subset @ SV107 @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1309,plain,
! [SV485: $i,SV321: $i,SV108: $i] :
( ( ~ ( func @ SV108 @ SV321 @ SV485 )
| ! [SY998: $i] :
( ~ ( in @ SY998 @ SV108 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV321 )
| ~ ( in @ ( kpair @ SY998 @ SY999 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SY998 )
= SY999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1310,plain,
( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1311,plain,
( ( ~ ( ~ ( in @ sK3_SY2 @ sK1_A )
| ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1312,plain,
! [SV322: $i,SV109: $i] :
( ( ( ~ ! [SY748: $i] :
~ ( ~ ( ~ ( in @ SY748 @ SV109 )
| ( in @ SY748 @ SV322 ) )
| ~ ( ~ ( in @ SY748 @ SV322 )
| ( in @ SY748 @ SV109 ) ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1313,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ~ ( in @ SV486 @ SV112 )
| ~ ( ~ ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) )
| ~ ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1314,plain,
! [SV325: $o,SV113: $i,SV487: $i] :
( ( ~ ( in @ SV487 @ SV113 )
| ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV113 )
| ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1003: $i] :
( ~ ( ~ SV325
| ( SY1003 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1003 != SY1002 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1315,plain,
! [SV113: $i,SV488: $i] :
( ( ~ ( in @ SV488 @ SV113 )
| ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV113 )
| ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1005: $i] :
( ~ ( ~ $true
| ( SY1005 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1005 != SY1004 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1316,plain,
! [SV113: $i,SV489: $i] :
( ( ~ ( in @ SV489 @ SV113 )
| ! [SY1006: $i] :
( ~ ( in @ SY1006 @ SV113 )
| ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1007: $i] :
( ~ ( ~ $false
| ( SY1007 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1007 != SY1006 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1317,plain,
! [SV114: $i] :
( ( ( SV114 != emptyset )
= $false )
| ( ( ~ ! [SY310: $i] :
~ ( in @ SY310 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1318,plain,
! [SV326: $i,SV115: $i,SV490: $i] :
( ( ! [SY1008: $i] :
( ~ ( in @ ( kpair @ SV490 @ SY1008 ) @ ( cartprod @ SV115 @ SV326 ) )
| ( in @ SY1008 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1319,plain,
! [SV327: $i > $o,SV116: $i,SV491: $i] :
( ( ~ ( in @ SV491
@ ( dsetconstr @ SV116
@ ^ [SY758: $i] : ( SV327 @ SY758 ) ) )
| ( in @ SV491 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1320,plain,
! [SV117: $i] :
( ( ( iskpair @ SV117 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV117 )
@ ^ [SY317: $i] : ( in @ ( setadjoin @ SY317 @ emptyset ) @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1321,plain,
! [SV118: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ SV118 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV328 @ emptyset ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1322,plain,
! [SV119: $i,SV329: $i] :
( ( ( ~ ( subset @ SV329 @ SV119 ) )
= $true )
| ( ( ( binintersect @ SV119 @ SV329 )
= SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1323,plain,
! [SV120: $i,SV330: $i,SV492: $i] :
( ( ~ ( in @ SV492 @ SV330 )
| ( in @ SV492 @ ( setadjoin @ SV120 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1324,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY760: $i] :
( ~ ( in @ SY760 @ SV121 )
| ! [SY761: $i] :
( ~ ( in @ SY761 @ SV121 )
| ~ ( SV331 @ SY760 )
| ~ ( SV331 @ SY761 )
| ( SY760 = SY761 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1325,plain,
! [SV332: $o,SV122: $i,SV493: $i] :
( ( ~ ( in @ SV493 @ SV122 )
| ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV122 )
| ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SY1010 )
= SY1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1326,plain,
! [SV122: $i,SV494: $i] :
( ( ~ ( in @ SV494 @ SV122 )
| ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV122 )
| ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SY1011 )
= SY1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1327,plain,
! [SV122: $i,SV495: $i] :
( ( ~ ( in @ SV495 @ SV122 )
| ! [SY1012: $i] :
( ~ ( in @ SY1012 @ SV122 )
| ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SY1012 )
= SY1012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1328,plain,
! [SV333: $i,SV496: $i > $i,SV123: $i] :
( ( ~ ! [SY1013: $i] :
( ~ ( in @ SY1013 @ SV123 )
| ( in @ ( SV496 @ SY1013 ) @ SV333 ) )
| ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1329,plain,
! [SV124: $o,SV334: $i] :
( ( ( ~ ( in @ SV334 @ ( prop2set @ SV124 ) ) )
= $true )
| ( SV124 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1330,plain,
! [SV335: $i] :
( ( ( ~ ( in @ SV335 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1331,plain,
! [SV336: $i] :
( ( ( ~ ( in @ SV336 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1332,plain,
! [SV337: $o,SV125: $i,SV497: $i] :
( ( ~ ( in @ SV497 @ SV125 )
| ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV125 )
| ( in @ ( if @ SV125 @ SV337 @ SV497 @ SY1016 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SY1016 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1333,plain,
! [SV125: $i,SV498: $i] :
( ( ~ ( in @ SV498 @ SV125 )
| ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV125 )
| ( in @ ( if @ SV125 @ $true @ SV498 @ SY1017 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SY1017 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1334,plain,
! [SV125: $i,SV499: $i] :
( ( ~ ( in @ SV499 @ SV125 )
| ! [SY1018: $i] :
( ~ ( in @ SY1018 @ SV125 )
| ( in @ ( if @ SV125 @ $false @ SV499 @ SY1018 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SY1018 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1335,plain,
! [SV338: $i,SV126: $i] :
( ( ( ~ ( subset @ SV126 @ SV338 ) )
= $true )
| ( ( ( binintersect @ SV126 @ SV338 )
= SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1336,plain,
! [SV341: $i,SV129: $i,SV500: $i] :
( ( ~ ( in @ SV500 @ SV129 )
| ~ ( in @ SV500 @ SV341 )
| ( in @ SV500 @ ( binintersect @ SV129 @ SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1337,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i] :
( ( ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV130 )
| ! [SY1020: $i] :
( ~ ( in @ SY1020 @ SV342 )
| ~ ( in @ ( kpair @ SY1019 @ SY1020 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SY1019 @ SY1020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1338,plain,
! [SV343: $i,SV131: $i] :
( ( ( ( binintersect @ SV131 @ SV343 )
!= SV131 )
= $true )
| ( ( subset @ SV131 @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1339,plain,
! [SV345: $o,SV133: $i,SV502: $i] :
( ( ~ ( in @ SV502 @ SV133 )
| ! [SY1023: $i] :
( ~ ( in @ SY1023 @ SV133 )
| ( in @ ( if @ SV133 @ SV345 @ SV502 @ SY1023 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1340,plain,
! [SV133: $i,SV503: $i] :
( ( ~ ( in @ SV503 @ SV133 )
| ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV133 )
| ( in @ ( if @ SV133 @ $true @ SV503 @ SY1024 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1341,plain,
! [SV133: $i,SV504: $i] :
( ( ~ ( in @ SV504 @ SV133 )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV133 )
| ( in @ ( if @ SV133 @ $false @ SV504 @ SY1025 ) @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1342,plain,
! [SV134: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( subset @ SV346 @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1343,plain,
! [SV347: $i,SV135: $i,SV505: $i] :
( ( ~ ~ ( in @ SV505 @ SV135 )
| ~ ( in @ SV505 @ SV347 )
| ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1344,plain,
! [SV506: $i,SV349: $i,SV137: $i] :
( ( ! [SY1026: $i] :
( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SV349 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SY1026 @ emptyset ) ) @ emptyset ) ) )
| ( SV349 = SY1026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1345,plain,
! [SV507: $i,SV350: $i,SV138: $i] :
( ( ! [SY1027: $i] :
( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV507 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV507 @ ( setadjoin @ SY1027 @ emptyset ) ) @ emptyset ) ) )
| ( SV138 = SV507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1346,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY786: $i] :
( ~ ( in @ SY786 @ SV139 )
| ! [SY787: $i] :
( ~ ( in @ SY787 @ SV139 )
| ~ ( SV351 @ SY786 )
| ~ ( SV351 @ SY787 )
| ( SY786 = SY787 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1347,plain,
! [SV141: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ SV141 ) )
= $true )
| ( ( in @ ( setadjoin @ SV353 @ emptyset ) @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1348,plain,
! [SV354: $i,SV142: $i] :
( ( ( ~ ( subset @ SV142 @ SV354 ) )
= $true )
| ( ( in @ SV142 @ ( powerset @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1349,plain,
! [SV355: $i,SV143: $i,SV508: $i] :
( ( ~ ( in @ SV508 @ SV143 )
| ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SV355 )
| ( in @ ( kpair @ SV508 @ SY1028 ) @ ( cartprod @ SV143 @ SV355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1350,plain,
! [SV144: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( in @ ( powerset @ SV356 ) @ ( powerset @ ( powerset @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1351,plain,
! [SV145: $i > $o] :
( ( ( ~ ! [SY378: $i] :
~ ~ ( ~ ( SV145 @ SY378 )
| ~ ! [SY379: $i] :
( ~ ( SV145 @ SY379 )
| ( SY378 = SY379 ) ) ) )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1352,plain,
! [SV358: $i,SV147: $i,SV509: $i] :
( ( ~ ( in @ SV509 @ ( binunion @ SV147 @ SV358 ) )
| ( in @ SV509 @ SV147 )
| ( in @ SV509 @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1353,plain,
! [SV149: $o] :
( ( SV149 = $false )
| ( ( set2prop @ ( prop2set @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1354,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1355,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1356,plain,
! [SV360: $o,SV150: $i,SV510: $i] :
( ( ~ ( in @ SV510 @ SV150 )
| ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1030: $i] :
( ~ ( ~ SV360
| ( SY1030 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1030 != SY1029 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1357,plain,
! [SV150: $i,SV511: $i] :
( ( ~ ( in @ SV511 @ SV150 )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1032: $i] :
( ~ ( ~ $true
| ( SY1032 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1032 != SY1031 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1358,plain,
! [SV150: $i,SV512: $i] :
( ( ~ ( in @ SV512 @ SV150 )
| ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1034: $i] :
( ~ ( ~ $false
| ( SY1034 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1034 != SY1033 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1359,plain,
! [SV151: $o] :
( ( SV151 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1360,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1361,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1362,plain,
! [SV152: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( powerset @ SV152 ) ) )
= $true )
| ( ( ! [SY796: $i] :
( ~ ( in @ SY796 @ ( powerset @ SV152 ) )
| ~ ! [SY797: $i] :
( ~ ( in @ SY797 @ SV152 )
| ~ ( in @ SY797 @ SV361 )
| ( in @ SY797 @ SY796 ) )
| ( subset @ SV361 @ SY796 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1363,plain,
! [SV153: $i > $o] :
( ( ( ~ ! [SY392: $i] :
~ ! [SY393: $i] :
~ ( ~ ( ~ ( SV153 @ SY393 )
| ( SY393 = SY392 ) )
| ~ ( ( SY393 != SY392 )
| ( SV153 @ SY393 ) ) ) )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1364,plain,
! [SV362: $i,SV154: $i] :
( ( ( SV154 != SV362 )
= $true )
| ( ( ( setunion @ SV154 )
= ( setunion @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1365,plain,
! [SV363: $i,SV155: $i] :
( ( ( ~ ! [SY798: $i] :
( ~ ( in @ SY798 @ SV155 )
| ( in @ SY798 @ SV363 ) ) )
= $true )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1366,plain,
! [SV364: $i,SV156: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
| ! [SY1035: $i] :
( ~ ( in @ SY1035 @ SV156 )
| ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV364 )
| ~ ( in @ ( kpair @ SY1035 @ SY1036 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SY1035 )
= SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1367,plain,
! [SV365: $i,SV157: $i,SV514: $i] :
( ( ~ ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV157 )
| ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SY1037 ) @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1368,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ~ ~ ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) )
| ~ ( in @ SV515 @ SV158 )
| ( in @ SV515 @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1369,plain,
! [SV367: $i,SV159: $i,SV516: $i] :
( ( ~ ( in @ SV516 @ ( cartprod @ SV159 @ SV367 ) )
| ( in @ ( ksnd @ SV516 ) @ SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1370,plain,
! [SV368: $i,SV161: $i,SV517: $i] :
( ( ~ ( in @ SV517 @ ( binintersect @ SV161 @ SV368 ) )
| ( in @ SV517 @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1371,plain,
! [SV518: $i,SV369: $i,SV162: $i] :
( ( ~ ( func @ SV162 @ SV369 @ SV518 )
| ! [SY1038: $i] :
( ~ ( func @ SV162 @ SV369 @ SY1038 )
| ~ ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1039 )
= ( ap @ SV162 @ SV369 @ SY1038 @ SY1039 ) ) )
| ( SV518 = SY1038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1372,plain,
! [SV163: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV163 )
| ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) ) )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1373,plain,
! [SV519: $i > $i > $o,SV370: $i,SV164: $i] :
( ( ! [SY1040: $i,SY1041: $i] :
( ~ ( in @ ( kpair @ SY1040 @ SY1041 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SY1042: $i,SY1043: $i] : ( SV519 @ SY1042 @ SY1043 ) ) )
| ( in @ SY1041 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1374,plain,
! [SV520: $i,SV371: $i,SV165: $i] :
( ( ~ ( func @ SV165 @ SV371 @ SV520 )
| ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV165 )
| ( in @ ( kpair @ SY1044 @ ( ap @ SV165 @ SV371 @ SV520 @ SY1044 ) ) @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1375,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ~ ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
| ! [SY1045: $o] :
( ~ ( ( SV521 != SV166 )
| SY1045 )
| ~ ( ~ ( in @ SV521 @ SV372 )
| SY1045 )
| SY1045 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1376,plain,
! [SV167: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ ( powerset @ SV167 ) ) )
= $true )
| ( ( ! [SY819: $i] :
( ~ ( in @ SY819 @ ( powerset @ SV167 ) )
| ( in @ ( binunion @ SV373 @ SY819 ) @ ( powerset @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1377,plain,
! [SV374: $i,SV168: $i,SV522: $i] :
( ( ~ ( in @ SV522 @ SV168 )
| ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV374 )
| ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SY1046 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1378,plain,
! [SV375: $i,SV169: $i,SV523: $i] :
( ( ~ ( subset @ SV523 @ SV169 )
| ~ ( subset @ SV523 @ SV375 )
| ( subset @ SV523 @ ( binintersect @ SV169 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1379,plain,
! [SV524: $i,SV376: $i,SV170: $i] :
( ( ! [SY1047: $i] :
( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SY1047 @ emptyset ) ) @ emptyset ) ) )
| ( SV524 != SY1047 )
| ( SV376 = SY1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1380,plain,
! [SV525: $i > $i > $o,SV377: $i,SV171: $i] :
( ( subset
@ ( dpsetconstr @ SV171 @ SV377
@ ^ [SY1048: $i,SY1049: $i] : ( SV525 @ SY1048 @ SY1049 ) )
@ ( cartprod @ SV171 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1381,plain,
! [SV378: $i,SV172: $i,SV526: $i] :
( ( ~ ( in @ SV526 @ ( cartprod @ SV172 @ SV378 ) )
| ( in @ ( kfst @ SV526 ) @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1382,plain,
! [SV379: $i,SV174: $i] :
( ( ( ~ ( subset @ SV174 @ SV379 ) )
= $true )
| ( ( ~ ( subset @ SV379 @ SV174 )
| ( SV174 = SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1383,plain,
! [SV175: $i > $o] :
( ( ( ~ ! [SY447: $i] :
~ ~ ( ~ ( SV175 @ SY447 )
| ~ ! [SY448: $i] :
( ~ ( SV175 @ SY448 )
| ( SY447 = SY448 ) ) ) )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1384,plain,
! [SV380: $i,SV176: $i,SV527: $i] :
( ( ~ ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) )
| ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV176 )
| ( in @ ( kpair @ SY1050 @ ( ap @ SV176 @ SV380 @ SV527 @ SY1050 ) ) @ SV527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1385,plain,
! [SV528: $i > $i > $o,SV381: $i,SV177: $i] :
( ( ! [SY1051: $i,SY1052: $i] :
( ~ ( in @ ( kpair @ SY1051 @ SY1052 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SY1053: $i,SY1054: $i] : ( SV528 @ SY1053 @ SY1054 ) ) )
| ( in @ SY1051 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1386,plain,
! [SV382: $i,SV178: $i] :
( ( ( ~ ~ ~ ! [SY836: $i] :
~ ~ ( ~ ( in @ SY836 @ SV178 )
| ~ ( in @ SY836 @ SV382 ) ) )
= $true )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1387,plain,
! [SV383: $i,SV179: $i,SV529: $i] :
( ( ~ ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
| ! [SY1055: $i > $o] :
( ~ ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV179 )
| ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV383 )
| ~ ( in @ ( kpair @ SY1056 @ SY1057 ) @ SV529 )
| ( SY1055 @ ( kpair @ SY1056 @ SY1057 ) ) ) )
| ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV529 )
| ( SY1055 @ SY1058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1388,plain,
! [SV384: $i,SV182: $i,SV530: $i] :
( ( ~ ~ ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
| ~ ~ ( in @ SV530 @ SV384 )
| ~ ( in @ SV530 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1389,plain,
! [SV385: $i,SV183: $i,SV531: $i] :
( ( ~ ( in @ SV531 @ ( funcSet @ SV183 @ SV385 ) )
| ( func @ SV183 @ SV385 @ SV531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1390,plain,
! [SV184: $i] :
( ( ( singleton @ SV184 )
= $false )
| ( ( in @ ( setunion @ SV184 ) @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1391,plain,
! [SV386: $i,SV185: $i,SV532: $i] :
( ( ~ ( in @ SV532 @ ( setminus @ SV185 @ SV386 ) )
| ( in @ SV532 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1392,plain,
! [SV387: $i,SV186: $i] :
( ( ( SV186 != SV387 )
= $true )
| ( ( in @ SV186 @ ( setadjoin @ SV387 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1393,plain,
! [SV388: $i,SV187: $i,SV533: $i] :
( ( ~ ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
| ~ ! [SY1059: $i] :
~ ~ ( ~ ( in @ SY1059 @ SV187 )
| ~ ~ ! [SY1060: $i] :
~ ~ ( ~ ( in @ SY1060 @ SV388 )
| ( SV533
!= ( kpair @ SY1059 @ SY1060 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1394,plain,
! [SV188: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( powerset @ SV188 ) ) )
= $true )
| ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ ( powerset @ SV188 ) )
| ( in @ ( binintersect @ SV389 @ SY848 ) @ ( powerset @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1395,plain,
! [SV190: $i] :
( ( ( in @ SV190 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1396,plain,
! [SV391: $i,SV191: $i,SV534: $i] :
( ( ~ ( in @ SV534 @ SV191 )
| ~ ~ ( in @ SV534 @ SV391 )
| ~ ( subset @ SV191 @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1397,plain,
! [SV392: $i,SV192: $i,SV535: $i] :
( ( ~ ( in @ SV535 @ SV192 )
| ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV392 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SY1061 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1398,plain,
! [SV536: $i,SV393: $i,SV193: $i] :
( ( ~ ( func @ SV193 @ SV393 @ SV536 )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV193 )
| ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1063: $i] : ( in @ ( kpair @ SY1062 @ SY1063 ) @ SV536 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1399,plain,
! [SV394: $i,SV537: $i,SV194: $i] :
( ( ~ ( subset @ SV194 @ SV537 )
| ( subset @ SV194 @ ( setadjoin @ SV394 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1400,plain,
! [SV395: $i,SV195: $i,SV538: $i] :
( ( ~ ( in @ SV538 @ ( funcSet @ SV195 @ SV395 ) )
| ( ( lam @ SV195 @ SV395
@ ^ [SY1064: $i] : ( ap @ SV195 @ SV395 @ SV538 @ SY1064 ) )
= SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1401,plain,
! [SV196: $i > $o] :
( ( ( ~ ! [SY497: $i] :
~ ( SV196 @ SY497 ) )
= $false )
| ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1402,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY858: $i,SY859: $i] :
( ( SY858 != SY859 )
| ~ ( ~ ( ~ ( SV197 @ SY858 )
| ( SV396 @ SY859 ) )
| ~ ( ~ ( SV396 @ SY859 )
| ( SV197 @ SY858 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1403,plain,
! [SV199: $i,SV398: $i,SV539: $i] :
( ( ~ ( in @ SV539 @ SV398 )
| ~ ( in @ SV539 @ ( setminus @ SV199 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1404,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( setunion @ SV200 ) ) )
= $true )
| ( ( ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ SY868 @ SV200 )
| ~ ( in @ SV399 @ SY868 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1405,plain,
! [SV540: $i > $i > $o,SV400: $i,SV201: $i] :
( ( subset
@ ( dpsetconstr @ SV201 @ SV400
@ ^ [SY1065: $i,SY1066: $i] : ( SV540 @ SY1065 @ SY1066 ) )
@ ( cartprod @ SV201 @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1406,plain,
! [SV401: $i,SV541: $i > $i,SV202: $i] :
( ( ~ ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV202 )
| ( in @ ( SV541 @ SY1067 ) @ SV401 ) )
| ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1407,plain,
! [SV542: $i,SV402: $i,SV203: $i] :
( ( ! [SY1070: $i] :
( ( ( kpair @ SV203 @ SV402 )
!= ( kpair @ SV542 @ SY1070 ) )
| ( SV203 = SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1408,plain,
! [SV403: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ ( setadjoin @ SV403 @ emptyset ) ) )
= $true )
| ( ( SV204 = SV403 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1409,plain,
! [SV404: $i,SV205: $i,SV543: $i] :
( ( ~ ( in @ SV543 @ SV205 )
| ~ ~ ( in @ SV543 @ SV404 )
| ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1410,plain,
! [SV544: $i,SV405: $i,SV206: $i] :
( ( ~ ( subset @ SV206 @ SV405 )
| ~ ( subset @ SV405 @ SV544 )
| ( subset @ SV206 @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1411,plain,
! [SV406: $i,SV207: $i,SV545: $i] :
( ( ~ ( in @ SV545 @ ( setadjoin @ SV207 @ ( setadjoin @ SV406 @ emptyset ) ) )
| ( SV545 = SV207 )
| ( SV545 = SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1412,plain,
! [SV407: $i,SV210: $i] :
( ( ( ~ ( ( SV210 != SV407 ) ) )
= $true )
| ( ( ~ ( in @ SV407 @ ( setadjoin @ SV210 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1413,plain,
! [SV408: $i,SV211: $i,SV546: $i] :
( ( ~ ( in @ SV546 @ ( cartprod @ SV211 @ SV408 ) )
| ( ( kpair @ ( kfst @ SV546 ) @ ( ksnd @ SV546 ) )
= SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1414,plain,
! [SV409: $i,SV212: $i] :
( ( ( ~ ( subset @ SV212 @ SV409 ) )
= $true )
| ( ( ( setminus @ SV212 @ SV409 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1415,plain,
! [SV410: $i,SV213: $i,SV547: $i] :
( ( ~ ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
| ! [SY1071: $i > $o] :
( ~ ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV213 )
| ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV410 )
| ~ ( in @ ( kpair @ SY1072 @ SY1073 ) @ SV547 )
| ( SY1071 @ ( kpair @ SY1072 @ SY1073 ) ) ) )
| ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV547 )
| ( SY1071 @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1416,plain,
! [SV214: $i,SV411: $i,SV548: $i] :
( ( ~ ( in @ SV548 @ SV411 )
| ( in @ SV548 @ ( binunion @ SV214 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1417,plain,
! [SV215: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ ( powerset @ SV215 ) ) )
= $true )
| ( ( in @ ( setminus @ SV215 @ SV412 ) @ ( powerset @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1418,plain,
! [SV216: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ ( powerset @ SV216 ) ) )
= $true )
| ( ( ! [SY888: $i] :
( ~ ( in @ SY888 @ SV216 )
| ~ ( in @ SY888 @ SV413 )
| ~ ( in @ SY888 @ ( setminus @ SV216 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1419,plain,
! [SV415: $i,SV218: $i] :
( ( ( SV218 != SV415 )
= $true )
| ( ( ! [SY889: $i > $o,SY890: $i > $o] :
( ~ ! [SY891: $i] :
( ~ ( in @ SY891 @ SV218 )
| ! [SY892: $i] :
( ~ ( in @ SY892 @ SV415 )
| ( SY891 != SY892 )
| ~ ( ~ ( ~ ( SY889 @ SY891 )
| ( SY890 @ SY892 ) )
| ~ ( ~ ( SY890 @ SY892 )
| ( SY889 @ SY891 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SX4: $i] : ( SY889 @ SX4 ) )
= ( dsetconstr @ SV415
@ ^ [SX4: $i] : ( SY890 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1420,plain,
! [SV220: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ SV220 ) )
= $true )
| ( ( in @ SV417 @ ( powerset @ ( setunion @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1421,plain,
! [SV222: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ ( powerset @ SV222 ) ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ ( powerset @ SV222 ) )
| ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV222 )
| ~ ( in @ SY896 @ SV419 )
| ( in @ SY896 @ SY895 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV222 )
| ~ ( in @ SY897 @ SY895 )
| ( in @ SY897 @ SV419 ) )
| ( SV419 = SY895 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1422,plain,
! [SV223: $i,SV420: $i] :
( ( ( ~ ( subset @ SV420 @ SV223 ) )
= $true )
| ( ( in @ SV420 @ ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1423,plain,
! [SV421: $i > $o,SV224: $i] :
( ( ( ~ ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV224 )
| ( SV421 @ SY898 ) ) )
= $true )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1424,plain,
! [SV422: $i > $o,SV225: $i,SV549: $i] :
( ( ~ ( in @ SV549 @ SV225 )
| ~ ( SV422 @ SV549 )
| ( in @ SV549
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1425,plain,
! [SV226: $i,SV550: $i,SV423: $i] :
( ( ~ ( in @ SV423 @ SV550 )
| ~ ( in @ SV550 @ SV226 )
| ( in @ SV423 @ ( setunion @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1426,plain,
! [SV424: $i,SV227: $i,SV551: $i] :
( ( ~ ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
| ! [SY1076: $i] :
( ~ ( subset @ SY1076 @ ( cartprod @ SV227 @ SV424 ) )
| ~ ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV227 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV424 )
| ~ ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV551 )
| ( in @ ( kpair @ SY1077 @ SY1078 ) @ SY1076 ) ) )
| ( subset @ SV551 @ SY1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1427,plain,
! [SV228: $i] :
( ( ( in @ SV228 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1428,plain,
! [SV425: $i,SV229: $i,SV552: $i] :
( ( ~ ~ ( in @ SV552 @ SV229 )
| ~ ( in @ SV552 @ ( setminus @ SV229 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1429,plain,
! [SV426: $i,SV230: $i,SV553: $i] :
( ( ! [SY1079: $i] :
( ~ ( in @ ( kpair @ SV553 @ SY1079 ) @ ( cartprod @ SV230 @ SV426 ) )
| ( in @ SV553 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1430,plain,
! [SV427: $i > $o,SV231: $i] :
( ( ( ~ ~ ! [SY910: $i] :
~ ~ ( ~ ( in @ SY910 @ SV231 )
| ~ ( SV427 @ SY910 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1431,plain,
! [SV232: $i] :
( ( ( subset @ SV232 @ emptyset )
= $false )
| ( ( SV232 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1432,plain,
! [SV233: $i > $o,SV1: $i,SV428: $i] :
( ( ( ~ ( in @ SV428 @ SV1 ) )
= $true )
| ( ( ~ ( SV233 @ SV428 )
| ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1433,plain,
! [SV234: $i,SV2: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ SV2 ) )
= $true )
| ( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV234 )
| ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SY913 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1434,plain,
! [SV235: $i,SV430: $i > $i,SV3: $i] :
( ( ( ~ ! [SY914: $i] :
( ~ ( in @ SY914 @ SV3 )
| ( in @ ( SV430 @ SY914 ) @ SV235 ) ) )
= $true )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1435,plain,
! [SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY596: $i] :
( ~ ( in @ SY596 @ SV236 )
| ~ ! [SY16: $i] :
~ ~ ( ~ ( SV4 @ SY596 @ SY16 )
| ~ ! [SY17: $i] :
( ~ ( SV4 @ SY596 @ SY17 )
| ( SY16 = SY17 ) ) ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1436,plain,
! [SV431: $i,SV237: $i,SV5: $i] :
( ( ( ~ ( func @ SV5 @ SV237 @ SV431 ) )
= $true )
| ( ( ! [SY917: $i] :
( ~ ( in @ SY917 @ SV5 )
| ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SY917 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1437,plain,
! [SV432: $i > $i > $o,SV238: $i,SV6: $i,SV554: $i] :
( ( ! [SY1080: $i] :
( ~ ( in @ ( kpair @ SV554 @ SY1080 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SY920: $i,SY921: $i] : ( SV432 @ SY920 @ SY921 ) ) )
| ( SV432 @ SV554 @ SY1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1438,plain,
! [SV8: $i,SV239: $i] :
( ( ( in @ SV239 @ ( powerset @ SV8 ) )
= $false )
| ( ( ! [SY610: $i] :
( ~ ( in @ SY610 @ ( powerset @ SV8 ) )
| ( in @ ( setminus @ SV239 @ SY610 ) @ ( powerset @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1439,plain,
! [SV433: $i,SV240: $i,SV9: $i] :
( ( ( ~ ( func @ SV9 @ SV240 @ SV433 ) )
= $true )
| ( ( ( lam @ SV9 @ SV240
@ ^ [SY922: $i] : ( ap @ SV9 @ SV240 @ SV433 @ SY922 ) )
= SV433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1440,plain,
! [SV241: $i,SV10: $i] :
( ( ( SV10 = SV241 )
= $false )
| ( ( ( powerset @ SV10 )
= ( powerset @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1441,plain,
! [SV242: $i,SV434: $i > $i,SV11: $i] :
( ( ( ~ ! [SY923: $i] :
( ~ ( in @ SY923 @ SV11 )
| ( in @ ( SV434 @ SY923 ) @ SV242 ) ) )
= $true )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1442,plain,
! [SV243: $i,SV12: $i] :
( ( ( SV12 = SV243 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV243 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1443,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( sK5_SY42 @ SV13 ) @ SV13 ) )
= $false )
| ( ( SV13 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1215]) ).
thf(1444,plain,
! [SV244: $o,SV14: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ SV14 ) )
= $true )
| ( ( ! [SY925: $i] :
( ~ ( in @ SY925 @ SV14 )
| ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY926: $i] :
( ~ ( ~ SV244
| ( SY926 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY926 != SY925 ) ) ) )
= ( setadjoin @ SY925 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1445,plain,
! [SV14: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV14 ) )
= $true )
| ( ( ! [SY927: $i] :
( ~ ( in @ SY927 @ SV14 )
| ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY928: $i] :
( ~ ( ~ $true
| ( SY928 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY928 != SY927 ) ) ) )
= ( setadjoin @ SY927 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1446,plain,
! [SV14: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV14 ) )
= $true )
| ( ( ! [SY929: $i] :
( ~ ( in @ SY929 @ SV14 )
| ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY930: $i] :
( ~ ( ~ $false
| ( SY930 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY930 != SY929 ) ) ) )
= ( setadjoin @ SY929 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1447,plain,
! [SV16: $i > $o] :
( ( ( ! [SY47: $i] :
~ ~ ( ~ ( SV16 @ SY47 )
| ~ ! [SY48: $i] :
( ~ ( SV16 @ SY48 )
| ( SY47 = SY48 ) ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1448,plain,
! [SV438: $i,SV245: $i,SV17: $i] :
( ( ( ~ ( func @ SV17 @ SV245 @ SV438 ) )
= $true )
| ( ( ! [SY931: $i] :
( ~ ( in @ SY931 @ SV17 )
| ( ( ap @ SV17 @ SV245 @ SV438 @ SY931 )
= ( ap @ SV17 @ SV245 @ SV438 @ SY931 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1449,plain,
! [SV18: $i] :
( ( ( ! [SY54: $i] :
~ ( in @ SY54 @ SV18 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1450,plain,
! [SV19: $i,SV555: $i] :
( ( ( ~ ( in @ SV555 @ SV19 )
| ( ( setunion @ SV19 )
= SV555 ) )
= $true )
| ( ( singleton @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1451,plain,
! [SV246: $i > $o,SV20: $i] :
( ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false )
| ( ( ! [SY622: $i] :
( ~ ( in @ SY622 @ SV20 )
| ! [SY623: $i] :
( ~ ( in @ SY623 @ SV20 )
| ~ ( SV246 @ SY622 )
| ~ ( SV246 @ SY623 )
| ( SY622 = SY623 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1452,plain,
! [SV247: $i,SV22: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV22 ) )
= $true )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ SV247 )
| ( ( kpair @ SV439 @ SY932 )
= ( kpair @ SV439 @ SY932 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1453,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
| ~ ! [SY942: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY942 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY942 ) )
| ~ ! [SY945: $i] :
~ ~ ! [SY946: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY945 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY946 @ SY942 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY945 )
| ~ ( in @ SX5 @ SY942 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY945 ) )
| ( in @ SY946 @ SY948 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1454,plain,
! [SV24: $i,SV248: $i] :
( ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false )
| ( ( ! [SY626: $o] :
( ~ ! [SY627: $i] :
( ~ ( in @ SV248 @ SY627 )
| ~ ( in @ SY627 @ SV24 )
| SY626 )
| SY626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1455,plain,
! [SV249: $i,SV26: $i] :
( ( ( SV26 = SV249 )
= $false )
| ( ( subset @ SV249 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1456,plain,
! [SV27: $i > $o] :
( ( ( ! [SY87: $i] :
~ ~ ( ~ ( SV27 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV27 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1457,plain,
! [SV250: $i,SV28: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ ( setadjoin @ SV28 @ SV250 ) ) )
= $true )
| ( ( ( SV440 = SV28 )
| ( in @ SV440 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1458,plain,
! [SV251: $i,SV29: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) ) )
= $true )
| ( ( ! [SY950: $i] :
( ~ ( in @ SY950 @ SV29 )
| ( ( ap @ SV29 @ SV251 @ SV441 @ SY950 )
= ( ap @ SV29 @ SV251 @ SV441 @ SY950 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1459,plain,
! [SV252: $i > $o,SV30: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV30 ) )
= $true )
| ( ( ~ ( SV252 @ SV442 )
| ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1460,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ( ~ ( in @ SV254 @ ( setunion @ SV33 ) )
| ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1461,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ( ~ ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) )
| ( in @ SV254 @ ( setunion @ SV33 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1462,plain,
! [SV255: $i,SV34: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV34 ) )
= $true )
| ( ( ~ ( in @ SV443 @ SV255 )
| ~ ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1463,plain,
! [SV256: $i,SV35: $i] :
( ( ( SV35 = SV256 )
= $false )
| ( ( ( setadjoin @ SV35 @ ( setadjoin @ SV256 @ emptyset ) )
= ( setadjoin @ SV35 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1464,plain,
! [SV36: $i] :
( ( ( ! [SY106: $i] :
~ ( in @ SY106 @ SV36 ) )
= $true )
| ( ( SV36 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1465,plain,
! [SV257: $i,SV37: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV37 ) )
= $true )
| ( ( ! [SY953: $i] :
( ~ ( in @ SY953 @ SV257 )
| ( ( kfst @ ( kpair @ SV444 @ SY953 ) )
= SV444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1466,plain,
! [SV258: $i,SV38: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV38 ) )
= $true )
| ( ( ~ ~ ( in @ SV445 @ SV258 )
| ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1467,plain,
! [SV259: $i,SV39: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV39 ) )
= $true )
| ( ( ~ ~ ( in @ SV446 @ SV259 )
| ( SV39 != SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1468,plain,
! [SV260: $i,SV40: $i] :
( ( ( ( setminus @ SV40 @ SV260 )
= emptyset )
= $false )
| ( ( subset @ SV40 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1469,plain,
! [SV261: $i,SV41: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( setadjoin @ SV41 @ ( setadjoin @ SV261 @ emptyset ) ) ) )
= $true )
| ( ( ( SV447 = SV41 )
| ( SV447 = SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1470,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY642: $i,SY643: $i] :
( ( SY642 != SY643 )
| ~ ( ~ ( ~ ( SV42 @ SY642 )
| ( SV262 @ SY643 ) )
| ~ ( ~ ( SV262 @ SY643 )
| ( SV42 @ SY642 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1471,plain,
! [SV448: $i,SV263: $i,SV43: $i] :
( ( ( ~ ( subset @ SV43 @ SV263 ) )
= $true )
| ( ( ~ ~ ( in @ SV448 @ SV263 )
| ~ ( in @ SV448 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1472,plain,
! [SV449: $i,SV264: $i,SV44: $i] :
( ( ( ~ ( func @ SV44 @ SV264 @ SV449 ) )
= $true )
| ( ( ! [SY954: $i] :
( ~ ( in @ SY954 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY955: $i] : ( in @ ( kpair @ SY954 @ SY955 ) @ SV449 ) ) )
@ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1473,plain,
! [SV265: $i,SV45: $i,SV450: $i] :
( ( ( ~ ~ ( in @ SV450 @ SV45 ) )
= $true )
| ( ( ~ ~ ( in @ SV450 @ SV265 )
| ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1474,plain,
! [SV47: $i,SV267: $i] :
( ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV267 )
| ( in @ SY657 @ SV47 ) ) )
= $false )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1475,plain,
! [SV268: $i > $o,SV48: $i] :
( ( ( ~ ! [SY658: $i] :
~ ~ ( ~ ( in @ SY658 @ SV48 )
| ~ ~ ( SV268 @ SY658 ) ) )
= $false )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1476,plain,
! [SV269: $i,SV451: $i > $i,SV49: $i] :
( ( ( ~ ! [SY956: $i] :
( ~ ( in @ SY956 @ SV49 )
| ( in @ ( SV451 @ SY956 ) @ SV269 ) ) )
= $true )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1477,plain,
! [SV452: $i,SV270: $i,SV50: $i] :
( ( ( ~ ( func @ SV50 @ SV270 @ SV452 ) )
= $true )
| ( ( in @ SV452 @ ( funcSet @ SV50 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1478,plain,
! [SV51: $i > $o] :
( ( ( ! [SY149: $i] :
~ ~ ( ~ ( SV51 @ SY149 )
| ~ ! [SY150: $i] :
( ~ ( SV51 @ SY150 )
| ( SY149 = SY150 ) ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1251]) ).
thf(1479,plain,
! [SV556: $o,SV272: $i,SV53: $i,SV453: $i] :
( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
| ~ ( ~ ( in @ SV453 @ SV53 )
| SV556 )
| ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1252]) ).
thf(1480,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
| ~ ( ~ ( in @ SV453 @ SV53 )
| $true )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1252]) ).
thf(1481,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
| ~ ( ~ ( in @ SV453 @ SV53 )
| $false )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1252]) ).
thf(1482,plain,
! [SV273: $i,SV54: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( setminus @ SV54 @ SV273 ) ) )
= $true )
| ( ( ~ ( in @ SV454 @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1483,plain,
! [SV455: $i,SV274: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV274 ) )
= $true )
| ( ( ~ ( in @ SV455 @ SV55 )
| ( in @ SV455 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1484,plain,
! [SV275: $i,SV56: $i] :
( ( ( SV56 = SV275 )
= $false )
| ( ( ! [SY669: $i,SY670: $i] :
( ( SY669 != SY670 )
| ( ( setadjoin @ SV56 @ SY669 )
= ( setadjoin @ SV275 @ SY670 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1485,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) ) )
= $true )
| ( ( ! [SY960: $o] :
( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SY960 )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SY960 )
| SY960 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1486,plain,
! [SV278: $i,SV59: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ ( cartprod @ SV59 @ SV278 ) ) )
= $true )
| ( ( iskpair @ SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1487,plain,
! [SV279: $i,SV60: $i] :
( ( ( ( binintersect @ SV60 @ SV279 )
= SV279 )
= $false )
| ( ( subset @ SV279 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1488,plain,
! [SV280: $i,SV61: $i] :
( ( ( ! [SY674: $i] :
( ~ ( in @ SY674 @ SV61 )
| ( in @ SY674 @ SV280 ) ) )
= $false )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1489,plain,
! [SV281: $o,SV62: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV62 ) )
= $true )
| ( ( ! [SY961: $i] :
( ~ ( in @ SY961 @ SV62 )
| ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SY961 )
= SV458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1490,plain,
! [SV62: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV62 ) )
= $true )
| ( ( ! [SY962: $i] :
( ~ ( in @ SY962 @ SV62 )
| ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SY962 )
= SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1491,plain,
! [SV62: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ SV62 ) )
= $true )
| ( ( ! [SY963: $i] :
( ~ ( in @ SY963 @ SV62 )
| ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SY963 )
= SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1492,plain,
! [SV462: $i,SV283: $i,SV64: $i] :
( ( ( ( setadjoin @ SV64 @ ( setadjoin @ SV283 @ emptyset ) )
!= ( setadjoin @ SV462 @ emptyset ) )
= $true )
| ( ( SV64 = SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1493,plain,
! [SV284: $i,SV65: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ SV65 ) )
= $true )
| ( ( in @ ( setadjoin @ SV463 @ emptyset ) @ ( powerset @ ( binunion @ SV65 @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1494,plain,
! [SV285: $i,SV66: $i] :
( ( ( ~ ( subset @ SV66 @ SV285 ) )
= $false )
| ( ( SV66 != SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1495,plain,
! [SV286: $o,SV67: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ SV67 ) )
= $true )
| ( ( ! [SY964: $i] :
( ~ ( in @ SY964 @ SV67 )
| ~ ~ SV286
| ( in @ SY964
@ ( dsetconstr @ SV67
@ ^ [SY965: $i] :
( ~ ( ~ SV286
| ( SY965 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY965 != SY964 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1496,plain,
! [SV67: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV67 ) )
= $true )
| ( ( ! [SY966: $i] :
( ~ ( in @ SY966 @ SV67 )
| ~ ~ $true
| ( in @ SY966
@ ( dsetconstr @ SV67
@ ^ [SY967: $i] :
( ~ ( ~ $true
| ( SY967 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY967 != SY966 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1497,plain,
! [SV67: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV67 ) )
= $true )
| ( ( ! [SY968: $i] :
( ~ ( in @ SY968 @ SV67 )
| ~ ~ $false
| ( in @ SY968
@ ( dsetconstr @ SV67
@ ^ [SY969: $i] :
( ~ ( ~ $false
| ( SY969 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY969 != SY968 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1498,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ! [SY684: $i] :
( ~ ( in @ SY684 @ SV68 )
| ~ ( SV287 @ SY684 ) ) )
= $false )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1499,plain,
! [SV288: $i > $o,SV69: $i] :
( ( ( ~ ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV69 )
| ~ ( SV288 @ SY686 ) ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1500,plain,
! [SV467: $i,SV70: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ ( powerset @ SV70 ) ) )
= $true )
| ( ( ~ ( in @ SV467 @ SV289 )
| ( in @ SV467 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1501,plain,
! [SV290: $i,SV71: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV71 ) )
= $true )
| ( ( in @ SV468 @ ( binunion @ SV71 @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1502,plain,
! [SV291: $i,SV73: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV73 ) )
= $true )
| ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ SV291 )
| ( ( ksnd @ ( kpair @ SV469 @ SY970 ) )
= SY970 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1503,plain,
! [SV292: $i,SV74: $i] :
( ( ( SV74 = SV292 )
= $false )
| ( ( ! [SY692: $i,SY693: $i] :
( ( SY692 != SY693 )
| ~ ( ~ ( ~ ( in @ SY692 @ SV74 )
| ( in @ SY693 @ SV292 ) )
| ~ ( ~ ( in @ SY693 @ SV292 )
| ( in @ SY692 @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1504,plain,
! [SV293: $i,SV470: $i > $i,SV75: $i] :
( ( ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SV75 )
| ( in @ ( SV470 @ SY971 ) @ SV293 ) ) )
= $true )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1505,plain,
! [SV294: $i > $o,SV76: $i] :
( ( ( ~ ! [SY697: $i] :
( ~ ( in @ SY697 @ SV76 )
| ( SV294 @ SY697 ) ) )
= $false )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1506,plain,
! [SV471: $i,SV295: $i,SV77: $i] :
( ( ( ~ ( func @ SV77 @ SV295 @ SV471 ) )
= $true )
| ( ( ! [SY973: $i] :
( ~ ( func @ SV77 @ SV295 @ SY973 )
| ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY974 )
= ( ap @ SV77 @ SV295 @ SY973 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV77 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV295 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SY973 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV471 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1507,plain,
! [SV296: $i,SV78: $i,SV472: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV296 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV78 = SV472 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1508,plain,
! [SV79: $i,SV297: $i] :
( ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false )
| ( ( ! [SY705: $i] :
( ~ ( in @ SY705 @ ( powerset @ SV79 ) )
| ! [SY706: $i] :
( ~ ( in @ SY706 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SY705 ) )
| ~ ( in @ SY706 @ SV297 )
| ( in @ SY706 @ SY705 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1509,plain,
! [SV80: $i > $o] :
( ( ( ! [SY222: $i] :
~ ~ ( ~ ( SV80 @ SY222 )
| ~ ! [SY223: $i] :
( ~ ( SV80 @ SY223 )
| ( SY222 = SY223 ) ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1510,plain,
! [SV81: $i,SV298: $i] :
( ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false )
| ( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ ( powerset @ SV81 ) )
| ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV81 )
| ~ ( in @ SY708 @ SV298 )
| ( in @ SY708 @ SY707 ) )
| ( in @ SV298 @ ( powerset @ SY707 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1511,plain,
! [SV299: $i,SV82: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) ) )
= $true )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ ( funcSet @ SV82 @ SV299 ) )
| ~ ! [SY978: $i] :
( ~ ( in @ SY978 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY978 )
= ( ap @ SV82 @ SV299 @ SY977 @ SY978 ) ) )
| ( SV473 = SY977 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1512,plain,
! [SV83: $i] :
( ( ( ~ ( in @ ( sK6_SY233 @ SV83 ) @ SV83 ) )
= $false )
| ( ( SV83 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1284]) ).
thf(1513,plain,
! [SV300: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
= ( setadjoin @ SV300 @ emptyset ) )
= $false )
| ( ( SV84 = SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1514,plain,
! [SV301: $i,SV85: $i,SV474: $i] :
( ( ( ~ ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) ) )
= $true )
| ( ( ! [SY979: $i] :
( ~ ( subset @ SY979 @ ( cartprod @ SV85 @ SV301 ) )
| ~ ! [SY980: $i] :
( ~ ( in @ SY980 @ SV85 )
| ! [SY981: $i] :
( ~ ( in @ SY981 @ SV301 )
| ~ ( in @ ( kpair @ SY980 @ SY981 ) @ SV474 )
| ( in @ ( kpair @ SY980 @ SY981 ) @ SY979 ) ) )
| ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV85 )
| ! [SY983: $i] :
( ~ ( in @ SY983 @ SV301 )
| ~ ( in @ ( kpair @ SY982 @ SY983 ) @ SY979 )
| ( in @ ( kpair @ SY982 @ SY983 ) @ SV474 ) ) )
| ( SV474 = SY979 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1515,plain,
! [SV302: $o,SV86: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV86 ) )
= $true )
| ( ( ! [SY984: $i] :
( ~ ( in @ SY984 @ SV86 )
| ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY985: $i] :
( ~ ( ~ SV302
| ( SY985 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY985 != SY984 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1516,plain,
! [SV86: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ SV86 ) )
= $true )
| ( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ SV86 )
| ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY987: $i] :
( ~ ( ~ $true
| ( SY987 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY987 != SY986 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1517,plain,
! [SV86: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV86 ) )
= $true )
| ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV86 )
| ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY989: $i] :
( ~ ( ~ $false
| ( SY989 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY989 != SY988 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1518,plain,
! [SV303: $i > $o,SV87: $i,SV478: $i] :
( ( ( ~ ( in @ SV478
@ ( dsetconstr @ SV87
@ ^ [SY722: $i] : ( SV303 @ SY722 ) ) ) )
= $true )
| ( ( SV303 @ SV478 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1519,plain,
! [SV557: $i,SV479: $i,SV304: $i,SV88: $i] :
( ( ( ( kpair @ SV88 @ SV304 )
!= ( kpair @ SV479 @ SV557 ) )
| ( SV304 = SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1520,plain,
! [SV89: $i] :
( ( ( SV89 = emptyset )
= $true )
| ( ( ~ ! [SY252: $i] :
~ ~ ( ~ ( in @ SY252 @ SV89 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1521,plain,
! [SV480: $i > $i > $o,SV305: $i,SV90: $i,SV558: $i] :
( ( ~ ( in @ SV558 @ SV90 )
| ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV305 )
| ~ ( SV480 @ SV558 @ SY1083 )
| ( in @ ( kpair @ SV558 @ SY1083 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1522,plain,
! [SV91: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV91 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV91 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1523,plain,
! [SV306: $i,SV92: $i] :
( ( ( ! [SY730: $i] :
( ~ ( in @ SY730 @ SV92 )
| ( in @ SY730 @ SV306 ) ) )
= $false )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1524,plain,
! [SV307: $i,SV93: $i] :
( ( ( subset @ SV93 @ SV307 )
= $false )
| ( ( subset @ ( powerset @ SV93 ) @ ( powerset @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1525,plain,
! [SV308: $i > $o,SV95: $i] :
( ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false )
| ( ( ~ ! [SY732: $i] :
~ ~ ( ~ ( in @ SY732 @ SV95 )
| ~ ( SV308 @ SY732 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1526,plain,
! [SV309: $i > $o,SV96: $i] :
( ( ( ~ ~ ! [SY733: $i] :
~ ~ ( ~ ( in @ SY733 @ SV96 )
| ~ ( SV309 @ SY733 ) ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1527,plain,
! [SV311: $i,SV98: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV98 ) )
= $true )
| ( ( ! [SY996: $i] :
( ~ ( in @ SY996 @ SV311 )
| ( in @ ( kpair @ SV481 @ SY996 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1528,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ( ~ ( in @ SV312 @ ( powerset @ SV99 ) )
| ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1529,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) )
| ( in @ SV312 @ ( powerset @ SV99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1530,plain,
! [SV313: $i,SV100: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ ( binintersect @ SV100 @ SV313 ) ) )
= $true )
| ( ( in @ SV482 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1531,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( ~ ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
| ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ~ ( ~ ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1532,plain,
! [SV315: $i,SV102: $i] :
( ( ( in @ SV102 @ ( setadjoin @ SV315 @ emptyset ) )
= $false )
| ( ( in @ SV315 @ ( setadjoin @ SV102 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1533,plain,
! [SV103: $i > $o,SV316: $i] :
( ( ( in @ SV316 @ emptyset )
= $false )
| ( ( SV103 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1534,plain,
! [SV317: $i,SV104: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ SV104 ) )
= $true )
| ( ( ! [SY997: $i] :
( ~ ( in @ SY997 @ SV317 )
| ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SY997 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1535,plain,
! [SV318: $i,SV105: $i] :
( ( ( SV105 = SV318 )
= $false )
| ( ( ! [SY743: $i,SY744: $i] :
( ( SY743 != SY744 )
| ~ ( in @ SY743 @ SV105 )
| ( in @ SY744 @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1536,plain,
! [SV320: $i,SV107: $i] :
( ( ( SV107 = SV320 )
= $false )
| ( ( subset @ SV107 @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1537,plain,
! [SV485: $i,SV321: $i,SV108: $i] :
( ( ( ~ ( func @ SV108 @ SV321 @ SV485 ) )
= $true )
| ( ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV108 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV321 )
| ~ ( in @ ( kpair @ SY998 @ SY999 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SY998 )
= SY999 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1538,plain,
( ( ~ ( in @ sK3_SY2 @ sK1_A )
| ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1539,plain,
! [SV322: $i,SV109: $i] :
( ( ( ! [SY748: $i] :
~ ( ~ ( ~ ( in @ SY748 @ SV109 )
| ( in @ SY748 @ SV322 ) )
| ~ ( ~ ( in @ SY748 @ SV322 )
| ( in @ SY748 @ SV109 ) ) ) )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1540,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ SV112 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) )
| ~ ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1541,plain,
! [SV325: $o,SV113: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ SV113 ) )
= $true )
| ( ( ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV113 )
| ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1003: $i] :
( ~ ( ~ SV325
| ( SY1003 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1003 != SY1002 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1542,plain,
! [SV113: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV113 ) )
= $true )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV113 )
| ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1005: $i] :
( ~ ( ~ $true
| ( SY1005 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1005 != SY1004 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1543,plain,
! [SV113: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ SV113 ) )
= $true )
| ( ( ! [SY1006: $i] :
( ~ ( in @ SY1006 @ SV113 )
| ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1007: $i] :
( ~ ( ~ $false
| ( SY1007 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1007 != SY1006 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1544,plain,
! [SV114: $i] :
( ( ( SV114 = emptyset )
= $true )
| ( ( ~ ! [SY310: $i] :
~ ( in @ SY310 @ SV114 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1545,plain,
! [SV326: $i,SV115: $i,SV559: $i,SV490: $i] :
( ( ~ ( in @ ( kpair @ SV490 @ SV559 ) @ ( cartprod @ SV115 @ SV326 ) )
| ( in @ SV559 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1546,plain,
! [SV327: $i > $o,SV116: $i,SV491: $i] :
( ( ( ~ ( in @ SV491
@ ( dsetconstr @ SV116
@ ^ [SY758: $i] : ( SV327 @ SY758 ) ) ) )
= $true )
| ( ( in @ SV491 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1547,plain,
! [SV118: $i,SV328: $i] :
( ( ( in @ SV328 @ SV118 )
= $false )
| ( ( subset @ ( setadjoin @ SV328 @ emptyset ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1548,plain,
! [SV119: $i,SV329: $i] :
( ( ( subset @ SV329 @ SV119 )
= $false )
| ( ( ( binintersect @ SV119 @ SV329 )
= SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1549,plain,
! [SV120: $i,SV330: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV330 ) )
= $true )
| ( ( in @ SV492 @ ( setadjoin @ SV120 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1550,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY760: $i] :
( ~ ( in @ SY760 @ SV121 )
| ! [SY761: $i] :
( ~ ( in @ SY761 @ SV121 )
| ~ ( SV331 @ SY760 )
| ~ ( SV331 @ SY761 )
| ( SY760 = SY761 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1551,plain,
! [SV332: $o,SV122: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ SV122 ) )
= $true )
| ( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV122 )
| ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SY1010 )
= SY1010 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1552,plain,
! [SV122: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV122 ) )
= $true )
| ( ( ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV122 )
| ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SY1011 )
= SY1011 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1326]) ).
thf(1553,plain,
! [SV122: $i,SV495: $i] :
( ( ( ~ ( in @ SV495 @ SV122 ) )
= $true )
| ( ( ! [SY1012: $i] :
( ~ ( in @ SY1012 @ SV122 )
| ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SY1012 )
= SY1012 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1554,plain,
! [SV333: $i,SV496: $i > $i,SV123: $i] :
( ( ( ~ ! [SY1013: $i] :
( ~ ( in @ SY1013 @ SV123 )
| ( in @ ( SV496 @ SY1013 ) @ SV333 ) ) )
= $true )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1555,plain,
! [SV124: $o,SV334: $i] :
( ( ( in @ SV334 @ ( prop2set @ SV124 ) )
= $false )
| ( SV124 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1556,plain,
! [SV335: $i] :
( ( ( in @ SV335 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1557,plain,
! [SV336: $i] :
( ( ( in @ SV336 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1558,plain,
! [SV337: $o,SV125: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV125 ) )
= $true )
| ( ( ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV125 )
| ( in @ ( if @ SV125 @ SV337 @ SV497 @ SY1016 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SY1016 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1559,plain,
! [SV125: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV125 ) )
= $true )
| ( ( ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV125 )
| ( in @ ( if @ SV125 @ $true @ SV498 @ SY1017 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SY1017 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1560,plain,
! [SV125: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ SV125 ) )
= $true )
| ( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ SV125 )
| ( in @ ( if @ SV125 @ $false @ SV499 @ SY1018 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SY1018 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1561,plain,
! [SV338: $i,SV126: $i] :
( ( ( subset @ SV126 @ SV338 )
= $false )
| ( ( ( binintersect @ SV126 @ SV338 )
= SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1562,plain,
! [SV341: $i,SV129: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV129 ) )
= $true )
| ( ( ~ ( in @ SV500 @ SV341 )
| ( in @ SV500 @ ( binintersect @ SV129 @ SV341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1563,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i,SV560: $i] :
( ( ~ ( in @ SV560 @ SV130 )
| ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV342 )
| ~ ( in @ ( kpair @ SV560 @ SY1086 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SY1086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1564,plain,
! [SV343: $i,SV131: $i] :
( ( ( ( binintersect @ SV131 @ SV343 )
= SV131 )
= $false )
| ( ( subset @ SV131 @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1565,plain,
! [SV345: $o,SV133: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV133 ) )
= $true )
| ( ( ! [SY1023: $i] :
( ~ ( in @ SY1023 @ SV133 )
| ( in @ ( if @ SV133 @ SV345 @ SV502 @ SY1023 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1566,plain,
! [SV133: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV133 ) )
= $true )
| ( ( ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV133 )
| ( in @ ( if @ SV133 @ $true @ SV503 @ SY1024 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1567,plain,
! [SV133: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV133 ) )
= $true )
| ( ( ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV133 )
| ( in @ ( if @ SV133 @ $false @ SV504 @ SY1025 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1568,plain,
! [SV134: $i,SV346: $i] :
( ( ( in @ SV346 @ ( powerset @ SV134 ) )
= $false )
| ( ( subset @ SV346 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1569,plain,
! [SV347: $i,SV135: $i,SV505: $i] :
( ( ( ~ ~ ( in @ SV505 @ SV135 ) )
= $true )
| ( ( ~ ( in @ SV505 @ SV347 )
| ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1570,plain,
! [SV561: $i,SV506: $i,SV349: $i,SV137: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SV349 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV561 @ emptyset ) ) @ emptyset ) ) )
| ( SV349 = SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1571,plain,
! [SV562: $i,SV507: $i,SV350: $i,SV138: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV507 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV507 @ ( setadjoin @ SV562 @ emptyset ) ) @ emptyset ) ) )
| ( SV138 = SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1572,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY786: $i] :
( ~ ( in @ SY786 @ SV139 )
| ! [SY787: $i] :
( ~ ( in @ SY787 @ SV139 )
| ~ ( SV351 @ SY786 )
| ~ ( SV351 @ SY787 )
| ( SY786 = SY787 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1573,plain,
! [SV141: $i,SV353: $i] :
( ( ( in @ SV353 @ SV141 )
= $false )
| ( ( in @ ( setadjoin @ SV353 @ emptyset ) @ ( powerset @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1574,plain,
! [SV354: $i,SV142: $i] :
( ( ( subset @ SV142 @ SV354 )
= $false )
| ( ( in @ SV142 @ ( powerset @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1575,plain,
! [SV355: $i,SV143: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV143 ) )
= $true )
| ( ( ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SV355 )
| ( in @ ( kpair @ SV508 @ SY1028 ) @ ( cartprod @ SV143 @ SV355 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1576,plain,
! [SV144: $i,SV356: $i] :
( ( ( in @ SV356 @ ( powerset @ SV144 ) )
= $false )
| ( ( in @ ( powerset @ SV356 ) @ ( powerset @ ( powerset @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1577,plain,
! [SV145: $i > $o] :
( ( ( ! [SY378: $i] :
~ ~ ( ~ ( SV145 @ SY378 )
| ~ ! [SY379: $i] :
( ~ ( SV145 @ SY379 )
| ( SY378 = SY379 ) ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1578,plain,
! [SV358: $i,SV147: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ ( binunion @ SV147 @ SV358 ) ) )
= $true )
| ( ( ( in @ SV509 @ SV147 )
| ( in @ SV509 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1579,plain,
! [SV360: $o,SV150: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV150 ) )
= $true )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1030: $i] :
( ~ ( ~ SV360
| ( SY1030 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1030 != SY1029 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1580,plain,
! [SV150: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV150 ) )
= $true )
| ( ( ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1032: $i] :
( ~ ( ~ $true
| ( SY1032 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1032 != SY1031 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1581,plain,
! [SV150: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV150 ) )
= $true )
| ( ( ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1034: $i] :
( ~ ( ~ $false
| ( SY1034 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1034 != SY1033 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1582,plain,
! [SV152: $i,SV361: $i] :
( ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false )
| ( ( ! [SY796: $i] :
( ~ ( in @ SY796 @ ( powerset @ SV152 ) )
| ~ ! [SY797: $i] :
( ~ ( in @ SY797 @ SV152 )
| ~ ( in @ SY797 @ SV361 )
| ( in @ SY797 @ SY796 ) )
| ( subset @ SV361 @ SY796 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1583,plain,
! [SV153: $i > $o] :
( ( ( ! [SY392: $i] :
~ ! [SY393: $i] :
~ ( ~ ( ~ ( SV153 @ SY393 )
| ( SY393 = SY392 ) )
| ~ ( ( SY393 != SY392 )
| ( SV153 @ SY393 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1363]) ).
thf(1584,plain,
! [SV362: $i,SV154: $i] :
( ( ( SV154 = SV362 )
= $false )
| ( ( ( setunion @ SV154 )
= ( setunion @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1585,plain,
! [SV363: $i,SV155: $i] :
( ( ( ! [SY798: $i] :
( ~ ( in @ SY798 @ SV155 )
| ( in @ SY798 @ SV363 ) ) )
= $false )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1586,plain,
! [SV364: $i,SV156: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) ) )
= $true )
| ( ( ! [SY1035: $i] :
( ~ ( in @ SY1035 @ SV156 )
| ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV364 )
| ~ ( in @ ( kpair @ SY1035 @ SY1036 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SY1035 )
= SY1036 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1587,plain,
! [SV365: $i,SV157: $i,SV514: $i] :
( ( ( ~ ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) ) )
= $true )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV157 )
| ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SY1037 ) @ SV365 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1588,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ( ~ ~ ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) ) )
= $true )
| ( ( ~ ( in @ SV515 @ SV158 )
| ( in @ SV515 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1589,plain,
! [SV367: $i,SV159: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ ( cartprod @ SV159 @ SV367 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV516 ) @ SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1590,plain,
! [SV368: $i,SV161: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ ( binintersect @ SV161 @ SV368 ) ) )
= $true )
| ( ( in @ SV517 @ SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1591,plain,
! [SV518: $i,SV369: $i,SV162: $i] :
( ( ( ~ ( func @ SV162 @ SV369 @ SV518 ) )
= $true )
| ( ( ! [SY1038: $i] :
( ~ ( func @ SV162 @ SV369 @ SY1038 )
| ~ ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1039 )
= ( ap @ SV162 @ SV369 @ SY1038 @ SY1039 ) ) )
| ( SV518 = SY1038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1592,plain,
! [SV163: $i] :
( ( ( ~ ( in @ emptyset @ SV163 )
| ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) )
= $true )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1593,plain,
! [SV519: $i > $i > $o,SV370: $i,SV164: $i,SV563: $i] :
( ( ! [SY1089: $i] :
( ~ ( in @ ( kpair @ SV563 @ SY1089 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SY1042: $i,SY1043: $i] : ( SV519 @ SY1042 @ SY1043 ) ) )
| ( in @ SY1089 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1594,plain,
! [SV520: $i,SV371: $i,SV165: $i] :
( ( ( ~ ( func @ SV165 @ SV371 @ SV520 ) )
= $true )
| ( ( ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV165 )
| ( in @ ( kpair @ SY1044 @ ( ap @ SV165 @ SV371 @ SV520 @ SY1044 ) ) @ SV520 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1595,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) ) )
= $true )
| ( ( ! [SY1045: $o] :
( ~ ( ( SV521 != SV166 )
| SY1045 )
| ~ ( ~ ( in @ SV521 @ SV372 )
| SY1045 )
| SY1045 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1596,plain,
! [SV167: $i,SV373: $i] :
( ( ( in @ SV373 @ ( powerset @ SV167 ) )
= $false )
| ( ( ! [SY819: $i] :
( ~ ( in @ SY819 @ ( powerset @ SV167 ) )
| ( in @ ( binunion @ SV373 @ SY819 ) @ ( powerset @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1597,plain,
! [SV374: $i,SV168: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV168 ) )
= $true )
| ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV374 )
| ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SY1046 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1598,plain,
! [SV375: $i,SV169: $i,SV523: $i] :
( ( ( ~ ( subset @ SV523 @ SV169 ) )
= $true )
| ( ( ~ ( subset @ SV523 @ SV375 )
| ( subset @ SV523 @ ( binintersect @ SV169 @ SV375 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1599,plain,
! [SV564: $i,SV524: $i,SV376: $i,SV170: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SV564 @ emptyset ) ) @ emptyset ) ) )
| ( SV524 != SV564 )
| ( SV376 = SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1600,plain,
! [SV378: $i,SV172: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ ( cartprod @ SV172 @ SV378 ) ) )
= $true )
| ( ( in @ ( kfst @ SV526 ) @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1601,plain,
! [SV379: $i,SV174: $i] :
( ( ( subset @ SV174 @ SV379 )
= $false )
| ( ( ~ ( subset @ SV379 @ SV174 )
| ( SV174 = SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1602,plain,
! [SV175: $i > $o] :
( ( ( ! [SY447: $i] :
~ ~ ( ~ ( SV175 @ SY447 )
| ~ ! [SY448: $i] :
( ~ ( SV175 @ SY448 )
| ( SY447 = SY448 ) ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1603,plain,
! [SV380: $i,SV176: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) ) )
= $true )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV176 )
| ( in @ ( kpair @ SY1050 @ ( ap @ SV176 @ SV380 @ SV527 @ SY1050 ) ) @ SV527 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1604,plain,
! [SV528: $i > $i > $o,SV381: $i,SV177: $i,SV565: $i] :
( ( ! [SY1092: $i] :
( ~ ( in @ ( kpair @ SV565 @ SY1092 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SY1053: $i,SY1054: $i] : ( SV528 @ SY1053 @ SY1054 ) ) )
| ( in @ SV565 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1605,plain,
! [SV382: $i,SV178: $i] :
( ( ( ~ ~ ! [SY836: $i] :
~ ~ ( ~ ( in @ SY836 @ SV178 )
| ~ ( in @ SY836 @ SV382 ) ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1606,plain,
! [SV383: $i,SV179: $i,SV529: $i] :
( ( ( ~ ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) ) )
= $true )
| ( ( ! [SY1055: $i > $o] :
( ~ ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV179 )
| ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV383 )
| ~ ( in @ ( kpair @ SY1056 @ SY1057 ) @ SV529 )
| ( SY1055 @ ( kpair @ SY1056 @ SY1057 ) ) ) )
| ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV529 )
| ( SY1055 @ SY1058 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1607,plain,
! [SV384: $i,SV182: $i,SV530: $i] :
( ( ( ~ ~ ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV530 @ SV384 )
| ~ ( in @ SV530 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1608,plain,
! [SV385: $i,SV183: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ ( funcSet @ SV183 @ SV385 ) ) )
= $true )
| ( ( func @ SV183 @ SV385 @ SV531 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1609,plain,
! [SV386: $i,SV185: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( setminus @ SV185 @ SV386 ) ) )
= $true )
| ( ( in @ SV532 @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1610,plain,
! [SV387: $i,SV186: $i] :
( ( ( SV186 = SV387 )
= $false )
| ( ( in @ SV186 @ ( setadjoin @ SV387 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1611,plain,
! [SV388: $i,SV187: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) ) )
= $true )
| ( ( ~ ! [SY1059: $i] :
~ ~ ( ~ ( in @ SY1059 @ SV187 )
| ~ ~ ! [SY1060: $i] :
~ ~ ( ~ ( in @ SY1060 @ SV388 )
| ( SV533
!= ( kpair @ SY1059 @ SY1060 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1612,plain,
! [SV188: $i,SV389: $i] :
( ( ( in @ SV389 @ ( powerset @ SV188 ) )
= $false )
| ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ ( powerset @ SV188 ) )
| ( in @ ( binintersect @ SV389 @ SY848 ) @ ( powerset @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1613,plain,
! [SV190: $i,SV566: $o] :
( ( SV566 = $true )
| ( ( in @ SV190 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1395]) ).
thf(1614,plain,
! [SV190: $i] :
( ( $true = $true )
| ( ( in @ SV190 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1395]) ).
thf(1615,plain,
! [SV190: $i] :
( ( $false = $true )
| ( ( in @ SV190 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1395]) ).
thf(1616,plain,
! [SV391: $i,SV191: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ SV191 ) )
= $true )
| ( ( ~ ~ ( in @ SV534 @ SV391 )
| ~ ( subset @ SV191 @ SV391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1617,plain,
! [SV392: $i,SV192: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV192 ) )
= $true )
| ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV392 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SY1061 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1618,plain,
! [SV536: $i,SV393: $i,SV193: $i] :
( ( ( ~ ( func @ SV193 @ SV393 @ SV536 ) )
= $true )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV193 )
| ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1063: $i] : ( in @ ( kpair @ SY1062 @ SY1063 ) @ SV536 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1619,plain,
! [SV394: $i,SV537: $i,SV194: $i] :
( ( ( ~ ( subset @ SV194 @ SV537 ) )
= $true )
| ( ( subset @ SV194 @ ( setadjoin @ SV394 @ SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1620,plain,
! [SV395: $i,SV195: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ ( funcSet @ SV195 @ SV395 ) ) )
= $true )
| ( ( ( lam @ SV195 @ SV395
@ ^ [SY1064: $i] : ( ap @ SV195 @ SV395 @ SV538 @ SY1064 ) )
= SV538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1621,plain,
! [SV196: $i > $o] :
( ( ( ! [SY497: $i] :
~ ( SV196 @ SY497 ) )
= $true )
| ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1622,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY858: $i,SY859: $i] :
( ( SY858 != SY859 )
| ~ ( ~ ( ~ ( SV197 @ SY858 )
| ( SV396 @ SY859 ) )
| ~ ( ~ ( SV396 @ SY859 )
| ( SV197 @ SY858 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1623,plain,
! [SV199: $i,SV398: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ SV398 ) )
= $true )
| ( ( ~ ( in @ SV539 @ ( setminus @ SV199 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1624,plain,
! [SV200: $i,SV399: $i] :
( ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false )
| ( ( ~ ! [SY868: $i] :
~ ~ ( ~ ( in @ SY868 @ SV200 )
| ~ ( in @ SV399 @ SY868 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1625,plain,
! [SV401: $i,SV541: $i > $i,SV202: $i] :
( ( ( ~ ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV202 )
| ( in @ ( SV541 @ SY1067 ) @ SV401 ) ) )
= $true )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1626,plain,
! [SV567: $i,SV542: $i,SV402: $i,SV203: $i] :
( ( ( ( kpair @ SV203 @ SV402 )
!= ( kpair @ SV542 @ SV567 ) )
| ( SV203 = SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1627,plain,
! [SV403: $i,SV204: $i] :
( ( ( in @ SV204 @ ( setadjoin @ SV403 @ emptyset ) )
= $false )
| ( ( SV204 = SV403 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1628,plain,
! [SV404: $i,SV205: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ SV205 ) )
= $true )
| ( ( ~ ~ ( in @ SV543 @ SV404 )
| ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1629,plain,
! [SV544: $i,SV405: $i,SV206: $i] :
( ( ( ~ ( subset @ SV206 @ SV405 ) )
= $true )
| ( ( ~ ( subset @ SV405 @ SV544 )
| ( subset @ SV206 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1630,plain,
! [SV406: $i,SV207: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ ( setadjoin @ SV207 @ ( setadjoin @ SV406 @ emptyset ) ) ) )
= $true )
| ( ( ( SV545 = SV207 )
| ( SV545 = SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1631,plain,
! [SV407: $i,SV210: $i] :
( ( ( SV210 != SV407 )
= $false )
| ( ( ~ ( in @ SV407 @ ( setadjoin @ SV210 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1632,plain,
! [SV408: $i,SV211: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ ( cartprod @ SV211 @ SV408 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV546 ) @ ( ksnd @ SV546 ) )
= SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1633,plain,
! [SV409: $i,SV212: $i] :
( ( ( subset @ SV212 @ SV409 )
= $false )
| ( ( ( setminus @ SV212 @ SV409 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1634,plain,
! [SV410: $i,SV213: $i,SV547: $i] :
( ( ( ~ ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) ) )
= $true )
| ( ( ! [SY1071: $i > $o] :
( ~ ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV213 )
| ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV410 )
| ~ ( in @ ( kpair @ SY1072 @ SY1073 ) @ SV547 )
| ( SY1071 @ ( kpair @ SY1072 @ SY1073 ) ) ) )
| ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV547 )
| ( SY1071 @ SY1074 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1635,plain,
! [SV214: $i,SV411: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ SV411 ) )
= $true )
| ( ( in @ SV548 @ ( binunion @ SV214 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1636,plain,
! [SV215: $i,SV412: $i] :
( ( ( in @ SV412 @ ( powerset @ SV215 ) )
= $false )
| ( ( in @ ( setminus @ SV215 @ SV412 ) @ ( powerset @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1637,plain,
! [SV216: $i,SV413: $i] :
( ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false )
| ( ( ! [SY888: $i] :
( ~ ( in @ SY888 @ SV216 )
| ~ ( in @ SY888 @ SV413 )
| ~ ( in @ SY888 @ ( setminus @ SV216 @ SV413 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1638,plain,
! [SV415: $i,SV218: $i] :
( ( ( SV218 = SV415 )
= $false )
| ( ( ! [SY889: $i > $o,SY890: $i > $o] :
( ~ ! [SY891: $i] :
( ~ ( in @ SY891 @ SV218 )
| ! [SY892: $i] :
( ~ ( in @ SY892 @ SV415 )
| ( SY891 != SY892 )
| ~ ( ~ ( ~ ( SY889 @ SY891 )
| ( SY890 @ SY892 ) )
| ~ ( ~ ( SY890 @ SY892 )
| ( SY889 @ SY891 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SX4: $i] : ( SY889 @ SX4 ) )
= ( dsetconstr @ SV415
@ ^ [SX4: $i] : ( SY890 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1639,plain,
! [SV220: $i,SV417: $i] :
( ( ( in @ SV417 @ SV220 )
= $false )
| ( ( in @ SV417 @ ( powerset @ ( setunion @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1640,plain,
! [SV222: $i,SV419: $i] :
( ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ ( powerset @ SV222 ) )
| ~ ! [SY896: $i] :
( ~ ( in @ SY896 @ SV222 )
| ~ ( in @ SY896 @ SV419 )
| ( in @ SY896 @ SY895 ) )
| ~ ! [SY897: $i] :
( ~ ( in @ SY897 @ SV222 )
| ~ ( in @ SY897 @ SY895 )
| ( in @ SY897 @ SV419 ) )
| ( SV419 = SY895 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1641,plain,
! [SV223: $i,SV420: $i] :
( ( ( subset @ SV420 @ SV223 )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1642,plain,
! [SV421: $i > $o,SV224: $i] :
( ( ( ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV224 )
| ( SV421 @ SY898 ) ) )
= $false )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1643,plain,
! [SV422: $i > $o,SV225: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ SV225 ) )
= $true )
| ( ( ~ ( SV422 @ SV549 )
| ( in @ SV549
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1644,plain,
! [SV226: $i,SV550: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV550 ) )
= $true )
| ( ( ~ ( in @ SV550 @ SV226 )
| ( in @ SV423 @ ( setunion @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1645,plain,
! [SV424: $i,SV227: $i,SV551: $i] :
( ( ( ~ ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) ) )
= $true )
| ( ( ! [SY1076: $i] :
( ~ ( subset @ SY1076 @ ( cartprod @ SV227 @ SV424 ) )
| ~ ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV227 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV424 )
| ~ ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV551 )
| ( in @ ( kpair @ SY1077 @ SY1078 ) @ SY1076 ) ) )
| ( subset @ SV551 @ SY1076 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1646,plain,
! [SV425: $i,SV229: $i,SV552: $i] :
( ( ( ~ ~ ( in @ SV552 @ SV229 ) )
= $true )
| ( ( ~ ( in @ SV552 @ ( setminus @ SV229 @ SV425 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1647,plain,
! [SV426: $i,SV230: $i,SV568: $i,SV553: $i] :
( ( ~ ( in @ ( kpair @ SV553 @ SV568 ) @ ( cartprod @ SV230 @ SV426 ) )
| ( in @ SV553 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1648,plain,
! [SV427: $i > $o,SV231: $i] :
( ( ( ~ ! [SY910: $i] :
~ ~ ( ~ ( in @ SY910 @ SV231 )
| ~ ( SV427 @ SY910 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1649,plain,
! [SV233: $i > $o,SV1: $i,SV428: $i] :
( ( ( in @ SV428 @ SV1 )
= $false )
| ( ( ~ ( SV233 @ SV428 )
| ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1650,plain,
! [SV234: $i,SV2: $i,SV429: $i] :
( ( ( in @ SV429 @ SV2 )
= $false )
| ( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV234 )
| ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SY913 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1651,plain,
! [SV235: $i,SV430: $i > $i,SV3: $i] :
( ( ( ! [SY914: $i] :
( ~ ( in @ SY914 @ SV3 )
| ( in @ ( SV430 @ SY914 ) @ SV235 ) ) )
= $false )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1652,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
| ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1435]) ).
thf(1653,plain,
! [SV431: $i,SV237: $i,SV5: $i] :
( ( ( func @ SV5 @ SV237 @ SV431 )
= $false )
| ( ( ! [SY917: $i] :
( ~ ( in @ SY917 @ SV5 )
| ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SY917 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1654,plain,
! [SV432: $i > $i > $o,SV238: $i,SV6: $i,SV569: $i,SV554: $i] :
( ( ~ ( in @ ( kpair @ SV554 @ SV569 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SY920: $i,SY921: $i] : ( SV432 @ SY920 @ SY921 ) ) )
| ( SV432 @ SV554 @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1655,plain,
! [SV239: $i,SV8: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ ( powerset @ SV8 ) )
| ( in @ ( setminus @ SV239 @ SV570 ) @ ( powerset @ SV8 ) ) )
= $true )
| ( ( in @ SV239 @ ( powerset @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1656,plain,
! [SV433: $i,SV240: $i,SV9: $i] :
( ( ( func @ SV9 @ SV240 @ SV433 )
= $false )
| ( ( ( lam @ SV9 @ SV240
@ ^ [SY922: $i] : ( ap @ SV9 @ SV240 @ SV433 @ SY922 ) )
= SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1657,plain,
! [SV242: $i,SV434: $i > $i,SV11: $i] :
( ( ( ! [SY923: $i] :
( ~ ( in @ SY923 @ SV11 )
| ( in @ ( SV434 @ SY923 ) @ SV242 ) ) )
= $false )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1658,plain,
! [SV13: $i] :
( ( ( in @ ( sK5_SY42 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1443]) ).
thf(1659,plain,
! [SV244: $o,SV14: $i,SV435: $i] :
( ( ( in @ SV435 @ SV14 )
= $false )
| ( ( ! [SY925: $i] :
( ~ ( in @ SY925 @ SV14 )
| ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY926: $i] :
( ~ ( ~ SV244
| ( SY926 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY926 != SY925 ) ) ) )
= ( setadjoin @ SY925 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1660,plain,
! [SV14: $i,SV436: $i] :
( ( ( in @ SV436 @ SV14 )
= $false )
| ( ( ! [SY927: $i] :
( ~ ( in @ SY927 @ SV14 )
| ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY928: $i] :
( ~ ( ~ $true
| ( SY928 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY928 != SY927 ) ) ) )
= ( setadjoin @ SY927 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1661,plain,
! [SV14: $i,SV437: $i] :
( ( ( in @ SV437 @ SV14 )
= $false )
| ( ( ! [SY929: $i] :
( ~ ( in @ SY929 @ SV14 )
| ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY930: $i] :
( ~ ( ~ $false
| ( SY930 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY930 != SY929 ) ) ) )
= ( setadjoin @ SY929 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1662,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ SV571 )
| ~ ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1663,plain,
! [SV438: $i,SV245: $i,SV17: $i] :
( ( ( func @ SV17 @ SV245 @ SV438 )
= $false )
| ( ( ! [SY931: $i] :
( ~ ( in @ SY931 @ SV17 )
| ( ( ap @ SV17 @ SV245 @ SV438 @ SY931 )
= ( ap @ SV17 @ SV245 @ SV438 @ SY931 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1664,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ( in @ SV572 @ SV18 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1665,plain,
! [SV19: $i,SV555: $i] :
( ( ( ~ ( in @ SV555 @ SV19 ) )
= $true )
| ( ( ( setunion @ SV19 )
= SV555 )
= $true )
| ( ( singleton @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1666,plain,
! [SV246: $i > $o,SV20: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ SV20 )
| ! [SY1100: $i] :
( ~ ( in @ SY1100 @ SV20 )
| ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SY1100 )
| ( SV573 = SY1100 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1667,plain,
! [SV247: $i,SV22: $i,SV439: $i] :
( ( ( in @ SV439 @ SV22 )
= $false )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ SV247 )
| ( ( kpair @ SV439 @ SY932 )
= ( kpair @ SV439 @ SY932 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1668,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
| ~ ! [SY942: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY942 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY942 ) )
| ~ ! [SY945: $i] :
~ ~ ! [SY946: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY945 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY946 @ SY942 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY945 )
| ~ ( in @ SX5 @ SY942 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY945 ) )
| ( in @ SY946 @ SY948 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1669,plain,
! [SV574: $o,SV24: $i,SV248: $i] :
( ( ( ~ ! [SY1101: $i] :
( ~ ( in @ SV248 @ SY1101 )
| ~ ( in @ SY1101 @ SV24 )
| SV574 )
| SV574 )
= $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1454]) ).
thf(1670,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $true )
| $true )
= $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1454]) ).
thf(1671,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $false )
| $false )
= $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1454]) ).
thf(1672,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ~ ( ~ ( SV27 @ SV575 )
| ~ ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1673,plain,
! [SV250: $i,SV28: $i,SV440: $i] :
( ( ( in @ SV440 @ ( setadjoin @ SV28 @ SV250 ) )
= $false )
| ( ( ( SV440 = SV28 )
| ( in @ SV440 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1674,plain,
! [SV251: $i,SV29: $i,SV441: $i] :
( ( ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) )
= $false )
| ( ( ! [SY950: $i] :
( ~ ( in @ SY950 @ SV29 )
| ( ( ap @ SV29 @ SV251 @ SV441 @ SY950 )
= ( ap @ SV29 @ SV251 @ SV441 @ SY950 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1675,plain,
! [SV252: $i > $o,SV30: $i,SV442: $i] :
( ( ( in @ SV442 @ SV30 )
= $false )
| ( ( ~ ( SV252 @ SV442 )
| ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1676,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ( in @ SV254 @ ( setunion @ SV33 ) )
| ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1677,plain,
! [SV33: $i,SV254: $i] :
( ( ~ ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) )
| ( in @ SV254 @ ( setunion @ SV33 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1678,plain,
! [SV255: $i,SV34: $i,SV443: $i] :
( ( ( in @ SV443 @ SV34 )
= $false )
| ( ( ~ ( in @ SV443 @ SV255 )
| ~ ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1679,plain,
! [SV36: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV36 ) )
= $true )
| ( ( SV36 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1680,plain,
! [SV257: $i,SV37: $i,SV444: $i] :
( ( ( in @ SV444 @ SV37 )
= $false )
| ( ( ! [SY953: $i] :
( ~ ( in @ SY953 @ SV257 )
| ( ( kfst @ ( kpair @ SV444 @ SY953 ) )
= SV444 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1681,plain,
! [SV258: $i,SV38: $i,SV445: $i] :
( ( ( in @ SV445 @ SV38 )
= $false )
| ( ( ~ ~ ( in @ SV445 @ SV258 )
| ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1682,plain,
! [SV259: $i,SV39: $i,SV446: $i] :
( ( ( in @ SV446 @ SV39 )
= $false )
| ( ( ~ ~ ( in @ SV446 @ SV259 )
| ( SV39 != SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1683,plain,
! [SV261: $i,SV41: $i,SV447: $i] :
( ( ( in @ SV447 @ ( setadjoin @ SV41 @ ( setadjoin @ SV261 @ emptyset ) ) )
= $false )
| ( ( ( SV447 = SV41 )
| ( SV447 = SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1684,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY1103: $i] :
( ( ( sK8_SY642 @ SV262 @ SV42 )
!= SY1103 )
| ~ ( ~ ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ SY1103 ) )
| ~ ( ~ ( SV262 @ SY1103 )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1470]) ).
thf(1685,plain,
! [SV448: $i,SV263: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV263 )
= $false )
| ( ( ~ ~ ( in @ SV448 @ SV263 )
| ~ ( in @ SV448 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1686,plain,
! [SV449: $i,SV264: $i,SV44: $i] :
( ( ( func @ SV44 @ SV264 @ SV449 )
= $false )
| ( ( ! [SY954: $i] :
( ~ ( in @ SY954 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY955: $i] : ( in @ ( kpair @ SY954 @ SY955 ) @ SV449 ) ) )
@ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1687,plain,
! [SV265: $i,SV45: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ SV45 ) )
= $false )
| ( ( ~ ~ ( in @ SV450 @ SV265 )
| ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1688,plain,
! [SV267: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK9_SY657 @ SV47 @ SV267 ) @ SV267 )
| ( in @ ( sK9_SY657 @ SV47 @ SV267 ) @ SV47 ) )
= $false )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1474]) ).
thf(1689,plain,
! [SV268: $i > $o,SV48: $i] :
( ( ( ! [SY658: $i] :
~ ~ ( ~ ( in @ SY658 @ SV48 )
| ~ ~ ( SV268 @ SY658 ) ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1690,plain,
! [SV269: $i,SV451: $i > $i,SV49: $i] :
( ( ( ! [SY956: $i] :
( ~ ( in @ SY956 @ SV49 )
| ( in @ ( SV451 @ SY956 ) @ SV269 ) ) )
= $false )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1691,plain,
! [SV452: $i,SV270: $i,SV50: $i] :
( ( ( func @ SV50 @ SV270 @ SV452 )
= $false )
| ( ( in @ SV452 @ ( funcSet @ SV50 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1692,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ~ ( ~ ( SV51 @ SV577 )
| ~ ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1693,plain,
! [SV556: $o,SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| SV556 )
| ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1694,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $true )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1695,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $false )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1696,plain,
! [SV273: $i,SV54: $i,SV454: $i] :
( ( ( in @ SV454 @ ( setminus @ SV54 @ SV273 ) )
= $false )
| ( ( ~ ( in @ SV454 @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1697,plain,
! [SV455: $i,SV274: $i,SV55: $i] :
( ( ( subset @ SV55 @ SV274 )
= $false )
| ( ( ~ ( in @ SV455 @ SV55 )
| ( in @ SV455 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1698,plain,
! [SV275: $i,SV56: $i,SV578: $i] :
( ( ( ! [SY1105: $i] :
( ( SV578 != SY1105 )
| ( ( setadjoin @ SV56 @ SV578 )
= ( setadjoin @ SV275 @ SY1105 ) ) ) )
= $true )
| ( ( SV56 = SV275 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1699,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false )
| ( ( ! [SY960: $o] :
( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SY960 )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SY960 )
| SY960 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1700,plain,
! [SV278: $i,SV59: $i,SV457: $i] :
( ( ( in @ SV457 @ ( cartprod @ SV59 @ SV278 ) )
= $false )
| ( ( iskpair @ SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1701,plain,
! [SV61: $i,SV280: $i] :
( ( ( ~ ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
| ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 ) )
= $false )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1488]) ).
thf(1702,plain,
! [SV281: $o,SV62: $i,SV458: $i] :
( ( ( in @ SV458 @ SV62 )
= $false )
| ( ( ! [SY961: $i] :
( ~ ( in @ SY961 @ SV62 )
| ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SY961 )
= SV458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1703,plain,
! [SV62: $i,SV459: $i] :
( ( ( in @ SV459 @ SV62 )
= $false )
| ( ( ! [SY962: $i] :
( ~ ( in @ SY962 @ SV62 )
| ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SY962 )
= SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1704,plain,
! [SV62: $i,SV460: $i] :
( ( ( in @ SV460 @ SV62 )
= $false )
| ( ( ! [SY963: $i] :
( ~ ( in @ SY963 @ SV62 )
| ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SY963 )
= SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1705,plain,
! [SV462: $i,SV283: $i,SV64: $i] :
( ( ( ( setadjoin @ SV64 @ ( setadjoin @ SV283 @ emptyset ) )
= ( setadjoin @ SV462 @ emptyset ) )
= $false )
| ( ( SV64 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1706,plain,
! [SV284: $i,SV65: $i,SV463: $i] :
( ( ( in @ SV463 @ SV65 )
= $false )
| ( ( in @ ( setadjoin @ SV463 @ emptyset ) @ ( powerset @ ( binunion @ SV65 @ SV284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1707,plain,
! [SV285: $i,SV66: $i] :
( ( ( subset @ SV66 @ SV285 )
= $true )
| ( ( SV66 != SV285 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1708,plain,
! [SV286: $o,SV67: $i,SV464: $i] :
( ( ( in @ SV464 @ SV67 )
= $false )
| ( ( ! [SY964: $i] :
( ~ ( in @ SY964 @ SV67 )
| ~ ~ SV286
| ( in @ SY964
@ ( dsetconstr @ SV67
@ ^ [SY965: $i] :
( ~ ( ~ SV286
| ( SY965 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY965 != SY964 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1709,plain,
! [SV67: $i,SV465: $i] :
( ( ( in @ SV465 @ SV67 )
= $false )
| ( ( ! [SY966: $i] :
( ~ ( in @ SY966 @ SV67 )
| ~ ~ $true
| ( in @ SY966
@ ( dsetconstr @ SV67
@ ^ [SY967: $i] :
( ~ ( ~ $true
| ( SY967 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY967 != SY966 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1710,plain,
! [SV67: $i,SV466: $i] :
( ( ( in @ SV466 @ SV67 )
= $false )
| ( ( ! [SY968: $i] :
( ~ ( in @ SY968 @ SV67 )
| ~ ~ $false
| ( in @ SY968
@ ( dsetconstr @ SV67
@ ^ [SY969: $i] :
( ~ ( ~ $false
| ( SY969 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY969 != SY968 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1711,plain,
! [SV68: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
| ~ ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) ) )
= $false )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1498]) ).
thf(1712,plain,
! [SV288: $i > $o,SV69: $i] :
( ( ( ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV69 )
| ~ ( SV288 @ SY686 ) ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1713,plain,
! [SV467: $i,SV70: $i,SV289: $i] :
( ( ( in @ SV289 @ ( powerset @ SV70 ) )
= $false )
| ( ( ~ ( in @ SV467 @ SV289 )
| ( in @ SV467 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1714,plain,
! [SV290: $i,SV71: $i,SV468: $i] :
( ( ( in @ SV468 @ SV71 )
= $false )
| ( ( in @ SV468 @ ( binunion @ SV71 @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1715,plain,
! [SV291: $i,SV73: $i,SV469: $i] :
( ( ( in @ SV469 @ SV73 )
= $false )
| ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ SV291 )
| ( ( ksnd @ ( kpair @ SV469 @ SY970 ) )
= SY970 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1716,plain,
! [SV292: $i,SV74: $i,SV579: $i] :
( ( ( ! [SY1106: $i] :
( ( SV579 != SY1106 )
| ~ ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SY1106 @ SV292 ) )
| ~ ( ~ ( in @ SY1106 @ SV292 )
| ( in @ SV579 @ SV74 ) ) ) ) )
= $true )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1717,plain,
! [SV293: $i,SV470: $i > $i,SV75: $i] :
( ( ( ! [SY971: $i] :
( ~ ( in @ SY971 @ SV75 )
| ( in @ ( SV470 @ SY971 ) @ SV293 ) ) )
= $false )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1718,plain,
! [SV294: $i > $o,SV76: $i] :
( ( ( ! [SY697: $i] :
( ~ ( in @ SY697 @ SV76 )
| ( SV294 @ SY697 ) ) )
= $true )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1719,plain,
! [SV471: $i,SV295: $i,SV77: $i] :
( ( ( func @ SV77 @ SV295 @ SV471 )
= $false )
| ( ( ! [SY973: $i] :
( ~ ( func @ SV77 @ SV295 @ SY973 )
| ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY974 )
= ( ap @ SV77 @ SV295 @ SY973 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV77 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV295 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SY973 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV471 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1720,plain,
! [SV296: $i,SV78: $i,SV472: $i] :
( ( ( in @ ( setadjoin @ SV472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV296 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV78 = SV472 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1721,plain,
! [SV297: $i,SV79: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ ( powerset @ SV79 ) )
| ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SY1107 @ SV297 )
| ( in @ SY1107 @ SV580 ) ) )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1722,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ~ ( ~ ( SV80 @ SV581 )
| ~ ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1723,plain,
! [SV298: $i,SV81: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ ( powerset @ SV81 ) )
| ~ ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV81 )
| ~ ( in @ SY1109 @ SV298 )
| ( in @ SY1109 @ SV582 ) )
| ( in @ SV298 @ ( powerset @ SV582 ) ) )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1724,plain,
! [SV299: $i,SV82: $i,SV473: $i] :
( ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ ( funcSet @ SV82 @ SV299 ) )
| ~ ! [SY978: $i] :
( ~ ( in @ SY978 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY978 )
= ( ap @ SV82 @ SV299 @ SY977 @ SY978 ) ) )
| ( SV473 = SY977 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1725,plain,
! [SV83: $i] :
( ( ( in @ ( sK6_SY233 @ SV83 ) @ SV83 )
= $true )
| ( ( SV83 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1726,plain,
! [SV301: $i,SV85: $i,SV474: $i] :
( ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( ! [SY979: $i] :
( ~ ( subset @ SY979 @ ( cartprod @ SV85 @ SV301 ) )
| ~ ! [SY980: $i] :
( ~ ( in @ SY980 @ SV85 )
| ! [SY981: $i] :
( ~ ( in @ SY981 @ SV301 )
| ~ ( in @ ( kpair @ SY980 @ SY981 ) @ SV474 )
| ( in @ ( kpair @ SY980 @ SY981 ) @ SY979 ) ) )
| ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV85 )
| ! [SY983: $i] :
( ~ ( in @ SY983 @ SV301 )
| ~ ( in @ ( kpair @ SY982 @ SY983 ) @ SY979 )
| ( in @ ( kpair @ SY982 @ SY983 ) @ SV474 ) ) )
| ( SV474 = SY979 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1727,plain,
! [SV302: $o,SV86: $i,SV475: $i] :
( ( ( in @ SV475 @ SV86 )
= $false )
| ( ( ! [SY984: $i] :
( ~ ( in @ SY984 @ SV86 )
| ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY985: $i] :
( ~ ( ~ SV302
| ( SY985 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY985 != SY984 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1728,plain,
! [SV86: $i,SV476: $i] :
( ( ( in @ SV476 @ SV86 )
= $false )
| ( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ SV86 )
| ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY987: $i] :
( ~ ( ~ $true
| ( SY987 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY987 != SY986 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1729,plain,
! [SV86: $i,SV477: $i] :
( ( ( in @ SV477 @ SV86 )
= $false )
| ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV86 )
| ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY989: $i] :
( ~ ( ~ $false
| ( SY989 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY989 != SY988 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1730,plain,
! [SV303: $i > $o,SV87: $i,SV478: $i] :
( ( ( in @ SV478
@ ( dsetconstr @ SV87
@ ^ [SY722: $i] : ( SV303 @ SY722 ) ) )
= $false )
| ( ( SV303 @ SV478 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1731,plain,
! [SV557: $i,SV479: $i,SV304: $i,SV88: $i] :
( ( ( ( kpair @ SV88 @ SV304 )
!= ( kpair @ SV479 @ SV557 ) )
= $true )
| ( ( SV304 = SV557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1732,plain,
! [SV89: $i] :
( ( ( ! [SY252: $i] :
~ ~ ( ~ ( in @ SY252 @ SV89 )
| ~ $true ) )
= $false )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1733,plain,
! [SV480: $i > $i > $o,SV305: $i,SV90: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ SV90 ) )
= $true )
| ( ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV305 )
| ~ ( SV480 @ SV558 @ SY1083 )
| ( in @ ( kpair @ SV558 @ SY1083 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1734,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ~ ( ~ ( SV91 @ SV583 )
| ~ ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1735,plain,
! [SV92: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK12_SY730 @ SV306 @ SV92 ) @ SV92 )
| ( in @ ( sK12_SY730 @ SV306 @ SV92 ) @ SV306 ) )
= $false )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1523]) ).
thf(1736,plain,
! [SV308: $i > $o,SV95: $i] :
( ( ( ! [SY732: $i] :
~ ~ ( ~ ( in @ SY732 @ SV95 )
| ~ ( SV308 @ SY732 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1737,plain,
! [SV309: $i > $o,SV96: $i] :
( ( ( ~ ! [SY733: $i] :
~ ~ ( ~ ( in @ SY733 @ SV96 )
| ~ ( SV309 @ SY733 ) ) )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1738,plain,
! [SV311: $i,SV98: $i,SV481: $i] :
( ( ( in @ SV481 @ SV98 )
= $false )
| ( ( ! [SY996: $i] :
( ~ ( in @ SY996 @ SV311 )
| ( in @ ( kpair @ SV481 @ SY996 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1739,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ( in @ SV312 @ ( powerset @ SV99 ) )
| ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1740,plain,
! [SV99: $i,SV312: $i] :
( ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) )
| ( in @ SV312 @ ( powerset @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1741,plain,
! [SV313: $i,SV100: $i,SV482: $i] :
( ( ( in @ SV482 @ ( binintersect @ SV100 @ SV313 ) )
= $false )
| ( ( in @ SV482 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1742,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( ~ ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
| ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1743,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( ~ ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1744,plain,
! [SV317: $i,SV104: $i,SV484: $i] :
( ( ( in @ SV484 @ SV104 )
= $false )
| ( ( ! [SY997: $i] :
( ~ ( in @ SY997 @ SV317 )
| ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SY997 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1745,plain,
! [SV318: $i,SV105: $i,SV584: $i] :
( ( ( ! [SY1111: $i] :
( ( SV584 != SY1111 )
| ~ ( in @ SV584 @ SV105 )
| ( in @ SY1111 @ SV318 ) ) )
= $true )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1746,plain,
! [SV485: $i,SV321: $i,SV108: $i] :
( ( ( func @ SV108 @ SV321 @ SV485 )
= $false )
| ( ( ! [SY998: $i] :
( ~ ( in @ SY998 @ SV108 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV321 )
| ~ ( in @ ( kpair @ SY998 @ SY999 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SY998 )
= SY999 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1747,plain,
( ( ~ ( in @ sK3_SY2 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1748,plain,
( ( ~ ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1749,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) ) )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1539]) ).
thf(1750,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( in @ SV486 @ SV112 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) )
| ~ ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1751,plain,
! [SV325: $o,SV113: $i,SV487: $i] :
( ( ( in @ SV487 @ SV113 )
= $false )
| ( ( ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV113 )
| ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1003: $i] :
( ~ ( ~ SV325
| ( SY1003 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1003 != SY1002 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1752,plain,
! [SV113: $i,SV488: $i] :
( ( ( in @ SV488 @ SV113 )
= $false )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV113 )
| ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1005: $i] :
( ~ ( ~ $true
| ( SY1005 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1005 != SY1004 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1753,plain,
! [SV113: $i,SV489: $i] :
( ( ( in @ SV489 @ SV113 )
= $false )
| ( ( ! [SY1006: $i] :
( ~ ( in @ SY1006 @ SV113 )
| ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1007: $i] :
( ~ ( ~ $false
| ( SY1007 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1007 != SY1006 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1754,plain,
! [SV114: $i] :
( ( ( ! [SY310: $i] :
~ ( in @ SY310 @ SV114 ) )
= $false )
| ( ( SV114 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1755,plain,
! [SV326: $i,SV115: $i,SV559: $i,SV490: $i] :
( ( ( ~ ( in @ ( kpair @ SV490 @ SV559 ) @ ( cartprod @ SV115 @ SV326 ) ) )
= $true )
| ( ( in @ SV559 @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1756,plain,
! [SV327: $i > $o,SV116: $i,SV491: $i] :
( ( ( in @ SV491
@ ( dsetconstr @ SV116
@ ^ [SY758: $i] : ( SV327 @ SY758 ) ) )
= $false )
| ( ( in @ SV491 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1757,plain,
! [SV120: $i,SV330: $i,SV492: $i] :
( ( ( in @ SV492 @ SV330 )
= $false )
| ( ( in @ SV492 @ ( setadjoin @ SV120 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1758,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
| ! [SY1112: $i] :
( ~ ( in @ SY1112 @ SV121 )
| ~ ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
| ~ ( SV331 @ SY1112 )
| ( ( sK14_SY760 @ SV331 @ SV121 )
= SY1112 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1550]) ).
thf(1759,plain,
! [SV332: $o,SV122: $i,SV493: $i] :
( ( ( in @ SV493 @ SV122 )
= $false )
| ( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV122 )
| ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SY1010 )
= SY1010 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1760,plain,
! [SV122: $i,SV494: $i] :
( ( ( in @ SV494 @ SV122 )
= $false )
| ( ( ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV122 )
| ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SY1011 )
= SY1011 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1761,plain,
! [SV122: $i,SV495: $i] :
( ( ( in @ SV495 @ SV122 )
= $false )
| ( ( ! [SY1012: $i] :
( ~ ( in @ SY1012 @ SV122 )
| ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SY1012 )
= SY1012 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1762,plain,
! [SV333: $i,SV496: $i > $i,SV123: $i] :
( ( ( ! [SY1013: $i] :
( ~ ( in @ SY1013 @ SV123 )
| ( in @ ( SV496 @ SY1013 ) @ SV333 ) ) )
= $false )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1763,plain,
! [SV337: $o,SV125: $i,SV497: $i] :
( ( ( in @ SV497 @ SV125 )
= $false )
| ( ( ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV125 )
| ( in @ ( if @ SV125 @ SV337 @ SV497 @ SY1016 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SY1016 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1764,plain,
! [SV125: $i,SV498: $i] :
( ( ( in @ SV498 @ SV125 )
= $false )
| ( ( ! [SY1017: $i] :
( ~ ( in @ SY1017 @ SV125 )
| ( in @ ( if @ SV125 @ $true @ SV498 @ SY1017 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SY1017 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1765,plain,
! [SV125: $i,SV499: $i] :
( ( ( in @ SV499 @ SV125 )
= $false )
| ( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ SV125 )
| ( in @ ( if @ SV125 @ $false @ SV499 @ SY1018 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SY1018 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1766,plain,
! [SV341: $i,SV129: $i,SV500: $i] :
( ( ( in @ SV500 @ SV129 )
= $false )
| ( ( ~ ( in @ SV500 @ SV341 )
| ( in @ SV500 @ ( binintersect @ SV129 @ SV341 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1767,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ SV130 ) )
= $true )
| ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV342 )
| ~ ( in @ ( kpair @ SV560 @ SY1086 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1768,plain,
! [SV345: $o,SV133: $i,SV502: $i] :
( ( ( in @ SV502 @ SV133 )
= $false )
| ( ( ! [SY1023: $i] :
( ~ ( in @ SY1023 @ SV133 )
| ( in @ ( if @ SV133 @ SV345 @ SV502 @ SY1023 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1769,plain,
! [SV133: $i,SV503: $i] :
( ( ( in @ SV503 @ SV133 )
= $false )
| ( ( ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV133 )
| ( in @ ( if @ SV133 @ $true @ SV503 @ SY1024 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1770,plain,
! [SV133: $i,SV504: $i] :
( ( ( in @ SV504 @ SV133 )
= $false )
| ( ( ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV133 )
| ( in @ ( if @ SV133 @ $false @ SV504 @ SY1025 ) @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1771,plain,
! [SV347: $i,SV135: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV135 ) )
= $false )
| ( ( ~ ( in @ SV505 @ SV347 )
| ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1772,plain,
! [SV561: $i,SV506: $i,SV349: $i,SV137: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SV349 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV561 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV349 = SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1773,plain,
! [SV562: $i,SV507: $i,SV350: $i,SV138: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV507 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV507 @ ( setadjoin @ SV562 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV138 = SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1774,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
| ! [SY1113: $i] :
( ~ ( in @ SY1113 @ SV139 )
| ~ ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
| ~ ( SV351 @ SY1113 )
| ( ( sK15_SY786 @ SV351 @ SV139 )
= SY1113 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1572]) ).
thf(1775,plain,
! [SV355: $i,SV143: $i,SV508: $i] :
( ( ( in @ SV508 @ SV143 )
= $false )
| ( ( ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SV355 )
| ( in @ ( kpair @ SV508 @ SY1028 ) @ ( cartprod @ SV143 @ SV355 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1776,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ~ ( ~ ( SV145 @ SV585 )
| ~ ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1777,plain,
! [SV358: $i,SV147: $i,SV509: $i] :
( ( ( in @ SV509 @ ( binunion @ SV147 @ SV358 ) )
= $false )
| ( ( ( in @ SV509 @ SV147 )
| ( in @ SV509 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1778,plain,
! [SV360: $o,SV150: $i,SV510: $i] :
( ( ( in @ SV510 @ SV150 )
= $false )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1030: $i] :
( ~ ( ~ SV360
| ( SY1030 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1030 != SY1029 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1779,plain,
! [SV150: $i,SV511: $i] :
( ( ( in @ SV511 @ SV150 )
= $false )
| ( ( ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1032: $i] :
( ~ ( ~ $true
| ( SY1032 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1032 != SY1031 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1780,plain,
! [SV150: $i,SV512: $i] :
( ( ( in @ SV512 @ SV150 )
= $false )
| ( ( ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1034: $i] :
( ~ ( ~ $false
| ( SY1034 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1034 != SY1033 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1781,plain,
! [SV361: $i,SV152: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( powerset @ SV152 ) )
| ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV152 )
| ~ ( in @ SY1115 @ SV361 )
| ( in @ SY1115 @ SV586 ) )
| ( subset @ SV361 @ SV586 ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1782,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ! [SY1116: $i] :
~ ( ~ ( ~ ( SV153 @ SY1116 )
| ( SY1116 = SV587 ) )
| ~ ( ( SY1116 != SV587 )
| ( SV153 @ SY1116 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1783,plain,
! [SV155: $i,SV363: $i] :
( ( ( ~ ( in @ ( sK16_SY798 @ SV363 @ SV155 ) @ SV155 )
| ( in @ ( sK16_SY798 @ SV363 @ SV155 ) @ SV363 ) )
= $false )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1585]) ).
thf(1784,plain,
! [SV364: $i,SV156: $i,SV513: $i] :
( ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false )
| ( ( ! [SY1035: $i] :
( ~ ( in @ SY1035 @ SV156 )
| ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV364 )
| ~ ( in @ ( kpair @ SY1035 @ SY1036 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SY1035 )
= SY1036 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1785,plain,
! [SV365: $i,SV157: $i,SV514: $i] :
( ( ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) )
= $false )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV157 )
| ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SY1037 ) @ SV365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1786,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) ) )
= $false )
| ( ( ~ ( in @ SV515 @ SV158 )
| ( in @ SV515 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1787,plain,
! [SV367: $i,SV159: $i,SV516: $i] :
( ( ( in @ SV516 @ ( cartprod @ SV159 @ SV367 ) )
= $false )
| ( ( in @ ( ksnd @ SV516 ) @ SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1788,plain,
! [SV368: $i,SV161: $i,SV517: $i] :
( ( ( in @ SV517 @ ( binintersect @ SV161 @ SV368 ) )
= $false )
| ( ( in @ SV517 @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1789,plain,
! [SV518: $i,SV369: $i,SV162: $i] :
( ( ( func @ SV162 @ SV369 @ SV518 )
= $false )
| ( ( ! [SY1038: $i] :
( ~ ( func @ SV162 @ SV369 @ SY1038 )
| ~ ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1039 )
= ( ap @ SV162 @ SV369 @ SY1038 @ SY1039 ) ) )
| ( SV518 = SY1038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1790,plain,
! [SV163: $i] :
( ( ( ~ ( in @ emptyset @ SV163 ) )
= $true )
| ( ( ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) )
= $true )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1791,plain,
! [SV519: $i > $i > $o,SV370: $i,SV164: $i,SV588: $i,SV563: $i] :
( ( ~ ( in @ ( kpair @ SV563 @ SV588 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SY1042: $i,SY1043: $i] : ( SV519 @ SY1042 @ SY1043 ) ) )
| ( in @ SV588 @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1792,plain,
! [SV520: $i,SV371: $i,SV165: $i] :
( ( ( func @ SV165 @ SV371 @ SV520 )
= $false )
| ( ( ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV165 )
| ( in @ ( kpair @ SY1044 @ ( ap @ SV165 @ SV371 @ SV520 @ SY1044 ) ) @ SV520 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1793,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false )
| ( ( ! [SY1045: $o] :
( ~ ( ( SV521 != SV166 )
| SY1045 )
| ~ ( ~ ( in @ SV521 @ SV372 )
| SY1045 )
| SY1045 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1794,plain,
! [SV373: $i,SV167: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ ( powerset @ SV167 ) )
| ( in @ ( binunion @ SV373 @ SV589 ) @ ( powerset @ SV167 ) ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1795,plain,
! [SV374: $i,SV168: $i,SV522: $i] :
( ( ( in @ SV522 @ SV168 )
= $false )
| ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV374 )
| ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SY1046 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1796,plain,
! [SV375: $i,SV169: $i,SV523: $i] :
( ( ( subset @ SV523 @ SV169 )
= $false )
| ( ( ~ ( subset @ SV523 @ SV375 )
| ( subset @ SV523 @ ( binintersect @ SV169 @ SV375 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1797,plain,
! [SV564: $i,SV524: $i,SV376: $i,SV170: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SV564 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV524 != SV564 )
| ( SV376 = SV564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1798,plain,
! [SV378: $i,SV172: $i,SV526: $i] :
( ( ( in @ SV526 @ ( cartprod @ SV172 @ SV378 ) )
= $false )
| ( ( in @ ( kfst @ SV526 ) @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1799,plain,
! [SV174: $i,SV379: $i] :
( ( ( ~ ( subset @ SV379 @ SV174 ) )
= $true )
| ( ( SV174 = SV379 )
= $true )
| ( ( subset @ SV174 @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1800,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ~ ( ~ ( SV175 @ SV590 )
| ~ ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1801,plain,
! [SV380: $i,SV176: $i,SV527: $i] :
( ( ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) )
= $false )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV176 )
| ( in @ ( kpair @ SY1050 @ ( ap @ SV176 @ SV380 @ SV527 @ SY1050 ) ) @ SV527 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1802,plain,
! [SV528: $i > $i > $o,SV381: $i,SV177: $i,SV591: $i,SV565: $i] :
( ( ~ ( in @ ( kpair @ SV565 @ SV591 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SY1053: $i,SY1054: $i] : ( SV528 @ SY1053 @ SY1054 ) ) )
| ( in @ SV565 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1803,plain,
! [SV382: $i,SV178: $i] :
( ( ( ~ ! [SY836: $i] :
~ ~ ( ~ ( in @ SY836 @ SV178 )
| ~ ( in @ SY836 @ SV382 ) ) )
= $true )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1804,plain,
! [SV383: $i,SV179: $i,SV529: $i] :
( ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false )
| ( ( ! [SY1055: $i > $o] :
( ~ ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV179 )
| ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV383 )
| ~ ( in @ ( kpair @ SY1056 @ SY1057 ) @ SV529 )
| ( SY1055 @ ( kpair @ SY1056 @ SY1057 ) ) ) )
| ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV529 )
| ( SY1055 @ SY1058 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1805,plain,
! [SV384: $i,SV182: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV530 @ SV384 )
| ~ ( in @ SV530 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1806,plain,
! [SV385: $i,SV183: $i,SV531: $i] :
( ( ( in @ SV531 @ ( funcSet @ SV183 @ SV385 ) )
= $false )
| ( ( func @ SV183 @ SV385 @ SV531 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1807,plain,
! [SV386: $i,SV185: $i,SV532: $i] :
( ( ( in @ SV532 @ ( setminus @ SV185 @ SV386 ) )
= $false )
| ( ( in @ SV532 @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1808,plain,
! [SV388: $i,SV187: $i,SV533: $i] :
( ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false )
| ( ( ~ ! [SY1059: $i] :
~ ~ ( ~ ( in @ SY1059 @ SV187 )
| ~ ~ ! [SY1060: $i] :
~ ~ ( ~ ( in @ SY1060 @ SV388 )
| ( SV533
!= ( kpair @ SY1059 @ SY1060 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1809,plain,
! [SV389: $i,SV188: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ ( powerset @ SV188 ) )
| ( in @ ( binintersect @ SV389 @ SV592 ) @ ( powerset @ SV188 ) ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1810,plain,
! [SV391: $i,SV191: $i,SV534: $i] :
( ( ( in @ SV534 @ SV191 )
= $false )
| ( ( ~ ~ ( in @ SV534 @ SV391 )
| ~ ( subset @ SV191 @ SV391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1811,plain,
! [SV392: $i,SV192: $i,SV535: $i] :
( ( ( in @ SV535 @ SV192 )
= $false )
| ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV392 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SY1061 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1812,plain,
! [SV536: $i,SV393: $i,SV193: $i] :
( ( ( func @ SV193 @ SV393 @ SV536 )
= $false )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV193 )
| ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1063: $i] : ( in @ ( kpair @ SY1062 @ SY1063 ) @ SV536 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1813,plain,
! [SV394: $i,SV537: $i,SV194: $i] :
( ( ( subset @ SV194 @ SV537 )
= $false )
| ( ( subset @ SV194 @ ( setadjoin @ SV394 @ SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1814,plain,
! [SV395: $i,SV195: $i,SV538: $i] :
( ( ( in @ SV538 @ ( funcSet @ SV195 @ SV395 ) )
= $false )
| ( ( ( lam @ SV195 @ SV395
@ ^ [SY1064: $i] : ( ap @ SV195 @ SV395 @ SV538 @ SY1064 ) )
= SV538 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1815,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV593 ) )
= $true )
| ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1816,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY1122: $i] :
( ( ( sK17_SY858 @ SV396 @ SV197 )
!= SY1122 )
| ~ ( ~ ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ SY1122 ) )
| ~ ( ~ ( SV396 @ SY1122 )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1622]) ).
thf(1817,plain,
! [SV199: $i,SV398: $i,SV539: $i] :
( ( ( in @ SV539 @ SV398 )
= $false )
| ( ( ~ ( in @ SV539 @ ( setminus @ SV199 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1818,plain,
! [SV399: $i,SV200: $i] :
( ( ( ! [SY868: $i] :
~ ~ ( ~ ( in @ SY868 @ SV200 )
| ~ ( in @ SV399 @ SY868 ) ) )
= $false )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1819,plain,
! [SV401: $i,SV541: $i > $i,SV202: $i] :
( ( ( ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV202 )
| ( in @ ( SV541 @ SY1067 ) @ SV401 ) ) )
= $false )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1820,plain,
! [SV567: $i,SV542: $i,SV402: $i,SV203: $i] :
( ( ( ( kpair @ SV203 @ SV402 )
!= ( kpair @ SV542 @ SV567 ) )
= $true )
| ( ( SV203 = SV542 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1821,plain,
! [SV404: $i,SV205: $i,SV543: $i] :
( ( ( in @ SV543 @ SV205 )
= $false )
| ( ( ~ ~ ( in @ SV543 @ SV404 )
| ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1822,plain,
! [SV544: $i,SV405: $i,SV206: $i] :
( ( ( subset @ SV206 @ SV405 )
= $false )
| ( ( ~ ( subset @ SV405 @ SV544 )
| ( subset @ SV206 @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1823,plain,
! [SV406: $i,SV207: $i,SV545: $i] :
( ( ( in @ SV545 @ ( setadjoin @ SV207 @ ( setadjoin @ SV406 @ emptyset ) ) )
= $false )
| ( ( ( SV545 = SV207 )
| ( SV545 = SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1824,plain,
! [SV407: $i,SV210: $i] :
( ( ( SV210 = SV407 )
= $true )
| ( ( ~ ( in @ SV407 @ ( setadjoin @ SV210 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1825,plain,
! [SV408: $i,SV211: $i,SV546: $i] :
( ( ( in @ SV546 @ ( cartprod @ SV211 @ SV408 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV546 ) @ ( ksnd @ SV546 ) )
= SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1826,plain,
! [SV410: $i,SV213: $i,SV547: $i] :
( ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false )
| ( ( ! [SY1071: $i > $o] :
( ~ ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV213 )
| ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV410 )
| ~ ( in @ ( kpair @ SY1072 @ SY1073 ) @ SV547 )
| ( SY1071 @ ( kpair @ SY1072 @ SY1073 ) ) ) )
| ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV547 )
| ( SY1071 @ SY1074 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1827,plain,
! [SV214: $i,SV411: $i,SV548: $i] :
( ( ( in @ SV548 @ SV411 )
= $false )
| ( ( in @ SV548 @ ( binunion @ SV214 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1828,plain,
! [SV413: $i,SV216: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV216 )
| ~ ( in @ SV594 @ SV413 )
| ~ ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1829,plain,
! [SV595: $i > $o,SV415: $i,SV218: $i] :
( ( ( ! [SY1123: $i > $o] :
( ~ ! [SY1124: $i] :
( ~ ( in @ SY1124 @ SV218 )
| ! [SY1125: $i] :
( ~ ( in @ SY1125 @ SV415 )
| ( SY1124 != SY1125 )
| ~ ( ~ ( ~ ( SV595 @ SY1124 )
| ( SY1123 @ SY1125 ) )
| ~ ( ~ ( SY1123 @ SY1125 )
| ( SV595 @ SY1124 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SX4: $i] : ( SY1123 @ SX4 ) ) ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1830,plain,
! [SV419: $i,SV222: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ ( powerset @ SV222 ) )
| ~ ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV222 )
| ~ ( in @ SY1128 @ SV419 )
| ( in @ SY1128 @ SV596 ) )
| ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1831,plain,
! [SV421: $i > $o,SV224: $i] :
( ( ( ! [SY898: $i] :
( ~ ( in @ SY898 @ SV224 )
| ( SV421 @ SY898 ) ) )
= $true )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1832,plain,
! [SV422: $i > $o,SV225: $i,SV549: $i] :
( ( ( in @ SV549 @ SV225 )
= $false )
| ( ( ~ ( SV422 @ SV549 )
| ( in @ SV549
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1833,plain,
! [SV226: $i,SV550: $i,SV423: $i] :
( ( ( in @ SV423 @ SV550 )
= $false )
| ( ( ~ ( in @ SV550 @ SV226 )
| ( in @ SV423 @ ( setunion @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1834,plain,
! [SV424: $i,SV227: $i,SV551: $i] :
( ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( ! [SY1076: $i] :
( ~ ( subset @ SY1076 @ ( cartprod @ SV227 @ SV424 ) )
| ~ ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV227 )
| ! [SY1078: $i] :
( ~ ( in @ SY1078 @ SV424 )
| ~ ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV551 )
| ( in @ ( kpair @ SY1077 @ SY1078 ) @ SY1076 ) ) )
| ( subset @ SV551 @ SY1076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1835,plain,
! [SV425: $i,SV229: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV229 ) )
= $false )
| ( ( ~ ( in @ SV552 @ ( setminus @ SV229 @ SV425 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1836,plain,
! [SV426: $i,SV230: $i,SV568: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ SV553 @ SV568 ) @ ( cartprod @ SV230 @ SV426 ) ) )
= $true )
| ( ( in @ SV553 @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1837,plain,
! [SV427: $i > $o,SV231: $i] :
( ( ( ! [SY910: $i] :
~ ~ ( ~ ( in @ SY910 @ SV231 )
| ~ ( SV427 @ SY910 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1838,plain,
! [SV1: $i,SV428: $i,SV233: $i > $o] :
( ( ( ~ ( SV233 @ SV428 ) )
= $true )
| ( ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset )
= $true )
| ( ( in @ SV428 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1839,plain,
! [SV2: $i,SV429: $i,SV234: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV234 )
| ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SV597 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) ) )
= $true )
| ( ( in @ SV429 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1840,plain,
! [SV3: $i,SV430: $i > $i,SV235: $i] :
( ( ( ~ ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 )
| ( in @ ( SV430 @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) ) @ SV235 ) )
= $false )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1651]) ).
thf(1841,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1842,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ! [SY1095: $i] :
~ ~ ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1843,plain,
! [SV431: $i,SV237: $i,SV5: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV5 )
| ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SV598 ) @ SV237 ) )
= $true )
| ( ( func @ SV5 @ SV237 @ SV431 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1844,plain,
! [SV432: $i > $i > $o,SV238: $i,SV6: $i,SV569: $i,SV554: $i] :
( ( ( ~ ( in @ ( kpair @ SV554 @ SV569 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SY920: $i,SY921: $i] : ( SV432 @ SY920 @ SY921 ) ) ) )
= $true )
| ( ( SV432 @ SV554 @ SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1845,plain,
! [SV239: $i,SV8: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( in @ ( setminus @ SV239 @ SV570 ) @ ( powerset @ SV8 ) )
= $true )
| ( ( in @ SV239 @ ( powerset @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1846,plain,
! [SV11: $i,SV434: $i > $i,SV242: $i] :
( ( ( ~ ( in @ ( sK19_SY923 @ SV242 @ SV434 @ SV11 ) @ SV11 )
| ( in @ ( SV434 @ ( sK19_SY923 @ SV242 @ SV434 @ SV11 ) ) @ SV242 ) )
= $false )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1657]) ).
thf(1847,plain,
! [SV435: $i,SV244: $o,SV14: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV14 )
| ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) ) )
= $true )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1848,plain,
! [SV436: $i,SV14: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV14 )
| ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) ) )
= $true )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1849,plain,
! [SV437: $i,SV14: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV14 )
| ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) ) )
= $true )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1850,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ SV571 )
| ~ ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) ) )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1851,plain,
! [SV438: $i,SV245: $i,SV17: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV17 )
| ( ( ap @ SV17 @ SV245 @ SV438 @ SV602 )
= ( ap @ SV17 @ SV245 @ SV438 @ SV602 ) ) )
= $true )
| ( ( func @ SV17 @ SV245 @ SV438 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1852,plain,
! [SV18: $i,SV572: $i] :
( ( ( in @ SV572 @ SV18 )
= $false )
| ( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1853,plain,
! [SV19: $i,SV555: $i] :
( ( ( in @ SV555 @ SV19 )
= $false )
| ( ( ( setunion @ SV19 )
= SV555 )
= $true )
| ( ( singleton @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1854,plain,
! [SV246: $i > $o,SV20: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ SV20 ) )
= $true )
| ( ( ! [SY1100: $i] :
( ~ ( in @ SY1100 @ SV20 )
| ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SY1100 )
| ( SV573 = SY1100 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1855,plain,
! [SV22: $i,SV439: $i,SV247: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV247 )
| ( ( kpair @ SV439 @ SV603 )
= ( kpair @ SV439 @ SV603 ) ) )
= $true )
| ( ( in @ SV439 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1856,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1857,plain,
! [SV23: $i] :
( ( ~ ! [SY942: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY942 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY942 ) )
| ~ ! [SY945: $i] :
~ ~ ! [SY946: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY945 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY946 @ SY942 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY945 )
| ~ ( in @ SX5 @ SY942 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY945 ) )
| ( in @ SY946 @ SY948 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1858,plain,
! [SV574: $o,SV24: $i,SV248: $i] :
( ( ( ~ ! [SY1101: $i] :
( ~ ( in @ SV248 @ SY1101 )
| ~ ( in @ SY1101 @ SV24 )
| SV574 ) )
= $true )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1859,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1860,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1861,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV575 )
| ~ ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) ) )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1862,plain,
! [SV250: $i,SV28: $i,SV440: $i] :
( ( ( SV440 = SV28 )
= $true )
| ( ( in @ SV440 @ SV250 )
= $true )
| ( ( in @ SV440 @ ( setadjoin @ SV28 @ SV250 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1863,plain,
! [SV441: $i,SV251: $i,SV29: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ SV29 )
| ( ( ap @ SV29 @ SV251 @ SV441 @ SV604 )
= ( ap @ SV29 @ SV251 @ SV441 @ SV604 ) ) )
= $true )
| ( ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1864,plain,
! [SV30: $i,SV442: $i,SV252: $i > $o] :
( ( ( ~ ( SV252 @ SV442 ) )
= $true )
| ( ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) )
= $true )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1865,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ ( setunion @ SV33 ) ) )
= $true )
| ( ( ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1866,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1867,plain,
! [SV34: $i,SV255: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV255 ) )
= $true )
| ( ( ~ ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) ) )
= $true )
| ( ( in @ SV443 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1868,plain,
! [SV36: $i,SV576: $i] :
( ( ( in @ SV576 @ SV36 )
= $false )
| ( ( SV36 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1869,plain,
! [SV37: $i,SV444: $i,SV257: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV257 )
| ( ( kfst @ ( kpair @ SV444 @ SV605 ) )
= SV444 ) )
= $true )
| ( ( in @ SV444 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1870,plain,
! [SV38: $i,SV258: $i,SV445: $i] :
( ( ( ~ ~ ( in @ SV445 @ SV258 ) )
= $true )
| ( ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) )
= $true )
| ( ( in @ SV445 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1871,plain,
! [SV39: $i,SV259: $i,SV446: $i] :
( ( ( ~ ~ ( in @ SV446 @ SV259 ) )
= $true )
| ( ( SV39 != SV259 )
= $true )
| ( ( in @ SV446 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1872,plain,
! [SV261: $i,SV41: $i,SV447: $i] :
( ( ( SV447 = SV41 )
= $true )
| ( ( SV447 = SV261 )
= $true )
| ( ( in @ SV447 @ ( setadjoin @ SV41 @ ( setadjoin @ SV261 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1873,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ( ( sK8_SY642 @ SV262 @ SV42 )
!= ( sK20_SY1103 @ SV42 @ SV262 ) )
| ~ ( ~ ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
| ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1684]) ).
thf(1874,plain,
! [SV43: $i,SV263: $i,SV448: $i] :
( ( ( ~ ~ ( in @ SV448 @ SV263 ) )
= $true )
| ( ( ~ ( in @ SV448 @ SV43 ) )
= $true )
| ( ( subset @ SV43 @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1875,plain,
! [SV449: $i,SV264: $i,SV44: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV44 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY1133: $i] : ( in @ ( kpair @ SV606 @ SY1133 ) @ SV449 ) ) )
@ SV264 ) )
= $true )
| ( ( func @ SV44 @ SV264 @ SV449 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1876,plain,
! [SV265: $i,SV45: $i,SV450: $i] :
( ( ( in @ SV450 @ SV45 )
= $true )
| ( ( ~ ~ ( in @ SV450 @ SV265 )
| ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1877,plain,
! [SV267: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK9_SY657 @ SV47 @ SV267 ) @ SV267 ) )
= $false )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1878,plain,
! [SV267: $i,SV47: $i] :
( ( ( in @ ( sK9_SY657 @ SV47 @ SV267 ) @ SV47 )
= $false )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1879,plain,
! [SV268: $i > $o,SV48: $i,SV607: $i] :
( ( ( ~ ~ ( ~ ( in @ SV607 @ SV48 )
| ~ ~ ( SV268 @ SV607 ) ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1880,plain,
! [SV49: $i,SV451: $i > $i,SV269: $i] :
( ( ( ~ ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 )
| ( in @ ( SV451 @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) ) @ SV269 ) )
= $false )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1690]) ).
thf(1881,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV577 )
| ~ ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) ) )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1882,plain,
! [SV556: $o,SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| SV556 )
| ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1883,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $true )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1884,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $false )
| ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1885,plain,
! [SV54: $i,SV273: $i,SV454: $i] :
( ( ( in @ SV454 @ SV273 )
= $false )
| ( ( in @ SV454 @ ( setminus @ SV54 @ SV273 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1886,plain,
! [SV274: $i,SV55: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV55 ) )
= $true )
| ( ( in @ SV455 @ SV274 )
= $true )
| ( ( subset @ SV55 @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1887,plain,
! [SV275: $i,SV56: $i,SV608: $i,SV578: $i] :
( ( ( ( SV578 != SV608 )
| ( ( setadjoin @ SV56 @ SV578 )
= ( setadjoin @ SV275 @ SV608 ) ) )
= $true )
| ( ( SV56 = SV275 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1888,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SV609 )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1699]) ).
thf(1889,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $true )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1699]) ).
thf(1890,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $false )
| ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1699]) ).
thf(1891,plain,
! [SV61: $i,SV280: $i] :
( ( ( ~ ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 ) )
= $false )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1892,plain,
! [SV61: $i,SV280: $i] :
( ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1701]) ).
thf(1893,plain,
! [SV458: $i,SV281: $o,SV62: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV62 )
| ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SV610 )
= SV458 ) )
= $true )
| ( ( in @ SV458 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1894,plain,
! [SV459: $i,SV62: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV62 )
| ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SV611 )
= SV459 ) )
= $true )
| ( ( in @ SV459 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1895,plain,
! [SV460: $i,SV62: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ SV62 )
| ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SV612 )
= SV460 ) )
= $true )
| ( ( in @ SV460 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1896,plain,
! [SV285: $i,SV66: $i] :
( ( ( SV66 = SV285 )
= $false )
| ( ( subset @ SV66 @ SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1897,plain,
! [SV464: $i,SV286: $o,SV67: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV67 )
| ~ ~ SV286
| ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1898,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( ( ~ ( in @ SV614 @ SV67 )
| ~ ~ $true
| ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) ) )
= $true )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1899,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ SV67 )
| ~ ~ $false
| ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) ) )
= $true )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1900,plain,
! [SV68: $i,SV287: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 ) )
= $false )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1901,plain,
! [SV68: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) ) )
= $false )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1902,plain,
! [SV288: $i > $o,SV69: $i] :
( ( ( ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV69 )
| ~ ( SV288 @ SY686 ) ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1903,plain,
! [SV70: $i,SV289: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ SV289 ) )
= $true )
| ( ( in @ SV467 @ SV70 )
= $true )
| ( ( in @ SV289 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1904,plain,
! [SV73: $i,SV469: $i,SV291: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV291 )
| ( ( ksnd @ ( kpair @ SV469 @ SV616 ) )
= SV616 ) )
= $true )
| ( ( in @ SV469 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1905,plain,
! [SV292: $i,SV74: $i,SV617: $i,SV579: $i] :
( ( ( ( SV579 != SV617 )
| ~ ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) )
| ~ ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) ) ) )
= $true )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1906,plain,
! [SV75: $i,SV470: $i > $i,SV293: $i] :
( ( ( ~ ( in @ ( sK22_SY971 @ SV293 @ SV470 @ SV75 ) @ SV75 )
| ( in @ ( SV470 @ ( sK22_SY971 @ SV293 @ SV470 @ SV75 ) ) @ SV293 ) )
= $false )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1717]) ).
thf(1907,plain,
! [SV294: $i > $o,SV76: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV76 )
| ( SV294 @ SV618 ) )
= $true )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1908,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i] :
( ( ( ~ ( func @ SV77 @ SV295 @ SV619 )
| ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY1137 )
= ( ap @ SV77 @ SV295 @ SV619 @ SY1137 ) ) )
| ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1909,plain,
! [SV297: $i,SV79: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SY1107 @ SV297 )
| ( in @ SY1107 @ SV580 ) ) )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1910,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV581 )
| ~ ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) ) )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1911,plain,
! [SV298: $i,SV81: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ ( powerset @ SV81 ) ) )
= $true )
| ( ( ~ ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV81 )
| ~ ( in @ SY1109 @ SV298 )
| ( in @ SY1109 @ SV582 ) )
| ( in @ SV298 @ ( powerset @ SV582 ) ) )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1912,plain,
! [SV473: $i,SV299: $i,SV82: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
| ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY1140 )
= ( ap @ SV82 @ SV299 @ SV620 @ SY1140 ) ) )
| ( SV473 = SV620 ) )
= $true )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1913,plain,
! [SV474: $i,SV301: $i,SV85: $i,SV621: $i] :
( ( ( ~ ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
| ~ ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV85 )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV301 )
| ~ ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV474 )
| ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV621 ) ) )
| ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1914,plain,
! [SV475: $i,SV302: $o,SV86: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ SV86 )
| ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY1145: $i] :
( ~ ( ~ SV302
| ( SY1145 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY1145 != SV622 ) ) ) ) ) )
= $true )
| ( ( in @ SV475 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1915,plain,
! [SV476: $i,SV86: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ SV86 )
| ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY1146: $i] :
( ~ ( ~ $true
| ( SY1146 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY1146 != SV623 ) ) ) ) ) )
= $true )
| ( ( in @ SV476 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1916,plain,
! [SV477: $i,SV86: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ SV86 )
| ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY1147: $i] :
( ~ ( ~ $false
| ( SY1147 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY1147 != SV624 ) ) ) ) ) )
= $true )
| ( ( in @ SV477 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1917,plain,
! [SV557: $i,SV479: $i,SV304: $i,SV88: $i] :
( ( ( ( kpair @ SV88 @ SV304 )
= ( kpair @ SV479 @ SV557 ) )
= $false )
| ( ( SV304 = SV557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1918,plain,
! [SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY252 @ SV89 ) @ SV89 )
| ~ $true ) )
= $false )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1732]) ).
thf(1919,plain,
! [SV480: $i > $i > $o,SV305: $i,SV90: $i,SV558: $i] :
( ( ( in @ SV558 @ SV90 )
= $false )
| ( ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV305 )
| ~ ( SV480 @ SV558 @ SY1083 )
| ( in @ ( kpair @ SV558 @ SY1083 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1920,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ( ~ ( SV91 @ SV583 )
| ~ ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) ) )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1921,plain,
! [SV92: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK12_SY730 @ SV306 @ SV92 ) @ SV92 ) )
= $false )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1922,plain,
! [SV92: $i,SV306: $i] :
( ( ( in @ ( sK12_SY730 @ SV306 @ SV92 ) @ SV306 )
= $false )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1735]) ).
thf(1923,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY732 @ SV308 @ SV95 ) @ SV95 )
| ~ ( SV308 @ ( sK24_SY732 @ SV308 @ SV95 ) ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1736]) ).
thf(1924,plain,
! [SV309: $i > $o,SV96: $i] :
( ( ( ! [SY733: $i] :
~ ~ ( ~ ( in @ SY733 @ SV96 )
| ~ ( SV309 @ SY733 ) ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1925,plain,
! [SV98: $i,SV481: $i,SV311: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV311 )
| ( in @ ( kpair @ SV481 @ SV625 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) ) )
= $true )
| ( ( in @ SV481 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1926,plain,
! [SV99: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ ( powerset @ SV99 ) ) )
= $true )
| ( ( ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1927,plain,
! [SV99: $i,SV312: $i] :
( ( ( ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) ) )
= $true )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1928,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
| ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1929,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ~ ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
| ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(1930,plain,
! [SV104: $i,SV484: $i,SV317: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV317 )
| ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SV626 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) ) )
= $true )
| ( ( in @ SV484 @ SV104 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1931,plain,
! [SV318: $i,SV105: $i,SV627: $i,SV584: $i] :
( ( ( ( SV584 != SV627 )
| ~ ( in @ SV584 @ SV105 )
| ( in @ SV627 @ SV318 ) )
= $true )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1932,plain,
! [SV485: $i,SV321: $i,SV108: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ SV108 )
| ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV321 )
| ~ ( in @ ( kpair @ SV628 @ SY1148 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SY1148 ) ) )
= $true )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1933,plain,
( ( in @ sK3_SY2 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1934,plain,
( ( ~ ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1935,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) )
| ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1936,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( ~ ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) )
| ~ ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) )
= $false )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1937,plain,
! [SV487: $i,SV325: $o,SV113: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV113 )
| ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1149: $i] :
( ~ ( ~ SV325
| ( SY1149 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1149 != SV629 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) )
= $true )
| ( ( in @ SV487 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1938,plain,
! [SV488: $i,SV113: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV113 )
| ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1150: $i] :
( ~ ( ~ $true
| ( SY1150 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1150 != SV630 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) )
= $true )
| ( ( in @ SV488 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1939,plain,
! [SV489: $i,SV113: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV113 )
| ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1151: $i] :
( ~ ( ~ $false
| ( SY1151 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1151 != SV631 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) )
= $true )
| ( ( in @ SV489 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1940,plain,
! [SV114: $i] :
( ( ( ~ ( in @ ( sK25_SY310 @ SV114 ) @ SV114 ) )
= $false )
| ( ( SV114 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1754]) ).
thf(1941,plain,
! [SV326: $i,SV115: $i,SV559: $i,SV490: $i] :
( ( ( in @ ( kpair @ SV490 @ SV559 ) @ ( cartprod @ SV115 @ SV326 ) )
= $false )
| ( ( in @ SV559 @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1942,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1943,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY1112: $i] :
( ~ ( in @ SY1112 @ SV121 )
| ~ ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
| ~ ( SV331 @ SY1112 )
| ( ( sK14_SY760 @ SV331 @ SV121 )
= SY1112 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1758]) ).
thf(1944,plain,
! [SV493: $i,SV332: $o,SV122: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV122 )
| ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 ) )
= $true )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(1945,plain,
! [SV494: $i,SV122: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV122 )
| ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 ) )
= $true )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1946,plain,
! [SV495: $i,SV122: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ SV122 )
| ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 ) )
= $true )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1947,plain,
! [SV123: $i,SV496: $i > $i,SV333: $i] :
( ( ( ~ ( in @ ( sK26_SY1013 @ SV333 @ SV496 @ SV123 ) @ SV123 )
| ( in @ ( SV496 @ ( sK26_SY1013 @ SV333 @ SV496 @ SV123 ) ) @ SV333 ) )
= $false )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1762]) ).
thf(1948,plain,
! [SV497: $i,SV337: $o,SV125: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV125 )
| ( in @ ( if @ SV125 @ SV337 @ SV497 @ SV635 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SV635 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV497 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(1949,plain,
! [SV498: $i,SV125: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV125 )
| ( in @ ( if @ SV125 @ $true @ SV498 @ SV636 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SV636 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV498 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1950,plain,
! [SV499: $i,SV125: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ SV125 )
| ( in @ ( if @ SV125 @ $false @ SV499 @ SV637 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SV637 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV499 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(1951,plain,
! [SV129: $i,SV341: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV341 ) )
= $true )
| ( ( in @ SV500 @ ( binintersect @ SV129 @ SV341 ) )
= $true )
| ( ( in @ SV500 @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1952,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i,SV560: $i] :
( ( ( in @ SV560 @ SV130 )
= $false )
| ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV342 )
| ~ ( in @ ( kpair @ SV560 @ SY1086 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SY1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1953,plain,
! [SV502: $i,SV345: $o,SV133: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV133 )
| ( in @ ( if @ SV133 @ SV345 @ SV502 @ SV638 ) @ SV133 ) )
= $true )
| ( ( in @ SV502 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1954,plain,
! [SV503: $i,SV133: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV133 )
| ( in @ ( if @ SV133 @ $true @ SV503 @ SV639 ) @ SV133 ) )
= $true )
| ( ( in @ SV503 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(1955,plain,
! [SV504: $i,SV133: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV133 )
| ( in @ ( if @ SV133 @ $false @ SV504 @ SV640 ) @ SV133 ) )
= $true )
| ( ( in @ SV504 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(1956,plain,
! [SV347: $i,SV135: $i,SV505: $i] :
( ( ( in @ SV505 @ SV135 )
= $true )
| ( ( ~ ( in @ SV505 @ SV347 )
| ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1957,plain,
! [SV561: $i,SV506: $i,SV349: $i,SV137: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV137 @ ( setadjoin @ SV349 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV561 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV349 = SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1958,plain,
! [SV562: $i,SV507: $i,SV350: $i,SV138: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV138 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV138 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV507 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV507 @ ( setadjoin @ SV562 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV138 = SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1959,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1774]) ).
thf(1960,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY1113: $i] :
( ~ ( in @ SY1113 @ SV139 )
| ~ ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
| ~ ( SV351 @ SY1113 )
| ( ( sK15_SY786 @ SV351 @ SV139 )
= SY1113 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1774]) ).
thf(1961,plain,
! [SV143: $i,SV508: $i,SV355: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV355 )
| ( in @ ( kpair @ SV508 @ SV641 ) @ ( cartprod @ SV143 @ SV355 ) ) )
= $true )
| ( ( in @ SV508 @ SV143 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1962,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( ~ ( SV145 @ SV585 )
| ~ ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) ) )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1963,plain,
! [SV358: $i,SV147: $i,SV509: $i] :
( ( ( in @ SV509 @ SV147 )
= $true )
| ( ( in @ SV509 @ SV358 )
= $true )
| ( ( in @ SV509 @ ( binunion @ SV147 @ SV358 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1964,plain,
! [SV510: $i,SV360: $o,SV150: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1152: $i] :
( ~ ( ~ SV360
| ( SY1152 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1152 != SV642 ) ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1965,plain,
! [SV511: $i,SV150: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1153: $i] :
( ~ ( ~ $true
| ( SY1153 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1153 != SV643 ) ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1966,plain,
! [SV512: $i,SV150: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV150 )
| ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1154: $i] :
( ~ ( ~ $false
| ( SY1154 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1154 != SV644 ) ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1967,plain,
! [SV361: $i,SV152: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( powerset @ SV152 ) ) )
= $true )
| ( ( ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV152 )
| ~ ( in @ SY1115 @ SV361 )
| ( in @ SY1115 @ SV586 ) )
| ( subset @ SV361 @ SV586 ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(1968,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY1116: $i] :
~ ( ~ ( ~ ( SV153 @ SY1116 )
| ( SY1116 = SV587 ) )
| ~ ( ( SY1116 != SV587 )
| ( SV153 @ SY1116 ) ) ) )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1969,plain,
! [SV155: $i,SV363: $i] :
( ( ( ~ ( in @ ( sK16_SY798 @ SV363 @ SV155 ) @ SV155 ) )
= $false )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1970,plain,
! [SV155: $i,SV363: $i] :
( ( ( in @ ( sK16_SY798 @ SV363 @ SV155 ) @ SV363 )
= $false )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1783]) ).
thf(1971,plain,
! [SV513: $i,SV364: $i,SV156: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV156 )
| ! [SY1155: $i] :
( ~ ( in @ SY1155 @ SV364 )
| ~ ( in @ ( kpair @ SV645 @ SY1155 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SY1155 ) ) )
= $true )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1972,plain,
! [SV514: $i,SV365: $i,SV157: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV157 )
| ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SV646 ) @ SV365 ) )
= $true )
| ( ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1973,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) )
= $true )
| ( ( ~ ( in @ SV515 @ SV158 )
| ( in @ SV515 @ SV366 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1974,plain,
! [SV518: $i,SV647: $i,SV369: $i,SV162: $i] :
( ( ( ~ ( func @ SV162 @ SV369 @ SV647 )
| ~ ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1156 )
= ( ap @ SV162 @ SV369 @ SV647 @ SY1156 ) ) )
| ( SV518 = SV647 ) )
= $true )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1975,plain,
! [SV163: $i] :
( ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ~ ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) )
= $true )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1976,plain,
! [SV519: $i > $i > $o,SV370: $i,SV164: $i,SV588: $i,SV563: $i] :
( ( ( ~ ( in @ ( kpair @ SV563 @ SV588 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SY1042: $i,SY1043: $i] : ( SV519 @ SY1042 @ SY1043 ) ) ) )
= $true )
| ( ( in @ SV588 @ SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(1977,plain,
! [SV520: $i,SV371: $i,SV165: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV165 )
| ( in @ ( kpair @ SV648 @ ( ap @ SV165 @ SV371 @ SV520 @ SV648 ) ) @ SV520 ) )
= $true )
| ( ( func @ SV165 @ SV371 @ SV520 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1978,plain,
! [SV372: $i,SV649: $o,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| SV649 )
| ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1793]) ).
thf(1979,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| $true )
| ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1793]) ).
thf(1980,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| $false )
| ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1793]) ).
thf(1981,plain,
! [SV373: $i,SV167: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ ( powerset @ SV167 ) ) )
= $true )
| ( ( in @ ( binunion @ SV373 @ SV589 ) @ ( powerset @ SV167 ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1982,plain,
! [SV168: $i,SV522: $i,SV374: $i,SV650: $i] :
( ( ( ~ ( in @ SV650 @ SV374 )
| ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SV650 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) ) )
= $true )
| ( ( in @ SV522 @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1983,plain,
! [SV169: $i,SV375: $i,SV523: $i] :
( ( ( ~ ( subset @ SV523 @ SV375 ) )
= $true )
| ( ( subset @ SV523 @ ( binintersect @ SV169 @ SV375 ) )
= $true )
| ( ( subset @ SV523 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1984,plain,
! [SV564: $i,SV524: $i,SV376: $i,SV170: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SV564 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV524 != SV564 )
| ( SV376 = SV564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1985,plain,
! [SV174: $i,SV379: $i] :
( ( ( subset @ SV379 @ SV174 )
= $false )
| ( ( SV174 = SV379 )
= $true )
| ( ( subset @ SV174 @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1986,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( ~ ( SV175 @ SV590 )
| ~ ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) ) )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1987,plain,
! [SV527: $i,SV380: $i,SV176: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV176 )
| ( in @ ( kpair @ SV651 @ ( ap @ SV176 @ SV380 @ SV527 @ SV651 ) ) @ SV527 ) )
= $true )
| ( ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(1988,plain,
! [SV528: $i > $i > $o,SV381: $i,SV177: $i,SV591: $i,SV565: $i] :
( ( ( ~ ( in @ ( kpair @ SV565 @ SV591 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SY1053: $i,SY1054: $i] : ( SV528 @ SY1053 @ SY1054 ) ) ) )
= $true )
| ( ( in @ SV565 @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(1989,plain,
! [SV382: $i,SV178: $i] :
( ( ( ! [SY836: $i] :
~ ~ ( ~ ( in @ SY836 @ SV178 )
| ~ ( in @ SY836 @ SV382 ) ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1990,plain,
! [SV652: $i > $o,SV529: $i,SV383: $i,SV179: $i] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV179 )
| ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV383 )
| ~ ( in @ ( kpair @ SY1157 @ SY1158 ) @ SV529 )
| ( SV652 @ ( kpair @ SY1157 @ SY1158 ) ) ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1991,plain,
! [SV384: $i,SV182: $i,SV530: $i] :
( ( ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
= $true )
| ( ( ~ ~ ( in @ SV530 @ SV384 )
| ~ ( in @ SV530 @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1992,plain,
! [SV533: $i,SV388: $i,SV187: $i] :
( ( ( ! [SY1059: $i] :
~ ~ ( ~ ( in @ SY1059 @ SV187 )
| ~ ~ ! [SY1060: $i] :
~ ~ ( ~ ( in @ SY1060 @ SV388 )
| ( SV533
!= ( kpair @ SY1059 @ SY1060 ) ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1993,plain,
! [SV389: $i,SV188: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ ( powerset @ SV188 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV389 @ SV592 ) @ ( powerset @ SV188 ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1994,plain,
! [SV191: $i,SV391: $i,SV534: $i] :
( ( ( ~ ~ ( in @ SV534 @ SV391 ) )
= $true )
| ( ( ~ ( subset @ SV191 @ SV391 ) )
= $true )
| ( ( in @ SV534 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1995,plain,
! [SV192: $i,SV535: $i,SV392: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ SV392 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SV653 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) ) )
= $true )
| ( ( in @ SV535 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(1996,plain,
! [SV536: $i,SV393: $i,SV193: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV193 )
| ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1160: $i] : ( in @ ( kpair @ SV654 @ SY1160 ) @ SV536 ) ) ) )
= $true )
| ( ( func @ SV193 @ SV393 @ SV536 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(1997,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ SV593 )
= $false )
| ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) )
| ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1998,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ( ( sK17_SY858 @ SV396 @ SV197 )
!= ( sK27_SY1122 @ SV197 @ SV396 ) )
| ~ ( ~ ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
| ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1816]) ).
thf(1999,plain,
! [SV398: $i,SV199: $i,SV539: $i] :
( ( ( in @ SV539 @ ( setminus @ SV199 @ SV398 ) )
= $false )
| ( ( in @ SV539 @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(2000,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY868 @ SV399 @ SV200 ) @ SV200 )
| ~ ( in @ SV399 @ ( sK28_SY868 @ SV399 @ SV200 ) ) ) )
= $false )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1818]) ).
thf(2001,plain,
! [SV202: $i,SV541: $i > $i,SV401: $i] :
( ( ( ~ ( in @ ( sK29_SY1067 @ SV401 @ SV541 @ SV202 ) @ SV202 )
| ( in @ ( SV541 @ ( sK29_SY1067 @ SV401 @ SV541 @ SV202 ) ) @ SV401 ) )
= $false )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1819]) ).
thf(2002,plain,
! [SV567: $i,SV542: $i,SV402: $i,SV203: $i] :
( ( ( ( kpair @ SV203 @ SV402 )
= ( kpair @ SV542 @ SV567 ) )
= $false )
| ( ( SV203 = SV542 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(2003,plain,
! [SV205: $i,SV404: $i,SV543: $i] :
( ( ( ~ ~ ( in @ SV543 @ SV404 ) )
= $true )
| ( ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) )
= $true )
| ( ( in @ SV543 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2004,plain,
! [SV206: $i,SV544: $i,SV405: $i] :
( ( ( ~ ( subset @ SV405 @ SV544 ) )
= $true )
| ( ( subset @ SV206 @ SV544 )
= $true )
| ( ( subset @ SV206 @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2005,plain,
! [SV406: $i,SV207: $i,SV545: $i] :
( ( ( SV545 = SV207 )
= $true )
| ( ( SV545 = SV406 )
= $true )
| ( ( in @ SV545 @ ( setadjoin @ SV207 @ ( setadjoin @ SV406 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2006,plain,
! [SV210: $i,SV407: $i] :
( ( ( in @ SV407 @ ( setadjoin @ SV210 @ emptyset ) )
= $false )
| ( ( SV210 = SV407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2007,plain,
! [SV655: $i > $o,SV547: $i,SV410: $i,SV213: $i] :
( ( ( ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV213 )
| ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV410 )
| ~ ( in @ ( kpair @ SY1161 @ SY1162 ) @ SV547 )
| ( SV655 @ ( kpair @ SY1161 @ SY1162 ) ) ) )
| ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2008,plain,
! [SV413: $i,SV216: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV594 @ SV413 )
| ~ ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2009,plain,
! [SV656: $i > $o,SV595: $i > $o,SV415: $i,SV218: $i] :
( ( ( ~ ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV218 )
| ! [SY1165: $i] :
( ~ ( in @ SY1165 @ SV415 )
| ( SY1164 != SY1165 )
| ~ ( ~ ( ~ ( SV595 @ SY1164 )
| ( SV656 @ SY1165 ) )
| ~ ( ~ ( SV656 @ SY1165 )
| ( SV595 @ SY1164 ) ) ) ) )
| ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2010,plain,
! [SV419: $i,SV222: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ ( powerset @ SV222 ) ) )
= $true )
| ( ( ~ ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV222 )
| ~ ( in @ SY1128 @ SV419 )
| ( in @ SY1128 @ SV596 ) )
| ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2011,plain,
! [SV421: $i > $o,SV224: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV224 )
| ( SV421 @ SV657 ) )
= $true )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2012,plain,
! [SV225: $i,SV549: $i,SV422: $i > $o] :
( ( ( ~ ( SV422 @ SV549 ) )
= $true )
| ( ( in @ SV549
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) )
= $true )
| ( ( in @ SV549 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2013,plain,
! [SV423: $i,SV226: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV226 ) )
= $true )
| ( ( in @ SV423 @ ( setunion @ SV226 ) )
= $true )
| ( ( in @ SV423 @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2014,plain,
! [SV551: $i,SV424: $i,SV227: $i,SV658: $i] :
( ( ( ~ ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
| ~ ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV227 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV424 )
| ~ ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV551 )
| ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV658 ) ) )
| ( subset @ SV551 @ SV658 ) )
= $true )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2015,plain,
! [SV425: $i,SV229: $i,SV552: $i] :
( ( ( in @ SV552 @ SV229 )
= $true )
| ( ( ~ ( in @ SV552 @ ( setminus @ SV229 @ SV425 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(2016,plain,
! [SV426: $i,SV230: $i,SV568: $i,SV553: $i] :
( ( ( in @ ( kpair @ SV553 @ SV568 ) @ ( cartprod @ SV230 @ SV426 ) )
= $false )
| ( ( in @ SV553 @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2017,plain,
! [SV427: $i > $o,SV231: $i,SV659: $i] :
( ( ( ~ ~ ( ~ ( in @ SV659 @ SV231 )
| ~ ( SV427 @ SV659 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2018,plain,
! [SV1: $i,SV428: $i,SV233: $i > $o] :
( ( ( SV233 @ SV428 )
= $false )
| ( ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
!= emptyset )
= $true )
| ( ( in @ SV428 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2019,plain,
! [SV2: $i,SV429: $i,SV234: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV234 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SV597 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) )
= $true )
| ( ( in @ SV429 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2020,plain,
! [SV3: $i,SV430: $i > $i,SV235: $i] :
( ( ( ~ ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(2021,plain,
! [SV3: $i,SV235: $i,SV430: $i > $i] :
( ( ( in @ ( SV430 @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) ) @ SV235 )
= $false )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(2022,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(2023,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ! [SY1095: $i] :
~ ~ ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1095 )
| ~ ! [SY1096: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1096 )
| ( SY1095 = SY1096 ) ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(2024,plain,
! [SV431: $i,SV237: $i,SV5: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV5 ) )
= $true )
| ( ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SV598 ) @ SV237 )
= $true )
| ( ( func @ SV5 @ SV237 @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2025,plain,
! [SV432: $i > $i > $o,SV238: $i,SV6: $i,SV569: $i,SV554: $i] :
( ( ( in @ ( kpair @ SV554 @ SV569 )
@ ( dpsetconstr @ SV6 @ SV238
@ ^ [SY920: $i,SY921: $i] : ( SV432 @ SY920 @ SY921 ) ) )
= $false )
| ( ( SV432 @ SV554 @ SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2026,plain,
! [SV239: $i,SV8: $i,SV570: $i] :
( ( ( in @ SV570 @ ( powerset @ SV8 ) )
= $false )
| ( ( in @ ( setminus @ SV239 @ SV570 ) @ ( powerset @ SV8 ) )
= $true )
| ( ( in @ SV239 @ ( powerset @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(2027,plain,
! [SV11: $i,SV434: $i > $i,SV242: $i] :
( ( ( ~ ( in @ ( sK19_SY923 @ SV242 @ SV434 @ SV11 ) @ SV11 ) )
= $false )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(2028,plain,
! [SV11: $i,SV242: $i,SV434: $i > $i] :
( ( ( in @ ( SV434 @ ( sK19_SY923 @ SV242 @ SV434 @ SV11 ) ) @ SV242 )
= $false )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1846]) ).
thf(2029,plain,
! [SV435: $i,SV244: $o,SV14: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV14 ) )
= $true )
| ( ( ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) ) )
= $true )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2030,plain,
! [SV436: $i,SV14: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV14 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) ) )
= $true )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2031,plain,
! [SV437: $i,SV14: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV14 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) ) )
= $true )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2032,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV571 )
| ~ ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(2033,plain,
! [SV438: $i,SV245: $i,SV17: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV17 ) )
= $true )
| ( ( ( ap @ SV17 @ SV245 @ SV438 @ SV602 )
= ( ap @ SV17 @ SV245 @ SV438 @ SV602 ) )
= $true )
| ( ( func @ SV17 @ SV245 @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2034,plain,
! [SV572: $i,SV18: $i] :
( ( ( ! [SY55: $i] :
~ ~ ( ~ ( in @ SY55 @ SV18 )
| ~ ~ ~ ! [SY56: $i] :
~ ~ ( ~ ( in @ SY56 @ SY55 )
| ~ ( in @ SY56 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2035,plain,
! [SV246: $i > $o,SV20: $i,SV573: $i] :
( ( ( in @ SV573 @ SV20 )
= $false )
| ( ( ! [SY1100: $i] :
( ~ ( in @ SY1100 @ SV20 )
| ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SY1100 )
| ( SV573 = SY1100 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2036,plain,
! [SV22: $i,SV439: $i,SV247: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV247 ) )
= $true )
| ( ( ( kpair @ SV439 @ SV603 )
= ( kpair @ SV439 @ SV603 ) )
= $true )
| ( ( in @ SV439 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2037,plain,
! [SV23: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(2038,plain,
! [SV23: $i] :
( ( ! [SY942: $i] :
( ~ ~ ( ~ ! [SY76: $i] :
( ~ ( in @ SY76 @ SY942 )
| ( in @ SY76 @ SV23 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY942 ) )
| ~ ! [SY945: $i] :
~ ~ ! [SY946: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY945 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY946 @ SY942 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY945 )
| ~ ( in @ SX5 @ SY942 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY945 ) )
| ( in @ SY946 @ SY948 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2039,plain,
! [SV574: $o,SV24: $i,SV248: $i] :
( ( ( ! [SY1101: $i] :
( ~ ( in @ SV248 @ SY1101 )
| ~ ( in @ SY1101 @ SV24 )
| SV574 ) )
= $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2040,plain,
! [SV24: $i,SV248: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2041,plain,
! [SV24: $i,SV248: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV248 @ SX0 )
| ~ ( in @ SX0 @ SV24 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2042,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV575 )
| ~ ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(2043,plain,
! [SV441: $i,SV251: $i,SV29: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ SV29 ) )
= $true )
| ( ( ( ap @ SV29 @ SV251 @ SV441 @ SV604 )
= ( ap @ SV29 @ SV251 @ SV441 @ SV604 ) )
= $true )
| ( ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2044,plain,
! [SV30: $i,SV442: $i,SV252: $i > $o] :
( ( ( SV252 @ SV442 )
= $false )
| ( ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) )
| ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) ) )
= $true )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2045,plain,
! [SV33: $i,SV254: $i] :
( ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false )
| ( ( ~ ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2046,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2047,plain,
! [SV34: $i,SV255: $i,SV443: $i] :
( ( ( in @ SV443 @ SV255 )
= $false )
| ( ( ~ ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) ) )
= $true )
| ( ( in @ SV443 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2048,plain,
! [SV576: $i,SV36: $i] :
( ( ( SV36 = emptyset )
= $false )
| ( ( in @ SV576 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2049,plain,
! [SV37: $i,SV444: $i,SV257: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV257 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV444 @ SV605 ) )
= SV444 )
= $true )
| ( ( in @ SV444 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2050,plain,
! [SV38: $i,SV258: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV258 ) )
= $false )
| ( ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) )
= $true )
| ( ( in @ SV445 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2051,plain,
! [SV39: $i,SV259: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV259 ) )
= $false )
| ( ( SV39 != SV259 )
= $true )
| ( ( in @ SV446 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(2052,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ( sK8_SY642 @ SV262 @ SV42 )
!= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(2053,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
| ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(2054,plain,
! [SV43: $i,SV263: $i,SV448: $i] :
( ( ( ~ ( in @ SV448 @ SV263 ) )
= $false )
| ( ( ~ ( in @ SV448 @ SV43 ) )
= $true )
| ( ( subset @ SV43 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2055,plain,
! [SV449: $i,SV264: $i,SV44: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV44 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY1133: $i] : ( in @ ( kpair @ SV606 @ SY1133 ) @ SV449 ) ) )
@ SV264 )
= $true )
| ( ( func @ SV44 @ SV264 @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2056,plain,
! [SV45: $i,SV265: $i,SV450: $i] :
( ( ( ~ ~ ( in @ SV450 @ SV265 ) )
= $true )
| ( ( ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true )
| ( ( in @ SV450 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2057,plain,
! [SV267: $i,SV47: $i] :
( ( ( in @ ( sK9_SY657 @ SV47 @ SV267 ) @ SV267 )
= $true )
| ( ( in @ SV267 @ ( powerset @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(2058,plain,
! [SV268: $i > $o,SV48: $i,SV607: $i] :
( ( ( ~ ( ~ ( in @ SV607 @ SV48 )
| ~ ~ ( SV268 @ SV607 ) ) )
= $false )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2059,plain,
! [SV49: $i,SV451: $i > $i,SV269: $i] :
( ( ( ~ ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 ) )
= $false )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(2060,plain,
! [SV49: $i,SV269: $i,SV451: $i > $i] :
( ( ( in @ ( SV451 @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) ) @ SV269 )
= $false )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(2061,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV577 )
| ~ ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(2062,plain,
! [SV272: $i,SV556: $o,SV53: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| SV556 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2063,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2064,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV53 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2065,plain,
! [SV274: $i,SV55: $i,SV455: $i] :
( ( ( in @ SV455 @ SV55 )
= $false )
| ( ( in @ SV455 @ SV274 )
= $true )
| ( ( subset @ SV55 @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2066,plain,
! [SV275: $i,SV56: $i,SV608: $i,SV578: $i] :
( ( ( SV578 != SV608 )
= $true )
| ( ( ( setadjoin @ SV56 @ SV578 )
= ( setadjoin @ SV275 @ SV608 ) )
= $true )
| ( ( SV56 = SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2067,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SV609 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2068,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2069,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2070,plain,
! [SV61: $i,SV280: $i] :
( ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true )
| ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) )
| ( SV61 = SV280 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(2071,plain,
! [SV61: $i,SV280: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) ) )
= $true )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2072,plain,
! [SV458: $i,SV281: $o,SV62: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV62 ) )
= $true )
| ( ( ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SV610 )
= SV458 ) )
= $true )
| ( ( in @ SV458 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2073,plain,
! [SV459: $i,SV62: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV62 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SV611 )
= SV459 ) )
= $true )
| ( ( in @ SV459 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2074,plain,
! [SV460: $i,SV62: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ SV62 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SV612 )
= SV460 ) )
= $true )
| ( ( in @ SV460 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2075,plain,
! [SV464: $i,SV286: $o,SV67: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV67 ) )
= $true )
| ( ( ~ ~ SV286
| ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2076,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( ( ~ ( in @ SV614 @ SV67 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) ) )
= $true )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2077,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ SV67 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) ) )
= $true )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2078,plain,
! [SV68: $i,SV287: $i > $o] :
( ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2079,plain,
! [SV68: $i,SV287: $i > $o] :
( ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true )
| ( ( ~ ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2080,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
| ~ ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) ) ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1902]) ).
thf(2081,plain,
! [SV70: $i,SV289: $i,SV467: $i] :
( ( ( in @ SV467 @ SV289 )
= $false )
| ( ( in @ SV467 @ SV70 )
= $true )
| ( ( in @ SV289 @ ( powerset @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2082,plain,
! [SV73: $i,SV469: $i,SV291: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV291 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV469 @ SV616 ) )
= SV616 )
= $true )
| ( ( in @ SV469 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2083,plain,
! [SV292: $i,SV74: $i,SV617: $i,SV579: $i] :
( ( ( SV579 != SV617 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) )
| ~ ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) ) ) )
= $true )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2084,plain,
! [SV75: $i,SV470: $i > $i,SV293: $i] :
( ( ( ~ ( in @ ( sK22_SY971 @ SV293 @ SV470 @ SV75 ) @ SV75 ) )
= $false )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2085,plain,
! [SV75: $i,SV293: $i,SV470: $i > $i] :
( ( ( in @ ( SV470 @ ( sK22_SY971 @ SV293 @ SV470 @ SV75 ) ) @ SV293 )
= $false )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2086,plain,
! [SV294: $i > $o,SV76: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV76 ) )
= $true )
| ( ( SV294 @ SV618 )
= $true )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2087,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i] :
( ( ( ~ ( func @ SV77 @ SV295 @ SV619 ) )
= $true )
| ( ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY1137 )
= ( ap @ SV77 @ SV295 @ SV619 @ SY1137 ) ) )
| ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2088,plain,
! [SV297: $i,SV79: $i,SV580: $i] :
( ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SY1107 @ SV297 )
| ( in @ SY1107 @ SV580 ) ) )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2089,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV581 )
| ~ ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(2090,plain,
! [SV298: $i,SV81: $i,SV582: $i] :
( ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( ~ ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV81 )
| ~ ( in @ SY1109 @ SV298 )
| ( in @ SY1109 @ SV582 ) )
| ( in @ SV298 @ ( powerset @ SV582 ) ) )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2091,plain,
! [SV473: $i,SV299: $i,SV82: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) ) )
= $true )
| ( ( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY1140 )
= ( ap @ SV82 @ SV299 @ SV620 @ SY1140 ) ) )
| ( SV473 = SV620 ) )
= $true )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2092,plain,
! [SV474: $i,SV301: $i,SV85: $i,SV621: $i] :
( ( ( ~ ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) ) )
= $true )
| ( ( ~ ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV85 )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV301 )
| ~ ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV474 )
| ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV621 ) ) )
| ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(2093,plain,
! [SV475: $i,SV302: $o,SV86: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ SV86 ) )
= $true )
| ( ( ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY1145: $i] :
( ~ ( ~ SV302
| ( SY1145 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY1145 != SV622 ) ) ) ) ) )
= $true )
| ( ( in @ SV475 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2094,plain,
! [SV476: $i,SV86: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ SV86 ) )
= $true )
| ( ( ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY1146: $i] :
( ~ ( ~ $true
| ( SY1146 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY1146 != SV623 ) ) ) ) ) )
= $true )
| ( ( in @ SV476 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2095,plain,
! [SV477: $i,SV86: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ SV86 ) )
= $true )
| ( ( ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY1147: $i] :
( ~ ( ~ $false
| ( SY1147 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY1147 != SV624 ) ) ) ) ) )
= $true )
| ( ( in @ SV477 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2096,plain,
! [SV89: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY252 @ SV89 ) @ SV89 )
| ~ $true ) )
= $true )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(2097,plain,
! [SV90: $i,SV558: $i,SV480: $i > $i > $o,SV305: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV305 )
| ~ ( SV480 @ SV558 @ SV660 )
| ( in @ ( kpair @ SV558 @ SV660 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) )
= $true )
| ( ( in @ SV558 @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2098,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV583 )
| ~ ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(2099,plain,
! [SV92: $i,SV306: $i] :
( ( ( in @ ( sK12_SY730 @ SV306 @ SV92 ) @ SV92 )
= $true )
| ( ( subset @ SV92 @ SV306 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(2100,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK24_SY732 @ SV308 @ SV95 ) @ SV95 )
| ~ ( SV308 @ ( sK24_SY732 @ SV308 @ SV95 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(2101,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
| ~ ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) ) ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1924]) ).
thf(2102,plain,
! [SV98: $i,SV481: $i,SV311: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV311 ) )
= $true )
| ( ( in @ ( kpair @ SV481 @ SV625 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) )
= $true )
| ( ( in @ SV481 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2103,plain,
! [SV99: $i,SV312: $i] :
( ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $false )
| ( ( ! [SY737: $i] :
( ~ ( in @ SY737 @ SV312 )
| ( in @ SY737 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2104,plain,
! [SV99: $i,SV312: $i] :
( ( ( ! [SY738: $i] :
( ~ ( in @ SY738 @ SV312 )
| ( in @ SY738 @ SV99 ) ) )
= $false )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2105,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) ) )
= $true )
| ( ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2106,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( ~ ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) ) )
= $true )
| ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2107,plain,
! [SV104: $i,SV484: $i,SV317: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV317 ) )
= $true )
| ( ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SV626 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) )
= $true )
| ( ( in @ SV484 @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2108,plain,
! [SV318: $i,SV105: $i,SV627: $i,SV584: $i] :
( ( ( SV584 != SV627 )
= $true )
| ( ( ~ ( in @ SV584 @ SV105 )
| ( in @ SV627 @ SV318 ) )
= $true )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2109,plain,
! [SV485: $i,SV321: $i,SV108: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ SV108 ) )
= $true )
| ( ( ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV321 )
| ~ ( in @ ( kpair @ SV628 @ SY1148 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SY1148 ) ) )
= $true )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2110,plain,
( ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
| ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2111,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2112,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( ~ ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) ) )
= $false )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2113,plain,
! [SV112: $i,SV486: $i,SV324: $i > $o] :
( ( ( ~ ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) ) )
= $false )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2114,plain,
! [SV487: $i,SV325: $o,SV113: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV113 ) )
= $true )
| ( ( ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1149: $i] :
( ~ ( ~ SV325
| ( SY1149 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1149 != SV629 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) )
= $true )
| ( ( in @ SV487 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2115,plain,
! [SV488: $i,SV113: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV113 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1150: $i] :
( ~ ( ~ $true
| ( SY1150 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1150 != SV630 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) )
= $true )
| ( ( in @ SV488 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2116,plain,
! [SV489: $i,SV113: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV113 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1151: $i] :
( ~ ( ~ $false
| ( SY1151 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1151 != SV631 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) )
= $true )
| ( ( in @ SV489 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2117,plain,
! [SV114: $i] :
( ( ( in @ ( sK25_SY310 @ SV114 ) @ SV114 )
= $true )
| ( ( SV114 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(2118,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2119,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
| ~ ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
| ~ ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
| ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1943]) ).
thf(2120,plain,
! [SV493: $i,SV332: $o,SV122: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV122 ) )
= $true )
| ( ( ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 ) )
= $true )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2121,plain,
! [SV494: $i,SV122: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV122 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 ) )
= $true )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2122,plain,
! [SV495: $i,SV122: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ SV122 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 ) )
= $true )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2123,plain,
! [SV123: $i,SV496: $i > $i,SV333: $i] :
( ( ( ~ ( in @ ( sK26_SY1013 @ SV333 @ SV496 @ SV123 ) @ SV123 ) )
= $false )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2124,plain,
! [SV123: $i,SV333: $i,SV496: $i > $i] :
( ( ( in @ ( SV496 @ ( sK26_SY1013 @ SV333 @ SV496 @ SV123 ) ) @ SV333 )
= $false )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(2125,plain,
! [SV497: $i,SV337: $o,SV125: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV125 ) )
= $true )
| ( ( in @ ( if @ SV125 @ SV337 @ SV497 @ SV635 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SV635 @ emptyset ) ) )
= $true )
| ( ( in @ SV497 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2126,plain,
! [SV498: $i,SV125: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV125 ) )
= $true )
| ( ( in @ ( if @ SV125 @ $true @ SV498 @ SV636 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SV636 @ emptyset ) ) )
= $true )
| ( ( in @ SV498 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2127,plain,
! [SV499: $i,SV125: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ SV125 ) )
= $true )
| ( ( in @ ( if @ SV125 @ $false @ SV499 @ SV637 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SV637 @ emptyset ) ) )
= $true )
| ( ( in @ SV499 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2128,plain,
! [SV129: $i,SV341: $i,SV500: $i] :
( ( ( in @ SV500 @ SV341 )
= $false )
| ( ( in @ SV500 @ ( binintersect @ SV129 @ SV341 ) )
= $true )
| ( ( in @ SV500 @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2129,plain,
! [SV501: $i > $i > $o,SV130: $i,SV560: $i,SV342: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV342 )
| ~ ( in @ ( kpair @ SV560 @ SV661 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SV661 ) )
= $true )
| ( ( in @ SV560 @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2130,plain,
! [SV502: $i,SV345: $o,SV133: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV133 ) )
= $true )
| ( ( in @ ( if @ SV133 @ SV345 @ SV502 @ SV638 ) @ SV133 )
= $true )
| ( ( in @ SV502 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2131,plain,
! [SV503: $i,SV133: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV133 ) )
= $true )
| ( ( in @ ( if @ SV133 @ $true @ SV503 @ SV639 ) @ SV133 )
= $true )
| ( ( in @ SV503 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2132,plain,
! [SV504: $i,SV133: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV133 ) )
= $true )
| ( ( in @ ( if @ SV133 @ $false @ SV504 @ SV640 ) @ SV133 )
= $true )
| ( ( in @ SV504 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2133,plain,
! [SV135: $i,SV347: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV347 ) )
= $true )
| ( ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) )
= $true )
| ( ( in @ SV505 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2134,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2135,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
| ~ ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
| ~ ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
| ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1960]) ).
thf(2136,plain,
! [SV143: $i,SV508: $i,SV355: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV355 ) )
= $true )
| ( ( in @ ( kpair @ SV508 @ SV641 ) @ ( cartprod @ SV143 @ SV355 ) )
= $true )
| ( ( in @ SV508 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2137,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ SV585 )
| ~ ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2138,plain,
! [SV510: $i,SV360: $o,SV150: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV150 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1152: $i] :
( ~ ( ~ SV360
| ( SY1152 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1152 != SV642 ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2139,plain,
! [SV511: $i,SV150: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV150 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1153: $i] :
( ~ ( ~ $true
| ( SY1153 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1153 != SV643 ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2140,plain,
! [SV512: $i,SV150: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV150 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1154: $i] :
( ~ ( ~ $false
| ( SY1154 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1154 != SV644 ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2141,plain,
! [SV361: $i,SV152: $i,SV586: $i] :
( ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV152 )
| ~ ( in @ SY1115 @ SV361 )
| ( in @ SY1115 @ SV586 ) )
| ( subset @ SV361 @ SV586 ) )
= $true )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2142,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
| ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 ) )
| ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) ) )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1968]) ).
thf(2143,plain,
! [SV155: $i,SV363: $i] :
( ( ( in @ ( sK16_SY798 @ SV363 @ SV155 ) @ SV155 )
= $true )
| ( ( subset @ SV155 @ SV363 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1969]) ).
thf(2144,plain,
! [SV513: $i,SV364: $i,SV156: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV156 ) )
= $true )
| ( ( ! [SY1155: $i] :
( ~ ( in @ SY1155 @ SV364 )
| ~ ( in @ ( kpair @ SV645 @ SY1155 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SY1155 ) ) )
= $true )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2145,plain,
! [SV514: $i,SV365: $i,SV157: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV157 ) )
= $true )
| ( ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SV646 ) @ SV365 )
= $true )
| ( ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2146,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ SV158 ) )
= $true )
| ( ( in @ SV515 @ SV366 )
= $true )
| ( ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2147,plain,
! [SV518: $i,SV647: $i,SV369: $i,SV162: $i] :
( ( ( ~ ( func @ SV162 @ SV369 @ SV647 ) )
= $true )
| ( ( ~ ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1156 )
= ( ap @ SV162 @ SV369 @ SV647 @ SY1156 ) ) )
| ( SV518 = SV647 ) )
= $true )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2148,plain,
! [SV163: $i] :
( ( ( ! [SY416: $i] :
( ~ ~ ( ~ ( in @ SY416 @ omega )
| ~ ( in @ SY416 @ SV163 ) )
| ( in @ ( setadjoin @ SY416 @ SY416 ) @ SV163 ) ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2149,plain,
! [SV519: $i > $i > $o,SV370: $i,SV164: $i,SV588: $i,SV563: $i] :
( ( ( in @ ( kpair @ SV563 @ SV588 )
@ ( dpsetconstr @ SV164 @ SV370
@ ^ [SY1042: $i,SY1043: $i] : ( SV519 @ SY1042 @ SY1043 ) ) )
= $false )
| ( ( in @ SV588 @ SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2150,plain,
! [SV520: $i,SV371: $i,SV165: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV165 ) )
= $true )
| ( ( in @ ( kpair @ SV648 @ ( ap @ SV165 @ SV371 @ SV520 @ SV648 ) ) @ SV520 )
= $true )
| ( ( func @ SV165 @ SV371 @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2151,plain,
! [SV372: $i,SV649: $o,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| SV649 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2152,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2153,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( ( SV521 != SV166 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2154,plain,
! [SV373: $i,SV167: $i,SV589: $i] :
( ( ( in @ SV589 @ ( powerset @ SV167 ) )
= $false )
| ( ( in @ ( binunion @ SV373 @ SV589 ) @ ( powerset @ SV167 ) )
= $true )
| ( ( in @ SV373 @ ( powerset @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2155,plain,
! [SV168: $i,SV522: $i,SV374: $i,SV650: $i] :
( ( ( ~ ( in @ SV650 @ SV374 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SV650 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) )
= $true )
| ( ( in @ SV522 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2156,plain,
! [SV169: $i,SV375: $i,SV523: $i] :
( ( ( subset @ SV523 @ SV375 )
= $false )
| ( ( subset @ SV523 @ ( binintersect @ SV169 @ SV375 ) )
= $true )
| ( ( subset @ SV523 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2157,plain,
! [SV170: $i,SV376: $i,SV564: $i,SV524: $i] :
( ( ( SV524 != SV564 )
= $true )
| ( ( SV376 = SV564 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SV564 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2158,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV590 )
| ~ ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2159,plain,
! [SV527: $i,SV380: $i,SV176: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV176 ) )
= $true )
| ( ( in @ ( kpair @ SV651 @ ( ap @ SV176 @ SV380 @ SV527 @ SV651 ) ) @ SV527 )
= $true )
| ( ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2160,plain,
! [SV528: $i > $i > $o,SV381: $i,SV177: $i,SV591: $i,SV565: $i] :
( ( ( in @ ( kpair @ SV565 @ SV591 )
@ ( dpsetconstr @ SV177 @ SV381
@ ^ [SY1053: $i,SY1054: $i] : ( SV528 @ SY1053 @ SY1054 ) ) )
= $false )
| ( ( in @ SV565 @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2161,plain,
! [SV178: $i,SV382: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV382 ) ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1989]) ).
thf(2162,plain,
! [SV652: $i > $o,SV529: $i,SV383: $i,SV179: $i] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV179 )
| ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV383 )
| ~ ( in @ ( kpair @ SY1157 @ SY1158 ) @ SV529 )
| ( SV652 @ ( kpair @ SY1157 @ SY1158 ) ) ) ) )
= $true )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2163,plain,
! [SV182: $i,SV384: $i,SV530: $i] :
( ( ( ~ ~ ( in @ SV530 @ SV384 ) )
= $true )
| ( ( ~ ( in @ SV530 @ SV182 ) )
= $true )
| ( ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2164,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SV187 )
| ~ ~ ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1992]) ).
thf(2165,plain,
! [SV389: $i,SV188: $i,SV592: $i] :
( ( ( in @ SV592 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ ( binintersect @ SV389 @ SV592 ) @ ( powerset @ SV188 ) )
= $true )
| ( ( in @ SV389 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2166,plain,
! [SV191: $i,SV391: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ SV391 ) )
= $false )
| ( ( ~ ( subset @ SV191 @ SV391 ) )
= $true )
| ( ( in @ SV534 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2167,plain,
! [SV192: $i,SV535: $i,SV392: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ SV392 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SV653 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) )
= $true )
| ( ( in @ SV535 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2168,plain,
! [SV536: $i,SV393: $i,SV193: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV193 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1160: $i] : ( in @ ( kpair @ SV654 @ SY1160 ) @ SV536 ) ) )
= $true )
| ( ( func @ SV193 @ SV393 @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2169,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) ) )
= $true )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2170,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ( sK17_SY858 @ SV396 @ SV197 )
!= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1998]) ).
thf(2171,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
| ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1998]) ).
thf(2172,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY868 @ SV399 @ SV200 ) @ SV200 )
| ~ ( in @ SV399 @ ( sK28_SY868 @ SV399 @ SV200 ) ) ) )
= $true )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2173,plain,
! [SV202: $i,SV541: $i > $i,SV401: $i] :
( ( ( ~ ( in @ ( sK29_SY1067 @ SV401 @ SV541 @ SV202 ) @ SV202 ) )
= $false )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2174,plain,
! [SV202: $i,SV401: $i,SV541: $i > $i] :
( ( ( in @ ( SV541 @ ( sK29_SY1067 @ SV401 @ SV541 @ SV202 ) ) @ SV401 )
= $false )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2175,plain,
! [SV205: $i,SV404: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ SV404 ) )
= $false )
| ( ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) )
= $true )
| ( ( in @ SV543 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2176,plain,
! [SV206: $i,SV544: $i,SV405: $i] :
( ( ( subset @ SV405 @ SV544 )
= $false )
| ( ( subset @ SV206 @ SV544 )
= $true )
| ( ( subset @ SV206 @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2177,plain,
! [SV655: $i > $o,SV547: $i,SV410: $i,SV213: $i] :
( ( ( ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV213 )
| ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV410 )
| ~ ( in @ ( kpair @ SY1161 @ SY1162 ) @ SV547 )
| ( SV655 @ ( kpair @ SY1161 @ SY1162 ) ) ) ) )
= $true )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2178,plain,
! [SV413: $i,SV216: $i,SV594: $i] :
( ( ( in @ SV594 @ SV216 )
= $false )
| ( ( ~ ( in @ SV594 @ SV413 )
| ~ ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2179,plain,
! [SV656: $i > $o,SV595: $i > $o,SV415: $i,SV218: $i] :
( ( ( ~ ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV218 )
| ! [SY1165: $i] :
( ~ ( in @ SY1165 @ SV415 )
| ( SY1164 != SY1165 )
| ~ ( ~ ( ~ ( SV595 @ SY1164 )
| ( SV656 @ SY1165 ) )
| ~ ( ~ ( SV656 @ SY1165 )
| ( SV595 @ SY1164 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2180,plain,
! [SV419: $i,SV222: $i,SV596: $i] :
( ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( ~ ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV222 )
| ~ ( in @ SY1128 @ SV419 )
| ( in @ SY1128 @ SV596 ) )
| ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2181,plain,
! [SV421: $i > $o,SV224: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV224 ) )
= $true )
| ( ( SV421 @ SV657 )
= $true )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2182,plain,
! [SV225: $i,SV549: $i,SV422: $i > $o] :
( ( ( SV422 @ SV549 )
= $false )
| ( ( in @ SV549
@ ( dsetconstr @ SV225
@ ^ [SY901: $i] : ( SV422 @ SY901 ) ) )
= $true )
| ( ( in @ SV549 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2183,plain,
! [SV423: $i,SV226: $i,SV550: $i] :
( ( ( in @ SV550 @ SV226 )
= $false )
| ( ( in @ SV423 @ ( setunion @ SV226 ) )
= $true )
| ( ( in @ SV423 @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2184,plain,
! [SV551: $i,SV424: $i,SV227: $i,SV658: $i] :
( ( ( ~ ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) ) )
= $true )
| ( ( ~ ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV227 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV424 )
| ~ ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV551 )
| ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV658 ) ) )
| ( subset @ SV551 @ SV658 ) )
= $true )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2185,plain,
! [SV425: $i,SV229: $i,SV552: $i] :
( ( ( in @ SV552 @ ( setminus @ SV229 @ SV425 ) )
= $false )
| ( ( in @ SV552 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2186,plain,
! [SV427: $i > $o,SV231: $i,SV659: $i] :
( ( ( ~ ( ~ ( in @ SV659 @ SV231 )
| ~ ( SV427 @ SV659 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2187,plain,
! [SV428: $i,SV233: $i > $o,SV1: $i] :
( ( ( ( dsetconstr @ SV1
@ ^ [SY589: $i] : ( SV233 @ SY589 ) )
= emptyset )
= $false )
| ( ( SV233 @ SV428 )
= $false )
| ( ( in @ SV428 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2188,plain,
! [SV2: $i,SV429: $i,SV234: $i,SV597: $i] :
( ( ( in @ SV597 @ SV234 )
= $false )
| ( ( subset @ ( setadjoin @ SV429 @ ( setadjoin @ SV597 @ emptyset ) ) @ ( binunion @ SV2 @ SV234 ) )
= $true )
| ( ( in @ SV429 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2189,plain,
! [SV3: $i,SV430: $i > $i,SV235: $i] :
( ( ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 )
= $true )
| ( ( ! [SY915: $i] :
( ~ ( in @ SY915 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SY915 )
= ( SV430 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2190,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV662 )
= ( SV430 @ SV662 ) ) )
= $true )
| ( ( in @ ( SV430 @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) ) @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2191,plain,
! [SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2192,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
| ~ ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2193,plain,
! [SV431: $i,SV237: $i,SV5: $i,SV598: $i] :
( ( ( in @ SV598 @ SV5 )
= $false )
| ( ( in @ ( ap @ SV5 @ SV237 @ SV431 @ SV598 ) @ SV237 )
= $true )
| ( ( func @ SV5 @ SV237 @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2194,plain,
! [SV11: $i,SV434: $i > $i,SV242: $i] :
( ( ( in @ ( sK19_SY923 @ SV242 @ SV434 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV242
@ ( lam @ SV11 @ SV242
@ ^ [SY924: $i] : ( SV434 @ SY924 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2195,plain,
! [SV435: $i,SV244: $o,SV14: $i,SV599: $i] :
( ( ( in @ SV599 @ SV14 )
= $false )
| ( ( ~ ~ SV244
| ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) ) )
= $true )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2196,plain,
! [SV436: $i,SV14: $i,SV600: $i] :
( ( ( in @ SV600 @ SV14 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) ) )
= $true )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2197,plain,
! [SV437: $i,SV14: $i,SV601: $i] :
( ( ( in @ SV601 @ SV14 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) ) )
= $true )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2198,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV571 ) )
= $true )
| ( ( ~ ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2199,plain,
! [SV438: $i,SV245: $i,SV17: $i,SV602: $i] :
( ( ( in @ SV602 @ SV17 )
= $false )
| ( ( ( ap @ SV17 @ SV245 @ SV438 @ SV602 )
= ( ap @ SV17 @ SV245 @ SV438 @ SV602 ) )
= $true )
| ( ( func @ SV17 @ SV245 @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2200,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY55 @ SV572 @ SV18 ) @ SV18 )
| ~ ~ ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2034]) ).
thf(2201,plain,
! [SV573: $i,SV246: $i > $o,SV20: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV20 )
| ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SV664 )
| ( SV573 = SV664 ) )
= $true )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2202,plain,
! [SV22: $i,SV439: $i,SV247: $i,SV603: $i] :
( ( ( in @ SV603 @ SV247 )
= $false )
| ( ( ( kpair @ SV439 @ SV603 )
= ( kpair @ SV439 @ SV603 ) )
= $true )
| ( ( in @ SV439 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2203,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
| ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2204,plain,
! [SV23: $i,SV665: $i] :
( ( ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) )
| ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
| ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2205,plain,
! [SV24: $i,SV574: $o,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) )
| ~ ( in @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) @ SV24 )
| SV574 )
= $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2039]) ).
thf(2206,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK39_SX0 @ SV24 @ SV248 ) )
| ~ ( in @ ( sK39_SX0 @ SV24 @ SV248 ) @ SV24 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2040]) ).
thf(2207,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK40_SX0 @ SV24 @ SV248 ) )
| ~ ( in @ ( sK40_SX0 @ SV24 @ SV248 ) @ SV24 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2041]) ).
thf(2208,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV575 ) )
= $true )
| ( ( ~ ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2209,plain,
! [SV441: $i,SV251: $i,SV29: $i,SV604: $i] :
( ( ( in @ SV604 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV251 @ SV441 @ SV604 )
= ( ap @ SV29 @ SV251 @ SV441 @ SV604 ) )
= $true )
| ( ( in @ SV441 @ ( funcSet @ SV29 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2210,plain,
! [SV442: $i,SV252: $i > $o,SV30: $i] :
( ( ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2211,plain,
! [SV33: $i,SV254: $i] :
( ( ( ! [SY634: $i] :
~ ~ ( ~ ( in @ SV254 @ SY634 )
| ~ ( in @ SY634 @ SV33 ) ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2212,plain,
! [SV33: $i,SV254: $i] :
( ( ( ! [SY635: $i] :
~ ~ ( ~ ( in @ SV254 @ SY635 )
| ~ ( in @ SY635 @ SV33 ) ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2213,plain,
! [SV255: $i,SV34: $i,SV443: $i] :
( ( ( in @ SV443 @ ( symdiff @ SV34 @ SV255 ) )
= $false )
| ( ( in @ SV443 @ SV255 )
= $false )
| ( ( in @ SV443 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2214,plain,
! [SV37: $i,SV444: $i,SV257: $i,SV605: $i] :
( ( ( in @ SV605 @ SV257 )
= $false )
| ( ( ( kfst @ ( kpair @ SV444 @ SV605 ) )
= SV444 )
= $true )
| ( ( in @ SV444 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2215,plain,
! [SV38: $i,SV258: $i,SV445: $i] :
( ( ( in @ SV445 @ SV258 )
= $true )
| ( ( in @ SV445 @ ( setminus @ SV38 @ SV258 ) )
= $true )
| ( ( in @ SV445 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2216,plain,
! [SV39: $i,SV259: $i,SV446: $i] :
( ( ( in @ SV446 @ SV259 )
= $true )
| ( ( SV39 != SV259 )
= $true )
| ( ( in @ SV446 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2217,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2218,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
| ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2219,plain,
! [SV43: $i,SV263: $i,SV448: $i] :
( ( ( in @ SV448 @ SV263 )
= $true )
| ( ( ~ ( in @ SV448 @ SV43 ) )
= $true )
| ( ( subset @ SV43 @ SV263 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2220,plain,
! [SV449: $i,SV264: $i,SV44: $i,SV606: $i] :
( ( ( in @ SV606 @ SV44 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV264
@ ^ [SY1133: $i] : ( in @ ( kpair @ SV606 @ SY1133 ) @ SV449 ) ) )
@ SV264 )
= $true )
| ( ( func @ SV44 @ SV264 @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2221,plain,
! [SV45: $i,SV265: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ SV265 ) )
= $false )
| ( ( ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true )
| ( ( in @ SV450 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2222,plain,
! [SV268: $i > $o,SV48: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV48 )
| ~ ~ ( SV268 @ SV607 ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2223,plain,
! [SV49: $i,SV451: $i > $i,SV269: $i] :
( ( ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 )
= $true )
| ( ( ! [SY957: $i] :
( ~ ( in @ SY957 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SY957 )
= ( SV451 @ SY957 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2224,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV666 )
= ( SV451 @ SV666 ) ) )
= $true )
| ( ( in @ ( SV451 @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) ) @ SV269 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2225,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV577 ) )
= $true )
| ( ( ~ ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2226,plain,
! [SV272: $i,SV556: $o,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 )
| SV556 )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2227,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2228,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2229,plain,
! [SV275: $i,SV56: $i,SV608: $i,SV578: $i] :
( ( ( SV578 = SV608 )
= $false )
| ( ( ( setadjoin @ SV56 @ SV578 )
= ( setadjoin @ SV275 @ SV608 ) )
= $true )
| ( ( SV56 = SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2230,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2231,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2232,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 )
| ~ ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2233,plain,
! [SV61: $i,SV280: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) ) )
= $true )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2234,plain,
! [SV61: $i,SV280: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2235,plain,
! [SV458: $i,SV281: $o,SV62: $i,SV610: $i] :
( ( ( in @ SV610 @ SV62 )
= $false )
| ( ( ~ SV281
| ( ( if @ SV62 @ SV281 @ SV458 @ SV610 )
= SV458 ) )
= $true )
| ( ( in @ SV458 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2236,plain,
! [SV459: $i,SV62: $i,SV611: $i] :
( ( ( in @ SV611 @ SV62 )
= $false )
| ( ( ~ $true
| ( ( if @ SV62 @ $true @ SV459 @ SV611 )
= SV459 ) )
= $true )
| ( ( in @ SV459 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2237,plain,
! [SV460: $i,SV62: $i,SV612: $i] :
( ( ( in @ SV612 @ SV62 )
= $false )
| ( ( ~ $false
| ( ( if @ SV62 @ $false @ SV460 @ SV612 )
= SV460 ) )
= $true )
| ( ( in @ SV460 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2238,plain,
! [SV464: $i,SV286: $o,SV67: $i,SV613: $i] :
( ( ( in @ SV613 @ SV67 )
= $false )
| ( ( ~ ~ SV286
| ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2239,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( ( in @ SV614 @ SV67 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) ) )
= $true )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2240,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( ( in @ SV615 @ SV67 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) ) )
= $true )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2241,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $false )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2242,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ~ ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $false )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2243,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
| ~ ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) ) ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2244,plain,
! [SV73: $i,SV469: $i,SV291: $i,SV616: $i] :
( ( ( in @ SV616 @ SV291 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV469 @ SV616 ) )
= SV616 )
= $true )
| ( ( in @ SV469 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2245,plain,
! [SV292: $i,SV74: $i,SV617: $i,SV579: $i] :
( ( ( SV579 = SV617 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) )
| ~ ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) ) ) )
= $true )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2246,plain,
! [SV75: $i,SV470: $i > $i,SV293: $i] :
( ( ( in @ ( sK22_SY971 @ SV293 @ SV470 @ SV75 ) @ SV75 )
= $true )
| ( ( in
@ ( lam @ SV75 @ SV293
@ ^ [SY972: $i] : ( SV470 @ SY972 ) )
@ ( funcSet @ SV75 @ SV293 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2247,plain,
! [SV294: $i > $o,SV76: $i,SV618: $i] :
( ( ( in @ SV618 @ SV76 )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2248,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i] :
( ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY1137 )
= ( ap @ SV77 @ SV295 @ SV619 @ SY1137 ) ) )
| ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2249,plain,
! [SV580: $i,SV297: $i,SV79: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV79 )
| ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SV667 @ SV297 )
| ( in @ SV667 @ SV580 ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2250,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV581 ) )
= $true )
| ( ( ~ ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2251,plain,
! [SV582: $i,SV298: $i,SV81: $i] :
( ( ( ~ ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV81 )
| ~ ( in @ SY1109 @ SV298 )
| ( in @ SY1109 @ SV582 ) ) )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2252,plain,
! [SV473: $i,SV299: $i,SV82: $i,SV620: $i] :
( ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY1140 )
= ( ap @ SV82 @ SV299 @ SV620 @ SY1140 ) ) )
| ( SV473 = SV620 ) )
= $true )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2253,plain,
! [SV474: $i,SV301: $i,SV85: $i,SV621: $i] :
( ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( ~ ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV85 )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV301 )
| ~ ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV474 )
| ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV621 ) ) )
| ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2254,plain,
! [SV475: $i,SV302: $o,SV86: $i,SV622: $i] :
( ( ( in @ SV622 @ SV86 )
= $false )
| ( ( ~ SV302
| ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY1145: $i] :
( ~ ( ~ SV302
| ( SY1145 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY1145 != SV622 ) ) ) ) ) )
= $true )
| ( ( in @ SV475 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2255,plain,
! [SV476: $i,SV86: $i,SV623: $i] :
( ( ( in @ SV623 @ SV86 )
= $false )
| ( ( ~ $true
| ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY1146: $i] :
( ~ ( ~ $true
| ( SY1146 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY1146 != SV623 ) ) ) ) ) )
= $true )
| ( ( in @ SV476 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2256,plain,
! [SV477: $i,SV86: $i,SV624: $i] :
( ( ( in @ SV624 @ SV86 )
= $false )
| ( ( ~ $false
| ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY1147: $i] :
( ~ ( ~ $false
| ( SY1147 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY1147 != SV624 ) ) ) ) ) )
= $true )
| ( ( in @ SV477 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2257,plain,
! [SV89: $i] :
( ( ( ~ ( in @ ( sK23_SY252 @ SV89 ) @ SV89 )
| ~ $true )
= $false )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2258,plain,
! [SV90: $i,SV558: $i,SV480: $i > $i > $o,SV305: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV305 ) )
= $true )
| ( ( ~ ( SV480 @ SV558 @ SV660 )
| ( in @ ( kpair @ SV558 @ SV660 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) )
= $true )
| ( ( in @ SV558 @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2259,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV583 ) )
= $true )
| ( ( ~ ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2260,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( ~ ( in @ ( sK24_SY732 @ SV308 @ SV95 ) @ SV95 )
| ~ ( SV308 @ ( sK24_SY732 @ SV308 @ SV95 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2261,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
| ~ ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) ) ) )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2101]) ).
thf(2262,plain,
! [SV98: $i,SV481: $i,SV311: $i,SV625: $i] :
( ( ( in @ SV625 @ SV311 )
= $false )
| ( ( in @ ( kpair @ SV481 @ SV625 ) @ ( powerset @ ( powerset @ ( binunion @ SV98 @ SV311 ) ) ) )
= $true )
| ( ( in @ SV481 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2263,plain,
! [SV99: $i,SV312: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ SV312 )
| ( in @ SV668 @ SV99 ) )
= $true )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2264,plain,
! [SV312: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK41_SY738 @ SV99 @ SV312 ) @ SV312 )
| ( in @ ( sK41_SY738 @ SV99 @ SV312 ) @ SV99 ) )
= $false )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2104]) ).
thf(2265,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $false )
| ( ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2266,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( ( SV483 = SV101 )
| ( in @ SV483 @ SV314 ) )
= $false )
| ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2267,plain,
! [SV104: $i,SV484: $i,SV317: $i,SV626: $i] :
( ( ( in @ SV626 @ SV317 )
= $false )
| ( ( in @ ( setadjoin @ SV484 @ ( setadjoin @ SV626 @ emptyset ) ) @ ( powerset @ ( binunion @ SV104 @ SV317 ) ) )
= $true )
| ( ( in @ SV484 @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2268,plain,
! [SV318: $i,SV105: $i,SV627: $i,SV584: $i] :
( ( ( SV584 = SV627 )
= $false )
| ( ( ~ ( in @ SV584 @ SV105 )
| ( in @ SV627 @ SV318 ) )
= $true )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2269,plain,
! [SV485: $i,SV321: $i,SV108: $i,SV628: $i] :
( ( ( in @ SV628 @ SV108 )
= $false )
| ( ( ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV321 )
| ~ ( in @ ( kpair @ SV628 @ SY1148 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SY1148 ) ) )
= $true )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2270,plain,
( ( ~ ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2271,plain,
( ( ~ ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2272,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2273,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
| ( SV324 @ SV486 ) )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2274,plain,
! [SV112: $i,SV486: $i,SV324: $i > $o] :
( ( ( ~ ( SV324 @ SV486 )
| ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) ) )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2275,plain,
! [SV487: $i,SV325: $o,SV113: $i,SV629: $i] :
( ( ( in @ SV629 @ SV113 )
= $false )
| ( ( ~ SV325
| ( ( dsetconstr @ SV113
@ ^ [SY1149: $i] :
( ~ ( ~ SV325
| ( SY1149 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1149 != SV629 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) ) )
= $true )
| ( ( in @ SV487 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2276,plain,
! [SV488: $i,SV113: $i,SV630: $i] :
( ( ( in @ SV630 @ SV113 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV113
@ ^ [SY1150: $i] :
( ~ ( ~ $true
| ( SY1150 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1150 != SV630 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) ) )
= $true )
| ( ( in @ SV488 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2277,plain,
! [SV489: $i,SV113: $i,SV631: $i] :
( ( ( in @ SV631 @ SV113 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV113
@ ^ [SY1151: $i] :
( ~ ( ~ $false
| ( SY1151 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1151 != SV631 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) ) )
= $true )
| ( ( in @ SV489 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2278,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2279,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2280,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
| ~ ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
| ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2281,plain,
! [SV493: $i,SV332: $o,SV122: $i,SV632: $i] :
( ( ( in @ SV632 @ SV122 )
= $false )
| ( ( ~ ~ SV332
| ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 ) )
= $true )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2282,plain,
! [SV494: $i,SV122: $i,SV633: $i] :
( ( ( in @ SV633 @ SV122 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 ) )
= $true )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2283,plain,
! [SV495: $i,SV122: $i,SV634: $i] :
( ( ( in @ SV634 @ SV122 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 ) )
= $true )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2284,plain,
! [SV123: $i,SV496: $i > $i,SV333: $i] :
( ( ( in @ ( sK26_SY1013 @ SV333 @ SV496 @ SV123 ) @ SV123 )
= $true )
| ( ( func @ SV123 @ SV333
@ ( dpsetconstr @ SV123 @ SV333
@ ^ [SY1014: $i,SY1015: $i] :
( ( SV496 @ SY1014 )
= SY1015 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2285,plain,
! [SV497: $i,SV337: $o,SV125: $i,SV635: $i] :
( ( ( in @ SV635 @ SV125 )
= $false )
| ( ( in @ ( if @ SV125 @ SV337 @ SV497 @ SV635 ) @ ( setadjoin @ SV497 @ ( setadjoin @ SV635 @ emptyset ) ) )
= $true )
| ( ( in @ SV497 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2286,plain,
! [SV498: $i,SV125: $i,SV636: $i] :
( ( ( in @ SV636 @ SV125 )
= $false )
| ( ( in @ ( if @ SV125 @ $true @ SV498 @ SV636 ) @ ( setadjoin @ SV498 @ ( setadjoin @ SV636 @ emptyset ) ) )
= $true )
| ( ( in @ SV498 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2287,plain,
! [SV499: $i,SV125: $i,SV637: $i] :
( ( ( in @ SV637 @ SV125 )
= $false )
| ( ( in @ ( if @ SV125 @ $false @ SV499 @ SV637 ) @ ( setadjoin @ SV499 @ ( setadjoin @ SV637 @ emptyset ) ) )
= $true )
| ( ( in @ SV499 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2288,plain,
! [SV501: $i > $i > $o,SV130: $i,SV560: $i,SV342: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV342 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV560 @ SV661 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SV661 ) )
= $true )
| ( ( in @ SV560 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2289,plain,
! [SV502: $i,SV345: $o,SV133: $i,SV638: $i] :
( ( ( in @ SV638 @ SV133 )
= $false )
| ( ( in @ ( if @ SV133 @ SV345 @ SV502 @ SV638 ) @ SV133 )
= $true )
| ( ( in @ SV502 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2290,plain,
! [SV503: $i,SV133: $i,SV639: $i] :
( ( ( in @ SV639 @ SV133 )
= $false )
| ( ( in @ ( if @ SV133 @ $true @ SV503 @ SV639 ) @ SV133 )
= $true )
| ( ( in @ SV503 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2291,plain,
! [SV504: $i,SV133: $i,SV640: $i] :
( ( ( in @ SV640 @ SV133 )
= $false )
| ( ( in @ ( if @ SV133 @ $false @ SV504 @ SV640 ) @ SV133 )
= $true )
| ( ( in @ SV504 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2292,plain,
! [SV135: $i,SV347: $i,SV505: $i] :
( ( ( in @ SV505 @ SV347 )
= $false )
| ( ( in @ SV505 @ ( symdiff @ SV135 @ SV347 ) )
= $true )
| ( ( in @ SV505 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2293,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2294,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2295,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
| ~ ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
| ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2296,plain,
! [SV143: $i,SV508: $i,SV355: $i,SV641: $i] :
( ( ( in @ SV641 @ SV355 )
= $false )
| ( ( in @ ( kpair @ SV508 @ SV641 ) @ ( cartprod @ SV143 @ SV355 ) )
= $true )
| ( ( in @ SV508 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2297,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ SV585 ) )
= $true )
| ( ( ~ ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2298,plain,
! [SV510: $i,SV360: $o,SV150: $i,SV642: $i] :
( ( ( in @ SV642 @ SV150 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1152: $i] :
( ~ ( ~ SV360
| ( SY1152 != SV510 ) )
| ~ ( ~ ~ SV360
| ( SY1152 != SV642 ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2299,plain,
! [SV511: $i,SV150: $i,SV643: $i] :
( ( ( in @ SV643 @ SV150 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1153: $i] :
( ~ ( ~ $true
| ( SY1153 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY1153 != SV643 ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2300,plain,
! [SV512: $i,SV150: $i,SV644: $i] :
( ( ( in @ SV644 @ SV150 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV150
@ ^ [SY1154: $i] :
( ~ ( ~ $false
| ( SY1154 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY1154 != SV644 ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2301,plain,
! [SV586: $i,SV361: $i,SV152: $i] :
( ( ( ~ ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV152 )
| ~ ( in @ SY1115 @ SV361 )
| ( in @ SY1115 @ SV586 ) ) )
= $true )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2302,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
| ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 ) )
| ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2303,plain,
! [SV513: $i,SV364: $i,SV156: $i,SV645: $i] :
( ( ( in @ SV645 @ SV156 )
= $false )
| ( ( ! [SY1155: $i] :
( ~ ( in @ SY1155 @ SV364 )
| ~ ( in @ ( kpair @ SV645 @ SY1155 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SY1155 ) ) )
= $true )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2304,plain,
! [SV514: $i,SV365: $i,SV157: $i,SV646: $i] :
( ( ( in @ SV646 @ SV157 )
= $false )
| ( ( in @ ( ap @ SV157 @ SV365 @ SV514 @ SV646 ) @ SV365 )
= $true )
| ( ( in @ SV514 @ ( funcSet @ SV157 @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2305,plain,
! [SV366: $i,SV158: $i,SV515: $i] :
( ( ( in @ SV515 @ SV158 )
= $false )
| ( ( in @ SV515 @ SV366 )
= $true )
| ( ( in @ SV515 @ ( setminus @ SV158 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2306,plain,
! [SV518: $i,SV647: $i,SV369: $i,SV162: $i] :
( ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( ~ ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1156 )
= ( ap @ SV162 @ SV369 @ SV647 @ SY1156 ) ) )
| ( SV518 = SV647 ) )
= $true )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2307,plain,
! [SV163: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ omega )
| ~ ( in @ ( sK42_SY416 @ SV163 ) @ SV163 ) )
| ( in @ ( setadjoin @ ( sK42_SY416 @ SV163 ) @ ( sK42_SY416 @ SV163 ) ) @ SV163 ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2148]) ).
thf(2308,plain,
! [SV520: $i,SV371: $i,SV165: $i,SV648: $i] :
( ( ( in @ SV648 @ SV165 )
= $false )
| ( ( in @ ( kpair @ SV648 @ ( ap @ SV165 @ SV371 @ SV520 @ SV648 ) ) @ SV520 )
= $true )
| ( ( func @ SV165 @ SV371 @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2309,plain,
! [SV372: $i,SV649: $o,SV166: $i,SV521: $i] :
( ( ( ( SV521 != SV166 )
| SV649 )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2310,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ( SV521 != SV166 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2311,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( ( SV521 != SV166 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2312,plain,
! [SV168: $i,SV522: $i,SV374: $i,SV650: $i] :
( ( ( in @ SV650 @ SV374 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV522 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV522 @ ( setadjoin @ SV650 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV168 @ SV374 ) ) ) )
= $true )
| ( ( in @ SV522 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2313,plain,
! [SV170: $i,SV376: $i,SV564: $i,SV524: $i] :
( ( ( SV524 = SV564 )
= $false )
| ( ( SV376 = SV564 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV170 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV170 @ ( setadjoin @ SV376 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV524 @ ( setadjoin @ SV564 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2314,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV590 ) )
= $true )
| ( ( ~ ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2315,plain,
! [SV527: $i,SV380: $i,SV176: $i,SV651: $i] :
( ( ( in @ SV651 @ SV176 )
= $false )
| ( ( in @ ( kpair @ SV651 @ ( ap @ SV176 @ SV380 @ SV527 @ SV651 ) ) @ SV527 )
= $true )
| ( ( in @ SV527 @ ( funcSet @ SV176 @ SV380 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2316,plain,
! [SV178: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV382 ) ) )
= $true )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2317,plain,
! [SV652: $i > $o,SV529: $i,SV383: $i,SV179: $i] :
( ( ( ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV179 )
| ! [SY1158: $i] :
( ~ ( in @ SY1158 @ SV383 )
| ~ ( in @ ( kpair @ SY1157 @ SY1158 ) @ SV529 )
| ( SV652 @ ( kpair @ SY1157 @ SY1158 ) ) ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2318,plain,
! [SV182: $i,SV384: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ SV384 ) )
= $false )
| ( ( ~ ( in @ SV530 @ SV182 ) )
= $true )
| ( ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2319,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SV187 )
| ~ ~ ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) ) )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2320,plain,
! [SV191: $i,SV391: $i,SV534: $i] :
( ( ( in @ SV534 @ SV391 )
= $true )
| ( ( ~ ( subset @ SV191 @ SV391 ) )
= $true )
| ( ( in @ SV534 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2166]) ).
thf(2321,plain,
! [SV192: $i,SV535: $i,SV392: $i,SV653: $i] :
( ( ( in @ SV653 @ SV392 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV535 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV535 @ ( setadjoin @ SV653 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV192 @ SV392 ) ) )
= $true )
| ( ( in @ SV535 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2322,plain,
! [SV536: $i,SV393: $i,SV193: $i,SV654: $i] :
( ( ( in @ SV654 @ SV193 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV393
@ ^ [SY1160: $i] : ( in @ ( kpair @ SV654 @ SY1160 ) @ SV536 ) ) )
= $true )
| ( ( func @ SV193 @ SV393 @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2323,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY498: $i,SY499: $i] :
( ~ ( SV196 @ SY498 )
| ~ ( SV196 @ SY499 )
| ( SY498 = SY499 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2324,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2325,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
| ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2326,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ( in @ ( sK28_SY868 @ SV399 @ SV200 ) @ SV200 )
| ~ ( in @ SV399 @ ( sK28_SY868 @ SV399 @ SV200 ) ) )
= $false )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2327,plain,
! [SV202: $i,SV541: $i > $i,SV401: $i] :
( ( ( in @ ( sK29_SY1067 @ SV401 @ SV541 @ SV202 ) @ SV202 )
= $true )
| ( ( ( lam @ SV202 @ SV401
@ ^ [SY1068: $i] : ( SV541 @ SY1068 ) )
= ( lam @ SV202 @ SV401
@ ^ [SY1069: $i] : ( SV541 @ SY1069 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2173]) ).
thf(2328,plain,
! [SV205: $i,SV404: $i,SV543: $i] :
( ( ( in @ SV543 @ SV404 )
= $true )
| ( ( in @ SV543 @ ( symdiff @ SV205 @ SV404 ) )
= $true )
| ( ( in @ SV543 @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2329,plain,
! [SV655: $i > $o,SV547: $i,SV410: $i,SV213: $i] :
( ( ( ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV213 )
| ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV410 )
| ~ ( in @ ( kpair @ SY1161 @ SY1162 ) @ SV547 )
| ( SV655 @ ( kpair @ SY1161 @ SY1162 ) ) ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2330,plain,
! [SV216: $i,SV413: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV413 ) )
= $true )
| ( ( ~ ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) ) )
= $true )
| ( ( in @ SV594 @ SV216 )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2331,plain,
! [SV656: $i > $o,SV595: $i > $o,SV415: $i,SV218: $i] :
( ( ( ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV218 )
| ! [SY1165: $i] :
( ~ ( in @ SY1165 @ SV415 )
| ( SY1164 != SY1165 )
| ~ ( ~ ( ~ ( SV595 @ SY1164 )
| ( SV656 @ SY1165 ) )
| ~ ( ~ ( SV656 @ SY1165 )
| ( SV595 @ SY1164 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2332,plain,
! [SV596: $i,SV419: $i,SV222: $i] :
( ( ( ~ ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV222 )
| ~ ( in @ SY1128 @ SV419 )
| ( in @ SY1128 @ SV596 ) ) )
= $true )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2333,plain,
! [SV421: $i > $o,SV224: $i,SV657: $i] :
( ( ( in @ SV657 @ SV224 )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2334,plain,
! [SV551: $i,SV424: $i,SV227: $i,SV658: $i] :
( ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( ~ ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV227 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV424 )
| ~ ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV551 )
| ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV658 ) ) )
| ( subset @ SV551 @ SV658 ) )
= $true )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2335,plain,
! [SV427: $i > $o,SV231: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV231 )
| ~ ( SV427 @ SV659 ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2336,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV3 )
| ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV669 )
= ( SV430 @ SV669 ) ) )
= $true )
| ( ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2337,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV3 ) )
= $true )
| ( ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV662 )
= ( SV430 @ SV662 ) )
= $true )
| ( ( in @ ( SV430 @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) ) @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2338,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ! [SY1187: $i] :
~ ( ~ ( ~ ( in @ SY1187 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1187 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1187 ) )
| ( in @ SY1187 @ ( sK43_SY599 @ SV4 @ SV236 ) ) ) ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2191]) ).
thf(2339,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
| ~ ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2340,plain,
! [SV599: $i,SV435: $i,SV14: $i,SV244: $o] :
( ( ( ~ ~ SV244 )
= $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) )
= $true )
| ( ( in @ SV599 @ SV14 )
= $false )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2195]) ).
thf(2341,plain,
! [SV600: $i,SV436: $i,SV14: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) )
= $true )
| ( ( in @ SV600 @ SV14 )
= $false )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2342,plain,
! [SV601: $i,SV437: $i,SV14: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) )
= $true )
| ( ( in @ SV601 @ SV14 )
= $false )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2343,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2344,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY55 @ SV572 @ SV18 ) @ SV18 )
| ~ ~ ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2345,plain,
! [SV573: $i,SV246: $i > $o,SV20: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV20 ) )
= $true )
| ( ( ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SV664 )
| ( SV573 = SV664 ) )
= $true )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2346,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2347,plain,
! [SV23: $i] :
( ( ~ ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2203]) ).
thf(2348,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) )
| ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2349,plain,
! [SV24: $i,SV574: $o,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) ) )
= $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2350,plain,
! [SV248: $i,SV24: $i,SV574: $o] :
( ( ( ~ ( in @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) @ SV24 )
| SV574 )
= $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2351,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK39_SX0 @ SV24 @ SV248 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2352,plain,
! [SV248: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK39_SX0 @ SV24 @ SV248 ) @ SV24 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2353,plain,
! [SV24: $i,SV248: $i] :
( ( ( ~ ( in @ SV248 @ ( sK40_SX0 @ SV24 @ SV248 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2207]) ).
thf(2354,plain,
! [SV248: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK40_SX0 @ SV24 @ SV248 ) @ SV24 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2207]) ).
thf(2355,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( SV27 @ SV575 )
= $false )
| ( ( ~ ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) )
= $true )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2356,plain,
! [SV442: $i,SV252: $i > $o,SV30: $i] :
( ( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ SV30 )
| ~ ( SV252 @ SY951 )
| ( SY951 = SV442 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2357,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ SV254 @ ( sK44_SY634 @ SV33 @ SV254 ) )
| ~ ( in @ ( sK44_SY634 @ SV33 @ SV254 ) @ SV33 ) ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2211]) ).
thf(2358,plain,
! [SV33: $i,SV670: $i,SV254: $i] :
( ( ( ~ ~ ( ~ ( in @ SV254 @ SV670 )
| ~ ( in @ SV670 @ SV33 ) ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2359,plain,
! [SV446: $i,SV259: $i,SV39: $i] :
( ( ( SV39 = SV259 )
= $false )
| ( ( in @ SV446 @ SV259 )
= $true )
| ( ( in @ SV446 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2360,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2361,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2362,plain,
! [SV263: $i,SV43: $i,SV448: $i] :
( ( ( in @ SV448 @ SV43 )
= $false )
| ( ( in @ SV448 @ SV263 )
= $true )
| ( ( subset @ SV43 @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2363,plain,
! [SV45: $i,SV265: $i,SV450: $i] :
( ( ( in @ SV450 @ SV265 )
= $true )
| ( ( ~ ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) ) )
= $true )
| ( ( in @ SV450 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2364,plain,
! [SV268: $i > $o,SV48: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV48 ) )
= $true )
| ( ( ~ ~ ( SV268 @ SV607 ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2365,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV49 )
| ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV671 )
= ( SV451 @ SV671 ) ) )
= $true )
| ( ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2366,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV49 ) )
= $true )
| ( ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV666 )
= ( SV451 @ SV666 ) )
= $true )
| ( ( in @ ( SV451 @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) ) @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2367,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) )
= $true )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2368,plain,
! [SV556: $o,SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2369,plain,
! [SV53: $i,SV272: $i,SV453: $i,SV556: $o] :
( ( SV556 = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2226]) ).
thf(2370,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2371,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2372,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV53 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2373,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2374,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2375,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2230]) ).
thf(2376,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2377,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2378,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2379,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2232]) ).
thf(2380,plain,
! [SV61: $i,SV280: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV280 )
| ( in @ SY675 @ SV61 ) ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2381,plain,
! [SV280: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK45_SY675 @ SV61 @ SV280 ) @ SV280 )
| ( in @ ( sK45_SY675 @ SV61 @ SV280 ) @ SV61 ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2234]) ).
thf(2382,plain,
! [SV610: $i,SV458: $i,SV62: $i,SV281: $o] :
( ( ( ~ SV281 ) = $true )
| ( ( ( if @ SV62 @ SV281 @ SV458 @ SV610 )
= SV458 )
= $true )
| ( ( in @ SV610 @ SV62 )
= $false )
| ( ( in @ SV458 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2383,plain,
! [SV611: $i,SV459: $i,SV62: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV62 @ $true @ SV459 @ SV611 )
= SV459 )
= $true )
| ( ( in @ SV611 @ SV62 )
= $false )
| ( ( in @ SV459 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2384,plain,
! [SV612: $i,SV460: $i,SV62: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV62 @ $false @ SV460 @ SV612 )
= SV460 )
= $true )
| ( ( in @ SV612 @ SV62 )
= $false )
| ( ( in @ SV460 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2385,plain,
! [SV464: $i,SV67: $i,SV613: $i,SV286: $o] :
( ( ( ~ ~ SV286 )
= $true )
| ( ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV67 )
= $false )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2386,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) )
= $true )
| ( ( in @ SV614 @ SV67 )
= $false )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2387,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) )
= $true )
| ( ( in @ SV615 @ SV67 )
= $false )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2388,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2389,plain,
! [SV287: $i > $o,SV68: $i] :
( ( ( ! [SY685: $i] :
~ ~ ( ~ ( in @ SY685 @ SV68 )
| ~ ( SV287 @ SY685 ) ) )
= $true )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2390,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
| ~ ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2391,plain,
! [SV292: $i,SV617: $i,SV74: $i,SV579: $i] :
( ( ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) )
| ~ ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) ) )
= $false )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2392,plain,
! [SV618: $i,SV294: $i > $o,SV76: $i] :
( ( ( ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV76 )
| ~ ~ ( SV294 @ SY698 ) ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2393,plain,
! [SV619: $i,SV471: $i,SV295: $i,SV77: $i] :
( ( ( ~ ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY1137 )
= ( ap @ SV77 @ SV295 @ SV619 @ SY1137 ) ) ) )
= $true )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2394,plain,
! [SV580: $i,SV297: $i,SV79: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV79 ) )
= $true )
| ( ( ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SV667 @ SV297 )
| ( in @ SV667 @ SV580 ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2395,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( SV80 @ SV581 )
= $false )
| ( ( ~ ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) )
= $true )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2396,plain,
! [SV582: $i,SV298: $i,SV81: $i] :
( ( ( ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV81 )
| ~ ( in @ SY1109 @ SV298 )
| ( in @ SY1109 @ SV582 ) ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2397,plain,
! [SV620: $i,SV473: $i,SV299: $i,SV82: $i] :
( ( ( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY1140 )
= ( ap @ SV82 @ SV299 @ SV620 @ SY1140 ) ) ) )
= $true )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2398,plain,
! [SV621: $i,SV474: $i,SV301: $i,SV85: $i] :
( ( ( ~ ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV85 )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV301 )
| ~ ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV474 )
| ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV621 ) ) ) )
= $true )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2399,plain,
! [SV622: $i,SV86: $i,SV475: $i,SV302: $o] :
( ( ( ~ SV302 ) = $true )
| ( ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY1145: $i] :
( ~ ( ~ SV302
| ( SY1145 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY1145 != SV622 ) ) ) ) )
= $true )
| ( ( in @ SV622 @ SV86 )
= $false )
| ( ( in @ SV475 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2400,plain,
! [SV623: $i,SV86: $i,SV476: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY1146: $i] :
( ~ ( ~ $true
| ( SY1146 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY1146 != SV623 ) ) ) ) )
= $true )
| ( ( in @ SV623 @ SV86 )
= $false )
| ( ( in @ SV476 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2401,plain,
! [SV624: $i,SV86: $i,SV477: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY1147: $i] :
( ~ ( ~ $false
| ( SY1147 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY1147 != SV624 ) ) ) ) )
= $true )
| ( ( in @ SV624 @ SV86 )
= $false )
| ( ( in @ SV477 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2402,plain,
! [SV89: $i] :
( ( ( ~ ( in @ ( sK23_SY252 @ SV89 ) @ SV89 ) )
= $false )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2403,plain,
! [SV89: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2404,plain,
! [SV90: $i,SV558: $i,SV480: $i > $i > $o,SV305: $i,SV660: $i] :
( ( ( in @ SV660 @ SV305 )
= $false )
| ( ( ~ ( SV480 @ SV558 @ SV660 )
| ( in @ ( kpair @ SV558 @ SV660 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) ) )
= $true )
| ( ( in @ SV558 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2405,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( SV91 @ SV583 )
= $false )
| ( ( ~ ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) )
= $true )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2406,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( ~ ( in @ ( sK24_SY732 @ SV308 @ SV95 ) @ SV95 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2407,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( ~ ( SV308 @ ( sK24_SY732 @ SV308 @ SV95 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2408,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
| ~ ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2409,plain,
! [SV99: $i,SV312: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ SV312 ) )
= $true )
| ( ( in @ SV668 @ SV99 )
= $true )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2410,plain,
! [SV312: $i,SV99: $i] :
( ( ( ~ ( in @ ( sK41_SY738 @ SV99 @ SV312 ) @ SV312 ) )
= $false )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2411,plain,
! [SV312: $i,SV99: $i] :
( ( ( in @ ( sK41_SY738 @ SV99 @ SV312 ) @ SV99 )
= $false )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2412,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( SV483 = SV101 )
= $true )
| ( ( in @ SV483 @ SV314 )
= $true )
| ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2413,plain,
! [SV314: $i,SV101: $i,SV483: $i] :
( ( ( SV483 = SV101 )
= $false )
| ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2414,plain,
! [SV101: $i,SV314: $i,SV483: $i] :
( ( ( in @ SV483 @ SV314 )
= $false )
| ( ( in @ SV483 @ ( setadjoin @ SV101 @ SV314 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2415,plain,
! [SV318: $i,SV627: $i,SV105: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV105 ) )
= $true )
| ( ( in @ SV627 @ SV318 )
= $true )
| ( ( SV584 = SV627 )
= $false )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2416,plain,
! [SV108: $i,SV485: $i,SV628: $i,SV321: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV321 )
| ~ ( in @ ( kpair @ SV628 @ SV672 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SV672 ) )
= $true )
| ( ( in @ SV628 @ SV108 )
= $false )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2417,plain,
( ( ~ ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2418,plain,
( ( ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2419,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2420,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2421,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( ~ ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) ) )
= $true )
| ( ( SV324 @ SV486 )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2422,plain,
! [SV112: $i,SV486: $i,SV324: $i > $o] :
( ( ( ~ ( SV324 @ SV486 ) )
= $true )
| ( ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2423,plain,
! [SV629: $i,SV487: $i,SV113: $i,SV325: $o] :
( ( ( ~ SV325 ) = $true )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1149: $i] :
( ~ ( ~ SV325
| ( SY1149 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1149 != SV629 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) )
= $true )
| ( ( in @ SV629 @ SV113 )
= $false )
| ( ( in @ SV487 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2424,plain,
! [SV630: $i,SV488: $i,SV113: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1150: $i] :
( ~ ( ~ $true
| ( SY1150 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1150 != SV630 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) )
= $true )
| ( ( in @ SV630 @ SV113 )
= $false )
| ( ( in @ SV488 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2425,plain,
! [SV631: $i,SV489: $i,SV113: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1151: $i] :
( ~ ( ~ $false
| ( SY1151 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1151 != SV631 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) )
= $true )
| ( ( in @ SV631 @ SV113 )
= $false )
| ( ( in @ SV489 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2426,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2427,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2428,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2429,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
| ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2280]) ).
thf(2430,plain,
! [SV632: $i,SV493: $i,SV122: $i,SV332: $o] :
( ( ( ~ ~ SV332 )
= $true )
| ( ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 )
= $true )
| ( ( in @ SV632 @ SV122 )
= $false )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2431,plain,
! [SV633: $i,SV494: $i,SV122: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 )
= $true )
| ( ( in @ SV633 @ SV122 )
= $false )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2432,plain,
! [SV634: $i,SV495: $i,SV122: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 )
= $true )
| ( ( in @ SV634 @ SV122 )
= $false )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2433,plain,
! [SV501: $i > $i > $o,SV130: $i,SV560: $i,SV342: $i,SV661: $i] :
( ( ( in @ SV661 @ SV342 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV560 @ SV661 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
| ( SV501 @ SV560 @ SV661 ) )
= $true )
| ( ( in @ SV560 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2434,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2435,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2436,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2437,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
| ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2295]) ).
thf(2438,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) )
= $true )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2439,plain,
! [SV586: $i,SV361: $i,SV152: $i] :
( ( ( ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV152 )
| ~ ( in @ SY1115 @ SV361 )
| ( in @ SY1115 @ SV586 ) ) )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2440,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
| ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 ) ) )
= $true )
| ( ( ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2441,plain,
! [SV156: $i,SV513: $i,SV645: $i,SV364: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV364 )
| ~ ( in @ ( kpair @ SV645 @ SV673 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SV673 ) )
= $true )
| ( ( in @ SV645 @ SV156 )
= $false )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2442,plain,
! [SV647: $i,SV518: $i,SV369: $i,SV162: $i] :
( ( ( ~ ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1156 )
= ( ap @ SV162 @ SV369 @ SV647 @ SY1156 ) ) ) )
= $true )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2443,plain,
! [SV163: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ omega )
| ~ ( in @ ( sK42_SY416 @ SV163 ) @ SV163 ) ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2444,plain,
! [SV163: $i] :
( ( ( in @ ( setadjoin @ ( sK42_SY416 @ SV163 ) @ ( sK42_SY416 @ SV163 ) ) @ SV163 )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2445,plain,
! [SV649: $o,SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 != SV166 )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2309]) ).
thf(2446,plain,
! [SV166: $i,SV372: $i,SV521: $i,SV649: $o] :
( ( SV649 = $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2309]) ).
thf(2447,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 != SV166 )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2448,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2449,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 != SV166 )
= $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2311]) ).
thf(2450,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2311]) ).
thf(2451,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) )
= $true )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2452,plain,
! [SV178: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV382 ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2453,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( ~ ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 )
| ! [SY1191: $i] :
( ~ ( in @ SY1191 @ SV383 )
| ~ ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SY1191 ) @ SV529 )
| ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SY1191 ) ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2317]) ).
thf(2454,plain,
! [SV182: $i,SV384: $i,SV530: $i] :
( ( ( in @ SV530 @ SV384 )
= $true )
| ( ( ~ ( in @ SV530 @ SV182 ) )
= $true )
| ( ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2455,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( ~ ( in @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SV187 )
| ~ ~ ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2456,plain,
! [SV534: $i,SV391: $i,SV191: $i] :
( ( ( subset @ SV191 @ SV391 )
= $false )
| ( ( in @ SV534 @ SV391 )
= $true )
| ( ( in @ SV534 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2457,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY1192: $i] :
( ~ ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
| ~ ( SV196 @ SY1192 )
| ( ( sK47_SY498 @ SV593 @ SV196 )
= SY1192 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2323]) ).
thf(2458,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2459,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2325]) ).
thf(2460,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ( in @ ( sK28_SY868 @ SV399 @ SV200 ) @ SV200 ) )
= $false )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2461,plain,
! [SV200: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( sK28_SY868 @ SV399 @ SV200 ) ) )
= $false )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2462,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 )
| ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV410 )
| ~ ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SY1193 ) @ SV547 )
| ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SY1193 ) ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2329]) ).
thf(2463,plain,
! [SV216: $i,SV413: $i,SV594: $i] :
( ( ( in @ SV594 @ SV413 )
= $false )
| ( ( ~ ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) ) )
= $true )
| ( ( in @ SV594 @ SV216 )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2464,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) @ SV218 )
| ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SV415 )
| ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
!= SY1194 )
| ~ ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ SY1194 ) )
| ~ ( ~ ( SV656 @ SY1194 )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2331]) ).
thf(2465,plain,
! [SV596: $i,SV419: $i,SV222: $i] :
( ( ( ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SV222 )
| ~ ( in @ SY1128 @ SV419 )
| ( in @ SY1128 @ SV596 ) ) )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2466,plain,
! [SV657: $i,SV421: $i > $o,SV224: $i] :
( ( ( ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV224 )
| ~ ~ ( SV421 @ SY899 ) ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2467,plain,
! [SV658: $i,SV551: $i,SV424: $i,SV227: $i] :
( ( ( ~ ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV227 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV424 )
| ~ ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV551 )
| ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV658 ) ) ) )
= $true )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2468,plain,
! [SV427: $i > $o,SV231: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV231 ) )
= $true )
| ( ( ~ ( SV427 @ SV659 ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2469,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV3 ) )
= $true )
| ( ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV669 )
= ( SV430 @ SV669 ) )
= $true )
| ( ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2470,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV662: $i] :
( ( ( in @ SV662 @ SV3 )
= $false )
| ( ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV662 )
= ( SV430 @ SV662 ) )
= $true )
| ( ( in @ ( SV430 @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) ) @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2471,plain,
! [SV236: $i,SV4: $i > $i > $o] :
( ( ( ! [SY1187: $i] :
~ ( ~ ( ~ ( in @ SY1187 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1187 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1187 ) )
| ( in @ SY1187 @ ( sK43_SY599 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2472,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
| ~ ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2473,plain,
! [SV599: $i,SV435: $i,SV14: $i,SV244: $o] :
( ( ( ~ SV244 ) = $false )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) )
= $true )
| ( ( in @ SV599 @ SV14 )
= $false )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2474,plain,
! [SV600: $i,SV436: $i,SV14: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) )
= $true )
| ( ( in @ SV600 @ SV14 )
= $false )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2475,plain,
! [SV601: $i,SV437: $i,SV14: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) )
= $true )
| ( ( in @ SV601 @ SV14 )
= $false )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2476,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ! [SY1099: $i] :
( ~ ( SV16 @ SY1099 )
| ( SV571 = SY1099 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2477,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK37_SY55 @ SV572 @ SV18 ) @ SV18 )
| ~ ~ ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2478,plain,
! [SV573: $i,SV246: $i > $o,SV20: $i,SV664: $i] :
( ( ( in @ SV664 @ SV20 )
= $false )
| ( ( ~ ( SV246 @ SV573 )
| ~ ( SV246 @ SV664 )
| ( SV573 = SV664 ) )
= $true )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2479,plain,
! [SV23: $i] :
( ( ~ ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2480,plain,
! [SV23: $i] :
( ( ! [SY938: $i,SY939: $i] :
( ~ ~ ( ~ ( in @ SY938 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY939 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY938 )
| ( in @ SX4 @ SY939 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY939 )
| ( in @ SX4 @ SY938 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2347]) ).
thf(2481,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) )
| ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) ) )
= $false )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2482,plain,
! [SV24: $i,SV574: $o,SV248: $i] :
( ( ( in @ SV248 @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) )
= $true )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2483,plain,
! [SV248: $i,SV24: $i,SV574: $o] :
( ( ( ~ ( in @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) @ SV24 ) )
= $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2484,plain,
! [SV24: $i,SV248: $i,SV574: $o] :
( ( SV574 = $false )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2485,plain,
! [SV24: $i,SV248: $i] :
( ( ( in @ SV248 @ ( sK39_SX0 @ SV24 @ SV248 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2486,plain,
! [SV248: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK39_SX0 @ SV24 @ SV248 ) @ SV24 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2352]) ).
thf(2487,plain,
! [SV24: $i,SV248: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2352]) ).
thf(2488,plain,
! [SV24: $i,SV248: $i] :
( ( ( in @ SV248 @ ( sK40_SX0 @ SV24 @ SV248 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2489,plain,
! [SV248: $i,SV24: $i] :
( ( ( ~ ( in @ ( sK40_SX0 @ SV24 @ SV248 ) @ SV24 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2490,plain,
! [SV24: $i,SV248: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2491,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ! [SY1102: $i] :
( ~ ( SV27 @ SY1102 )
| ( SV575 = SY1102 ) ) )
= $false )
| ( ( SV27 @ SV575 )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2492,plain,
! [SV30: $i,SV252: $i > $o,SV442: $i] :
( ( ( ~ ( in @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) @ SV30 )
| ~ ( SV252 @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) )
| ( ( sK50_SY951 @ SV442 @ SV252 @ SV30 )
= SV442 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2356]) ).
thf(2493,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ SV254 @ ( sK44_SY634 @ SV33 @ SV254 ) )
| ~ ( in @ ( sK44_SY634 @ SV33 @ SV254 ) @ SV33 ) ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2494,plain,
! [SV33: $i,SV670: $i,SV254: $i] :
( ( ( ~ ( ~ ( in @ SV254 @ SV670 )
| ~ ( in @ SV670 @ SV33 ) ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2495,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2496,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2497,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
| ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
= $false )
| ( ( ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2498,plain,
! [SV265: $i,SV45: $i,SV450: $i] :
( ( ( in @ SV450 @ ( symdiff @ SV45 @ SV265 ) )
= $false )
| ( ( in @ SV450 @ SV265 )
= $true )
| ( ( in @ SV450 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2499,plain,
! [SV268: $i > $o,SV48: $i,SV607: $i] :
( ( ( in @ SV607 @ SV48 )
= $false )
| ( ( ~ ~ ( SV268 @ SV607 ) )
= $true )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2500,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV49 ) )
= $true )
| ( ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV671 )
= ( SV451 @ SV671 ) )
= $true )
| ( ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2501,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV666: $i] :
( ( ( in @ SV666 @ SV49 )
= $false )
| ( ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV666 )
= ( SV451 @ SV666 ) )
= $true )
| ( ( in @ ( SV451 @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) ) @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2502,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ! [SY1104: $i] :
( ~ ( SV51 @ SY1104 )
| ( SV577 = SY1104 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2503,plain,
! [SV556: $o,SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ SV53 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 )
| SV556 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2504,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 ) )
= $true )
| ( SV556 = $true )
| ( SV556 = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2505,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ SV53 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2506,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2507,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( ( in @ SV453 @ SV53 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2508,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2509,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2510,plain,
! [SV609: $o,SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2511,plain,
! [SV277: $i,SV58: $i,SV456: $i,SV609: $o] :
( ( SV609 = $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2512,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2376]) ).
thf(2513,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2514,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2515,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2516,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2517,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2518,plain,
! [SV280: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK51_SY675 @ SV61 @ SV280 ) @ SV280 )
| ( in @ ( sK51_SY675 @ SV61 @ SV280 ) @ SV61 ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2380]) ).
thf(2519,plain,
! [SV280: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK45_SY675 @ SV61 @ SV280 ) @ SV280 ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2520,plain,
! [SV280: $i,SV61: $i] :
( ( ( in @ ( sK45_SY675 @ SV61 @ SV280 ) @ SV61 )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2381]) ).
thf(2521,plain,
! [SV610: $i,SV458: $i,SV62: $i,SV281: $o] :
( ( SV281 = $false )
| ( ( ( if @ SV62 @ SV281 @ SV458 @ SV610 )
= SV458 )
= $true )
| ( ( in @ SV610 @ SV62 )
= $false )
| ( ( in @ SV458 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2522,plain,
! [SV611: $i,SV459: $i,SV62: $i] :
( ( $true = $false )
| ( ( ( if @ SV62 @ $true @ SV459 @ SV611 )
= SV459 )
= $true )
| ( ( in @ SV611 @ SV62 )
= $false )
| ( ( in @ SV459 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2523,plain,
! [SV612: $i,SV460: $i,SV62: $i] :
( ( $false = $false )
| ( ( ( if @ SV62 @ $false @ SV460 @ SV612 )
= SV460 )
= $true )
| ( ( in @ SV612 @ SV62 )
= $false )
| ( ( in @ SV460 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2524,plain,
! [SV464: $i,SV67: $i,SV613: $i,SV286: $o] :
( ( ( ~ SV286 ) = $false )
| ( ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV67 )
= $false )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2525,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) )
= $true )
| ( ( in @ SV614 @ SV67 )
= $false )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2526,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) )
= $true )
| ( ( in @ SV615 @ SV67 )
= $false )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2527,plain,
! [SV287: $i > $o,SV68: $i,SV674: $i] :
( ( ( ~ ~ ( ~ ( in @ SV674 @ SV68 )
| ~ ( SV287 @ SV674 ) ) )
= $true )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2528,plain,
! [SV287: $i > $o,SV68: $i,SV675: $i] :
( ( ( ~ ~ ( ~ ( in @ SV675 @ SV68 )
| ~ ( SV287 @ SV675 ) ) )
= $true )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2529,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2390]) ).
thf(2530,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( ~ ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2390]) ).
thf(2531,plain,
! [SV292: $i,SV617: $i,SV74: $i,SV579: $i] :
( ( ( ~ ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) ) )
= $false )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2391]) ).
thf(2532,plain,
! [SV74: $i,SV579: $i,SV292: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) ) )
= $false )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2391]) ).
thf(2533,plain,
! [SV76: $i,SV294: $i > $o,SV618: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) @ SV76 )
| ~ ~ ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) ) ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2392]) ).
thf(2534,plain,
! [SV619: $i,SV471: $i,SV295: $i,SV77: $i] :
( ( ( ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ SY1137 )
= ( ap @ SV77 @ SV295 @ SV619 @ SY1137 ) ) ) )
= $false )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2535,plain,
! [SV580: $i,SV297: $i,SV79: $i,SV667: $i] :
( ( ( in @ SV667 @ SV79 )
= $false )
| ( ( ~ ( in @ SV297 @ ( powerset @ SV580 ) )
| ~ ( in @ SV667 @ SV297 )
| ( in @ SV667 @ SV580 ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2536,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ! [SY1108: $i] :
( ~ ( SV80 @ SY1108 )
| ( SV581 = SY1108 ) ) )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2537,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( ~ ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV81 )
| ~ ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV298 )
| ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV582 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2396]) ).
thf(2538,plain,
! [SV620: $i,SV473: $i,SV299: $i,SV82: $i] :
( ( ( ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ SY1140 )
= ( ap @ SV82 @ SV299 @ SV620 @ SY1140 ) ) ) )
= $false )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2539,plain,
! [SV621: $i,SV474: $i,SV301: $i,SV85: $i] :
( ( ( ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV85 )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV301 )
| ~ ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV474 )
| ( in @ ( kpair @ SY1141 @ SY1142 ) @ SV621 ) ) ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2540,plain,
! [SV622: $i,SV86: $i,SV475: $i,SV302: $o] :
( ( SV302 = $false )
| ( ( in @ SV475
@ ( dsetconstr @ SV86
@ ^ [SY1145: $i] :
( ~ ( ~ SV302
| ( SY1145 != SV475 ) )
| ~ ( ~ ~ SV302
| ( SY1145 != SV622 ) ) ) ) )
= $true )
| ( ( in @ SV622 @ SV86 )
= $false )
| ( ( in @ SV475 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2541,plain,
! [SV623: $i,SV86: $i,SV476: $i] :
( ( $true = $false )
| ( ( in @ SV476
@ ( dsetconstr @ SV86
@ ^ [SY1146: $i] :
( ~ ( ~ $true
| ( SY1146 != SV476 ) )
| ~ ( ~ ~ $true
| ( SY1146 != SV623 ) ) ) ) )
= $true )
| ( ( in @ SV623 @ SV86 )
= $false )
| ( ( in @ SV476 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2542,plain,
! [SV624: $i,SV86: $i,SV477: $i] :
( ( $false = $false )
| ( ( in @ SV477
@ ( dsetconstr @ SV86
@ ^ [SY1147: $i] :
( ~ ( ~ $false
| ( SY1147 != SV477 ) )
| ~ ( ~ ~ $false
| ( SY1147 != SV624 ) ) ) ) )
= $true )
| ( ( in @ SV624 @ SV86 )
= $false )
| ( ( in @ SV477 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2543,plain,
! [SV89: $i] :
( ( ( in @ ( sK23_SY252 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2544,plain,
! [SV89: $i] :
( ( $true = $true )
| ( ( SV89 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2545,plain,
! [SV305: $i,SV90: $i,SV660: $i,SV558: $i,SV480: $i > $i > $o] :
( ( ( ~ ( SV480 @ SV558 @ SV660 ) )
= $true )
| ( ( in @ ( kpair @ SV558 @ SV660 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) )
= $true )
| ( ( in @ SV660 @ SV305 )
= $false )
| ( ( in @ SV558 @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2546,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ! [SY1110: $i] :
( ~ ( SV91 @ SY1110 )
| ( SV583 = SY1110 ) ) )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2547,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( in @ ( sK24_SY732 @ SV308 @ SV95 ) @ SV95 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2548,plain,
! [SV95: $i,SV308: $i > $o] :
( ( ( SV308 @ ( sK24_SY732 @ SV308 @ SV95 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV95
@ ^ [SY731: $i] : ( SV308 @ SY731 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2549,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2550,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( ~ ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) ) )
= $false )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2551,plain,
! [SV99: $i,SV312: $i,SV668: $i] :
( ( ( in @ SV668 @ SV312 )
= $false )
| ( ( in @ SV668 @ SV99 )
= $true )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2552,plain,
! [SV312: $i,SV99: $i] :
( ( ( in @ ( sK41_SY738 @ SV99 @ SV312 ) @ SV312 )
= $true )
| ( ( in @ SV312 @ ( powerset @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2553,plain,
! [SV318: $i,SV627: $i,SV105: $i,SV584: $i] :
( ( ( in @ SV584 @ SV105 )
= $false )
| ( ( in @ SV627 @ SV318 )
= $true )
| ( ( SV584 = SV627 )
= $false )
| ( ( SV105 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2554,plain,
! [SV108: $i,SV485: $i,SV628: $i,SV321: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV321 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV628 @ SV672 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SV672 ) )
= $true )
| ( ( in @ SV628 @ SV108 )
= $false )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2555,plain,
( ( in @ sK3_SY2 @ ( setminus @ sK1_A @ sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2556,plain,
( ( in @ sK3_SY2 @ sK2_SY0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2557,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) ) )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2558,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2559,plain,
! [SV324: $i > $o,SV112: $i,SV486: $i] :
( ( ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY750: $i] : ( SV324 @ SY750 ) ) )
= $false )
| ( ( SV324 @ SV486 )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2560,plain,
! [SV112: $i,SV486: $i,SV324: $i > $o] :
( ( ( SV324 @ SV486 )
= $false )
| ( ( in @ SV486
@ ( dsetconstr @ SV112
@ ^ [SY751: $i] : ( SV324 @ SY751 ) ) )
= $true )
| ( ( in @ SV486 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2561,plain,
! [SV629: $i,SV487: $i,SV113: $i,SV325: $o] :
( ( SV325 = $false )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1149: $i] :
( ~ ( ~ SV325
| ( SY1149 != SV487 ) )
| ~ ( ~ ~ SV325
| ( SY1149 != SV629 ) ) ) )
= ( setadjoin @ SV487 @ emptyset ) )
= $true )
| ( ( in @ SV629 @ SV113 )
= $false )
| ( ( in @ SV487 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2562,plain,
! [SV630: $i,SV488: $i,SV113: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1150: $i] :
( ~ ( ~ $true
| ( SY1150 != SV488 ) )
| ~ ( ~ ~ $true
| ( SY1150 != SV630 ) ) ) )
= ( setadjoin @ SV488 @ emptyset ) )
= $true )
| ( ( in @ SV630 @ SV113 )
= $false )
| ( ( in @ SV488 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2563,plain,
! [SV631: $i,SV489: $i,SV113: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV113
@ ^ [SY1151: $i] :
( ~ ( ~ $false
| ( SY1151 != SV489 ) )
| ~ ( ~ ~ $false
| ( SY1151 != SV631 ) ) ) )
= ( setadjoin @ SV489 @ emptyset ) )
= $true )
| ( ( in @ SV631 @ SV113 )
= $false )
| ( ( in @ SV489 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2564,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2426]) ).
thf(2565,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2566,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2567,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ~ ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2429]) ).
thf(2568,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2429]) ).
thf(2569,plain,
! [SV632: $i,SV493: $i,SV122: $i,SV332: $o] :
( ( ( ~ SV332 ) = $false )
| ( ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 )
= $true )
| ( ( in @ SV632 @ SV122 )
= $false )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2570,plain,
! [SV633: $i,SV494: $i,SV122: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 )
= $true )
| ( ( in @ SV633 @ SV122 )
= $false )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2571,plain,
! [SV634: $i,SV495: $i,SV122: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 )
= $true )
| ( ( in @ SV634 @ SV122 )
= $false )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2572,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i,SV661: $i,SV560: $i] :
( ( ( ~ ( in @ ( kpair @ SV560 @ SV661 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) ) )
= $true )
| ( ( SV501 @ SV560 @ SV661 )
= $true )
| ( ( in @ SV661 @ SV342 )
= $false )
| ( ( in @ SV560 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2573,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2574,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2575,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2576,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2437]) ).
thf(2577,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2437]) ).
thf(2578,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ! [SY1114: $i] :
( ~ ( SV145 @ SY1114 )
| ( SV585 = SY1114 ) ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2579,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV361 )
| ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV586 ) )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2439]) ).
thf(2580,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
| ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 ) )
= $false )
| ( ( ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2581,plain,
! [SV156: $i,SV513: $i,SV645: $i,SV364: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV364 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV645 @ SV673 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SV673 ) )
= $true )
| ( ( in @ SV645 @ SV156 )
= $false )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2582,plain,
! [SV647: $i,SV518: $i,SV369: $i,SV162: $i] :
( ( ( ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ SY1156 )
= ( ap @ SV162 @ SV369 @ SV647 @ SY1156 ) ) ) )
= $false )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2583,plain,
! [SV163: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ omega )
| ~ ( in @ ( sK42_SY416 @ SV163 ) @ SV163 ) ) )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2584,plain,
! [SV163: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ omega )
| ( in @ SV676 @ SV163 ) )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( setadjoin @ ( sK42_SY416 @ SV163 ) @ ( sK42_SY416 @ SV163 ) ) @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2585,plain,
! [SV649: $o,SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 = SV166 )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 )
| SV649 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2445]) ).
thf(2586,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 ) )
= $true )
| ( SV649 = $true )
| ( SV649 = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2587,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 = SV166 )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true )
| $true )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2588,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2589,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( ( SV521 = SV166 )
= $true )
| ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false )
| $false )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2590,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2591,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ! [SY1119: $i] :
( ~ ( SV175 @ SY1119 )
| ( SV590 = SY1119 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2592,plain,
! [SV178: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV178 ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2593,plain,
! [SV178: $i,SV382: $i] :
( ( ( ~ ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV382 ) )
= $false )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2594,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( ~ ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2595,plain,
! [SV179: $i,SV529: $i,SV652: $i > $o,SV383: $i] :
( ( ( ! [SY1191: $i] :
( ~ ( in @ SY1191 @ SV383 )
| ~ ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SY1191 ) @ SV529 )
| ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SY1191 ) ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2596,plain,
! [SV384: $i,SV182: $i,SV530: $i] :
( ( ( in @ SV530 @ SV182 )
= $false )
| ( ( in @ SV530 @ SV384 )
= $true )
| ( ( in @ SV530 @ ( setminus @ SV182 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2597,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( ~ ( in @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SV187 ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2598,plain,
! [SV187: $i,SV533: $i,SV388: $i] :
( ( ( ~ ~ ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2599,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
| ~ ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
| ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2457]) ).
thf(2600,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2601,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
| ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
= $false )
| ( ( ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2602,plain,
! [SV200: $i,SV399: $i] :
( ( ( in @ ( sK28_SY868 @ SV399 @ SV200 ) @ SV200 )
= $true )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2603,plain,
! [SV200: $i,SV399: $i] :
( ( ( in @ SV399 @ ( sK28_SY868 @ SV399 @ SV200 ) )
= $true )
| ( ( in @ SV399 @ ( setunion @ SV200 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2461]) ).
thf(2604,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2605,plain,
! [SV213: $i,SV547: $i,SV655: $i > $o,SV410: $i] :
( ( ( ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV410 )
| ~ ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SY1193 ) @ SV547 )
| ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SY1193 ) ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2606,plain,
! [SV413: $i,SV216: $i,SV594: $i] :
( ( ( in @ SV594 @ ( setminus @ SV216 @ SV413 ) )
= $false )
| ( ( in @ SV594 @ SV413 )
= $false )
| ( ( in @ SV594 @ SV216 )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2607,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) @ SV218 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2608,plain,
! [SV218: $i,SV595: $i > $o,SV656: $i > $o,SV415: $i] :
( ( ( ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SV415 )
| ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
!= SY1194 )
| ~ ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ SY1194 ) )
| ~ ( ~ ( SV656 @ SY1194 )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2609,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( ~ ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
| ~ ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
| ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 ) )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2465]) ).
thf(2610,plain,
! [SV224: $i,SV421: $i > $o,SV657: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) @ SV224 )
| ~ ~ ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) ) ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2466]) ).
thf(2611,plain,
! [SV658: $i,SV551: $i,SV424: $i,SV227: $i] :
( ( ( ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV227 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV424 )
| ~ ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV551 )
| ( in @ ( kpair @ SY1168 @ SY1169 ) @ SV658 ) ) ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2612,plain,
! [SV427: $i > $o,SV231: $i,SV659: $i] :
( ( ( in @ SV659 @ SV231 )
= $false )
| ( ( ~ ( SV427 @ SV659 ) )
= $true )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2613,plain,
! [SV430: $i > $i,SV235: $i,SV3: $i,SV669: $i] :
( ( ( in @ SV669 @ SV3 )
= $false )
| ( ( ( ap @ SV3 @ SV235
@ ( lam @ SV3 @ SV235
@ ^ [SY916: $i] : ( SV430 @ SY916 ) )
@ SV669 )
= ( SV430 @ SV669 ) )
= $true )
| ( ( in @ ( sK18_SY914 @ SV235 @ SV430 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2614,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
| ~ ( ~ ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) )
| ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2615,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 ) )
= $true )
| ( ( ~ ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2616,plain,
! [SV599: $i,SV435: $i,SV14: $i,SV244: $o] :
( ( SV244 = $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1130: $i] :
( ~ ( ~ SV244
| ( SY1130 != SV435 ) )
| ~ ( ~ ~ SV244
| ( SY1130 != SV599 ) ) ) )
= ( setadjoin @ SV599 @ emptyset ) )
= $true )
| ( ( in @ SV599 @ SV14 )
= $false )
| ( ( in @ SV435 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2617,plain,
! [SV600: $i,SV436: $i,SV14: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1131: $i] :
( ~ ( ~ $true
| ( SY1131 != SV436 ) )
| ~ ( ~ ~ $true
| ( SY1131 != SV600 ) ) ) )
= ( setadjoin @ SV600 @ emptyset ) )
= $true )
| ( ( in @ SV600 @ SV14 )
= $false )
| ( ( in @ SV436 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2618,plain,
! [SV601: $i,SV437: $i,SV14: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV14
@ ^ [SY1132: $i] :
( ~ ( ~ $false
| ( SY1132 != SV437 ) )
| ~ ( ~ ~ $false
| ( SY1132 != SV601 ) ) ) )
= ( setadjoin @ SV601 @ emptyset ) )
= $true )
| ( ( in @ SV601 @ SV14 )
= $false )
| ( ( in @ SV437 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2475]) ).
thf(2619,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
| ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2476]) ).
thf(2620,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK37_SY55 @ SV572 @ SV18 ) @ SV18 ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2477]) ).
thf(2621,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ~ ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2477]) ).
thf(2622,plain,
! [SV20: $i,SV664: $i,SV573: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV573 ) )
= $true )
| ( ( ~ ( SV246 @ SV664 )
| ( SV573 = SV664 ) )
= $true )
| ( ( in @ SV664 @ SV20 )
= $false )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2623,plain,
! [SV23: $i] :
( ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) )
| ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2624,plain,
! [SV23: $i,SV678: $i] :
( ( ! [SY1197: $i] :
( ~ ~ ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1197 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SY1198: $i] :
( ~ ( in @ SY1198 @ SV678 )
| ( in @ SY1198 @ SY1197 ) )
| ! [SY1199: $i] :
( ~ ( in @ SY1199 @ SY1197 )
| ( in @ SY1199 @ SV678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2625,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) )
| ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2626,plain,
! [SV248: $i,SV24: $i,SV574: $o] :
( ( ( in @ ( sK38_SY1101 @ SV574 @ SV24 @ SV248 ) @ SV24 )
= $true )
| ( SV574 = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2627,plain,
! [SV248: $i,SV24: $i] :
( ( ( in @ ( sK39_SX0 @ SV24 @ SV248 ) @ SV24 )
= $true )
| ( $true = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2628,plain,
! [SV248: $i,SV24: $i] :
( ( ( in @ ( sK40_SX0 @ SV24 @ SV248 ) @ SV24 )
= $true )
| ( $false = $true )
| ( ( in @ SV248 @ ( setunion @ SV24 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2629,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ ( sK59_SY1102 @ SV575 @ SV27 ) )
| ( SV575
= ( sK59_SY1102 @ SV575 @ SV27 ) ) )
= $false )
| ( ( SV27 @ SV575 )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2491]) ).
thf(2630,plain,
! [SV30: $i,SV252: $i > $o,SV442: $i] :
( ( ( ~ ( in @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) @ SV30 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2631,plain,
! [SV30: $i,SV442: $i,SV252: $i > $o] :
( ( ( ~ ( SV252 @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) )
| ( ( sK50_SY951 @ SV442 @ SV252 @ SV30 )
= SV442 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2632,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ ( sK44_SY634 @ SV33 @ SV254 ) )
| ~ ( in @ ( sK44_SY634 @ SV33 @ SV254 ) @ SV33 ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2633,plain,
! [SV33: $i,SV670: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV670 )
| ~ ( in @ SV670 @ SV33 ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2494]) ).
thf(2634,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2635,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2636,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) )
= $false )
| ( ( ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2637,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2638,plain,
! [SV48: $i,SV607: $i,SV268: $i > $o] :
( ( ( ~ ( SV268 @ SV607 ) )
= $false )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2639,plain,
! [SV451: $i > $i,SV269: $i,SV49: $i,SV671: $i] :
( ( ( in @ SV671 @ SV49 )
= $false )
| ( ( ( ap @ SV49 @ SV269
@ ( lam @ SV49 @ SV269
@ ^ [SY958: $i] : ( SV451 @ SY958 ) )
@ SV671 )
= ( SV451 @ SV671 ) )
= $true )
| ( ( in @ ( sK21_SY956 @ SV269 @ SV451 @ SV49 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2640,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
| ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2502]) ).
thf(2641,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| SV556 ) )
= $true )
| ( SV556 = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2642,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| SV556 )
= $false )
| ( SV556 = $true )
| ( SV556 = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2643,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2644,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2645,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV272 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2646,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2647,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 ) )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2648,plain,
! [SV609: $o,SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2649,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 ) )
= $true )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2650,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2651,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2513]) ).
thf(2652,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2653,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2654,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2655,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2656,plain,
! [SV280: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK51_SY675 @ SV61 @ SV280 ) @ SV280 ) )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2518]) ).
thf(2657,plain,
! [SV280: $i,SV61: $i] :
( ( ( in @ ( sK51_SY675 @ SV61 @ SV280 ) @ SV61 )
= $false )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2518]) ).
thf(2658,plain,
! [SV280: $i,SV61: $i] :
( ( ( in @ ( sK45_SY675 @ SV61 @ SV280 ) @ SV280 )
= $true )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2659,plain,
! [SV464: $i,SV67: $i,SV613: $i,SV286: $o] :
( ( SV286 = $true )
| ( ( in @ SV613
@ ( dsetconstr @ SV67
@ ^ [SY1134: $i] :
( ~ ( ~ SV286
| ( SY1134 != SV464 ) )
| ~ ( ~ ~ SV286
| ( SY1134 != SV613 ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV67 )
= $false )
| ( ( in @ SV464 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2524]) ).
thf(2660,plain,
! [SV465: $i,SV67: $i,SV614: $i] :
( ( $true = $true )
| ( ( in @ SV614
@ ( dsetconstr @ SV67
@ ^ [SY1135: $i] :
( ~ ( ~ $true
| ( SY1135 != SV465 ) )
| ~ ( ~ ~ $true
| ( SY1135 != SV614 ) ) ) ) )
= $true )
| ( ( in @ SV614 @ SV67 )
= $false )
| ( ( in @ SV465 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2661,plain,
! [SV466: $i,SV67: $i,SV615: $i] :
( ( $false = $true )
| ( ( in @ SV615
@ ( dsetconstr @ SV67
@ ^ [SY1136: $i] :
( ~ ( ~ $false
| ( SY1136 != SV466 ) )
| ~ ( ~ ~ $false
| ( SY1136 != SV615 ) ) ) ) )
= $true )
| ( ( in @ SV615 @ SV67 )
= $false )
| ( ( in @ SV466 @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2526]) ).
thf(2662,plain,
! [SV287: $i > $o,SV68: $i,SV674: $i] :
( ( ( ~ ( ~ ( in @ SV674 @ SV68 )
| ~ ( SV287 @ SV674 ) ) )
= $false )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2663,plain,
! [SV287: $i > $o,SV68: $i,SV675: $i] :
( ( ( ~ ( ~ ( in @ SV675 @ SV68 )
| ~ ( SV287 @ SV675 ) ) )
= $false )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2664,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2665,plain,
! [SV69: $i,SV288: $i > $o] :
( ( ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV69 )
| ~ ( SV288 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2666,plain,
! [SV292: $i,SV617: $i,SV74: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV74 )
| ( in @ SV617 @ SV292 ) )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2667,plain,
! [SV74: $i,SV579: $i,SV292: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ SV292 )
| ( in @ SV579 @ SV74 ) )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2532]) ).
thf(2668,plain,
! [SV76: $i,SV294: $i > $o,SV618: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) @ SV76 )
| ~ ~ ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) ) ) )
= $true )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2669,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i] :
( ( ( ~ ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
| ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) ) )
= $false )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2534]) ).
thf(2670,plain,
! [SV79: $i,SV667: $i,SV580: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( powerset @ SV580 ) ) )
= $true )
| ( ( ~ ( in @ SV667 @ SV297 )
| ( in @ SV667 @ SV580 ) )
= $true )
| ( ( in @ SV667 @ SV79 )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2671,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
| ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) ) )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2536]) ).
thf(2672,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( ~ ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2537]) ).
thf(2673,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( ~ ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV298 )
| ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV582 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2537]) ).
thf(2674,plain,
! [SV82: $i,SV299: $i,SV473: $i,SV620: $i] :
( ( ( ~ ( in @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) @ SV82 )
| ( ( ap @ SV82 @ SV299 @ SV473 @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) )
= ( ap @ SV82 @ SV299 @ SV620 @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) ) ) )
= $false )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2538]) ).
thf(2675,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( ~ ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
| ! [SY1200: $i] :
( ~ ( in @ SY1200 @ SV301 )
| ~ ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SY1200 ) @ SV474 )
| ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SY1200 ) @ SV621 ) ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2539]) ).
thf(2676,plain,
! [SV305: $i,SV90: $i,SV660: $i,SV558: $i,SV480: $i > $i > $o] :
( ( ( SV480 @ SV558 @ SV660 )
= $false )
| ( ( in @ ( kpair @ SV558 @ SV660 )
@ ( dpsetconstr @ SV90 @ SV305
@ ^ [SY994: $i,SY995: $i] : ( SV480 @ SY994 @ SY995 ) ) )
= $true )
| ( ( in @ SV660 @ SV305 )
= $false )
| ( ( in @ SV558 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2677,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
| ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2546]) ).
thf(2678,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2679,plain,
! [SV96: $i,SV309: $i > $o] :
( ( ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) )
= $true )
| ( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ SV96 )
| ~ ( SV309 @ SY734 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2550]) ).
thf(2680,plain,
! [SV108: $i,SV485: $i,SV628: $i,SV321: $i,SV672: $i] :
( ( ( in @ SV672 @ SV321 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV628 @ SV672 ) @ SV485 )
| ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SV672 ) )
= $true )
| ( ( in @ SV628 @ SV108 )
= $false )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2681,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
| ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 ) )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2682,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2683,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2684,plain,
! [SV331: $i > $o,SV121: $i,SV679: $i] :
( ( ( ~ ~ ( ~ ( in @ SV679 @ SV121 )
| ~ ( SV331 @ SV679 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2685,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2686,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2687,plain,
! [SV121: $i,SV331: $i > $o] :
( ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true )
| ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) )
| ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2688,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2689,plain,
! [SV632: $i,SV493: $i,SV122: $i,SV332: $o] :
( ( SV332 = $true )
| ( ( ( if @ SV122 @ SV332 @ SV493 @ SV632 )
= SV632 )
= $true )
| ( ( in @ SV632 @ SV122 )
= $false )
| ( ( in @ SV493 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2690,plain,
! [SV633: $i,SV494: $i,SV122: $i] :
( ( $true = $true )
| ( ( ( if @ SV122 @ $true @ SV494 @ SV633 )
= SV633 )
= $true )
| ( ( in @ SV633 @ SV122 )
= $false )
| ( ( in @ SV494 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2691,plain,
! [SV634: $i,SV495: $i,SV122: $i] :
( ( $false = $true )
| ( ( ( if @ SV122 @ $false @ SV495 @ SV634 )
= SV634 )
= $true )
| ( ( in @ SV634 @ SV122 )
= $false )
| ( ( in @ SV495 @ SV122 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2692,plain,
! [SV501: $i > $i > $o,SV342: $i,SV130: $i,SV661: $i,SV560: $i] :
( ( ( in @ ( kpair @ SV560 @ SV661 )
@ ( dpsetconstr @ SV130 @ SV342
@ ^ [SY1021: $i,SY1022: $i] : ( SV501 @ SY1021 @ SY1022 ) ) )
= $false )
| ( ( SV501 @ SV560 @ SV661 )
= $true )
| ( ( in @ SV661 @ SV342 )
= $false )
| ( ( in @ SV560 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2693,plain,
! [SV351: $i > $o,SV139: $i,SV680: $i] :
( ( ( ~ ~ ( ~ ( in @ SV680 @ SV139 )
| ~ ( SV351 @ SV680 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2694,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2695,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2696,plain,
! [SV139: $i,SV351: $i > $o] :
( ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true )
| ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) )
| ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2576]) ).
thf(2697,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2698,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) )
| ( SV585
= ( sK66_SY1114 @ SV585 @ SV145 ) ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2578]) ).
thf(2699,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV152 ) )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2700,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV361 )
| ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV586 ) )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2701,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) )
= $false )
| ( ( ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2702,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2703,plain,
! [SV156: $i,SV513: $i,SV645: $i,SV364: $i,SV673: $i] :
( ( ( in @ SV673 @ SV364 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV645 @ SV673 ) @ SV513 )
| ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SV673 ) )
= $true )
| ( ( in @ SV645 @ SV156 )
= $false )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2704,plain,
! [SV162: $i,SV369: $i,SV518: $i,SV647: $i] :
( ( ( ~ ( in @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) @ SV162 )
| ( ( ap @ SV162 @ SV369 @ SV518 @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) )
= ( ap @ SV162 @ SV369 @ SV647 @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) ) ) )
= $false )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2582]) ).
thf(2705,plain,
! [SV163: $i] :
( ( ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ omega )
| ~ ( in @ ( sK42_SY416 @ SV163 ) @ SV163 ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2706,plain,
! [SV163: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ omega ) )
= $true )
| ( ( in @ SV676 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( setadjoin @ ( sK42_SY416 @ SV163 ) @ ( sK42_SY416 @ SV163 ) ) @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2707,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| SV649 ) )
= $true )
| ( SV649 = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2708,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| SV649 )
= $false )
| ( SV649 = $true )
| ( SV649 = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2709,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2710,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2711,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521 @ SV372 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2712,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2713,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
| ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2591]) ).
thf(2714,plain,
! [SV178: $i,SV382: $i] :
( ( ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV178 )
= $true )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2715,plain,
! [SV178: $i,SV382: $i] :
( ( ( in @ ( sK35_SY836 @ SV382 @ SV178 ) @ SV382 )
= $true )
| ( ( ( binintersect @ SV178 @ SV382 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2593]) ).
thf(2716,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 )
= $true )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2594]) ).
thf(2717,plain,
! [SV383: $i,SV652: $i > $o,SV529: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 )
| ~ ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
| ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2595]) ).
thf(2718,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( in @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SV187 )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2597]) ).
thf(2719,plain,
! [SV187: $i,SV533: $i,SV388: $i] :
( ( ( ~ ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2720,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2721,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
| ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2722,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2723,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) )
= $false )
| ( ( ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2724,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2725,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 )
= $true )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2726,plain,
! [SV410: $i,SV655: $i > $o,SV547: $i,SV213: $i] :
( ( ( ~ ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 )
| ~ ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
| ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2605]) ).
thf(2727,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( in @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) @ SV218 )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2728,plain,
! [SV415: $i,SV656: $i > $o,SV595: $i > $o,SV218: $i] :
( ( ( ~ ( in @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) @ SV415 )
| ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
!= ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ~ ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
| ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2608]) ).
thf(2729,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( ~ ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 ) )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2609]) ).
thf(2730,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( ~ ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
| ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 ) )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2609]) ).
thf(2731,plain,
! [SV224: $i,SV421: $i > $o,SV657: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) @ SV224 )
| ~ ~ ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) ) ) )
= $true )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2732,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SV227 )
| ! [SY1201: $i] :
( ~ ( in @ SY1201 @ SV424 )
| ~ ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SY1201 ) @ SV551 )
| ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SY1201 ) @ SV658 ) ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2611]) ).
thf(2733,plain,
! [SV231: $i,SV659: $i,SV427: $i > $o] :
( ( ( SV427 @ SV659 )
= $false )
| ( ( in @ SV659 @ SV231 )
= $false )
| ( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2734,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( ~ ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
| ~ ( ~ ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) )
| ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2735,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2736,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2737,plain,
! [SV16: $i > $o,SV571: $i] :
( ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2738,plain,
! [SV18: $i,SV572: $i] :
( ( ( in @ ( sK37_SY55 @ SV572 @ SV18 ) @ SV18 )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2620]) ).
thf(2739,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2740,plain,
! [SV20: $i,SV664: $i,SV573: $i,SV246: $i > $o] :
( ( ( SV246 @ SV573 )
= $false )
| ( ( ~ ( SV246 @ SV664 )
| ( SV573 = SV664 ) )
= $true )
| ( ( in @ SV664 @ SV20 )
= $false )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2741,plain,
! [SV23: $i] :
( ( ~ ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2742,plain,
! [SV23: $i] :
( ( ~ ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2743,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ~ ~ ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) )
| ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2744,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) ) )
= $true )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2745,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ ( sK59_SY1102 @ SV575 @ SV27 ) ) )
= $false )
| ( ( SV27 @ SV575 )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2746,plain,
! [SV27: $i > $o,SV575: $i] :
( ( ( SV575
= ( sK59_SY1102 @ SV575 @ SV27 ) )
= $false )
| ( ( SV27 @ SV575 )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2747,plain,
! [SV30: $i,SV252: $i > $o,SV442: $i] :
( ( ( in @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) @ SV30 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2748,plain,
! [SV30: $i,SV442: $i,SV252: $i > $o] :
( ( ( ~ ( SV252 @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2749,plain,
! [SV30: $i,SV252: $i > $o,SV442: $i] :
( ( ( ( sK50_SY951 @ SV442 @ SV252 @ SV30 )
= SV442 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2631]) ).
thf(2750,plain,
! [SV33: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ ( sK44_SY634 @ SV33 @ SV254 ) ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2751,plain,
! [SV254: $i,SV33: $i] :
( ( ( ~ ( in @ ( sK44_SY634 @ SV33 @ SV254 ) @ SV33 ) )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2752,plain,
! [SV33: $i,SV670: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV670 ) )
= $true )
| ( ( ~ ( in @ SV670 @ SV33 ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2753,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2754,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2755,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2756,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2757,plain,
! [SV48: $i,SV607: $i,SV268: $i > $o] :
( ( ( SV268 @ SV607 )
= $true )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2758,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2640]) ).
thf(2759,plain,
! [SV51: $i > $o,SV577: $i] :
( ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2640]) ).
thf(2760,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| SV556 )
= $false )
| ( SV556 = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2761,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( SV556 = $true )
| ( SV556 = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2762,plain,
! [SV272: $i,SV53: $i,SV453: $i,SV556: $o] :
( ( SV556 = $false )
| ( SV556 = $true )
| ( SV556 = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2642]) ).
thf(2763,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2764,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2765,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2766,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2767,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2768,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2769,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2770,plain,
! [SV609: $o,SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
| SV609 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2771,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2772,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2773,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
| $true )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2774,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2775,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2776,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
| $false )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2777,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2778,plain,
! [SV280: $i,SV61: $i] :
( ( ( in @ ( sK51_SY675 @ SV61 @ SV280 ) @ SV280 )
= $true )
| ( ( SV61 = SV280 )
= $true )
| ( ( in @ ( sK10_SY674 @ SV280 @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2779,plain,
! [SV287: $i > $o,SV68: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV68 )
| ~ ( SV287 @ SV674 ) )
= $true )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2780,plain,
! [SV287: $i > $o,SV68: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV68 )
| ~ ( SV287 @ SV675 ) )
= $true )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2781,plain,
! [SV288: $i > $o,SV69: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV69 )
| ~ ( SV288 @ SV682 ) )
= $true )
| ( ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(2782,plain,
! [SV288: $i > $o,SV69: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV69 )
| ~ ( SV288 @ SV683 ) )
= $true )
| ( ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(2783,plain,
! [SV292: $i,SV617: $i,SV74: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV74 ) )
= $true )
| ( ( in @ SV617 @ SV292 )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2784,plain,
! [SV74: $i,SV579: $i,SV292: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ SV292 ) )
= $true )
| ( ( in @ SV579 @ SV74 )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2785,plain,
! [SV76: $i,SV294: $i > $o,SV618: $i] :
( ( ( ~ ( in @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) @ SV76 )
| ~ ~ ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2786,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i] :
( ( ( ~ ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 ) )
= $false )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2669]) ).
thf(2787,plain,
! [SV619: $i,SV471: $i,SV295: $i,SV77: $i] :
( ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2669]) ).
thf(2788,plain,
! [SV79: $i,SV667: $i,SV580: $i,SV297: $i] :
( ( ( in @ SV297 @ ( powerset @ SV580 ) )
= $false )
| ( ( ~ ( in @ SV667 @ SV297 )
| ( in @ SV667 @ SV580 ) )
= $true )
| ( ( in @ SV667 @ SV79 )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2789,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) ) )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2790,plain,
! [SV80: $i > $o,SV581: $i] :
( ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2791,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV81 )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2792,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( ~ ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV298 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2793,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV582 )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2794,plain,
! [SV82: $i,SV299: $i,SV473: $i,SV620: $i] :
( ( ( ~ ( in @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) @ SV82 ) )
= $false )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2795,plain,
! [SV620: $i,SV473: $i,SV299: $i,SV82: $i] :
( ( ( ( ap @ SV82 @ SV299 @ SV473 @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) )
= ( ap @ SV82 @ SV299 @ SV620 @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) ) )
= $false )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2674]) ).
thf(2796,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( ~ ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2797,plain,
! [SV85: $i,SV474: $i,SV621: $i,SV301: $i] :
( ( ( ! [SY1200: $i] :
( ~ ( in @ SY1200 @ SV301 )
| ~ ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SY1200 ) @ SV474 )
| ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SY1200 ) @ SV621 ) ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2798,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) ) )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2799,plain,
! [SV91: $i > $o,SV583: $i] :
( ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2800,plain,
! [SV309: $i > $o,SV96: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV96 )
| ~ ( SV309 @ SV684 ) )
= $true )
| ( ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(2801,plain,
! [SV309: $i > $o,SV96: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV96 )
| ~ ( SV309 @ SV685 ) )
= $true )
| ( ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(2802,plain,
! [SV321: $i,SV108: $i,SV485: $i,SV672: $i,SV628: $i] :
( ( ( ~ ( in @ ( kpair @ SV628 @ SV672 ) @ SV485 ) )
= $true )
| ( ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SV672 )
= $true )
| ( ( in @ SV672 @ SV321 )
= $false )
| ( ( in @ SV628 @ SV108 )
= $false )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2803,plain,
! [SV109: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 ) )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2804,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $false )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2805,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $true )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $false )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2682]) ).
thf(2806,plain,
! [SV331: $i > $o,SV121: $i,SV679: $i] :
( ( ( ~ ( ~ ( in @ SV679 @ SV121 )
| ~ ( SV331 @ SV679 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2807,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2808,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2809,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2810,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2811,plain,
! [SV351: $i > $o,SV139: $i,SV680: $i] :
( ( ( ~ ( ~ ( in @ SV680 @ SV139 )
| ~ ( SV351 @ SV680 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2812,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2813,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2814,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2696]) ).
thf(2815,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2816,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2817,plain,
! [SV145: $i > $o,SV585: $i] :
( ( ( SV585
= ( sK66_SY1114 @ SV585 @ SV145 ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2818,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV152 )
= $true )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2819,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV361 ) )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2700]) ).
thf(2820,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV586 )
= $false )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2700]) ).
thf(2821,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ~ ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2701]) ).
thf(2822,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2823,plain,
! [SV364: $i,SV156: $i,SV513: $i,SV673: $i,SV645: $i] :
( ( ( ~ ( in @ ( kpair @ SV645 @ SV673 ) @ SV513 ) )
= $true )
| ( ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SV673 )
= $true )
| ( ( in @ SV673 @ SV364 )
= $false )
| ( ( in @ SV645 @ SV156 )
= $false )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2824,plain,
! [SV162: $i,SV369: $i,SV518: $i,SV647: $i] :
( ( ( ~ ( in @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) @ SV162 ) )
= $false )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2704]) ).
thf(2825,plain,
! [SV647: $i,SV518: $i,SV369: $i,SV162: $i] :
( ( ( ( ap @ SV162 @ SV369 @ SV518 @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) )
= ( ap @ SV162 @ SV369 @ SV647 @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) ) )
= $false )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2704]) ).
thf(2826,plain,
! [SV163: $i] :
( ( ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2827,plain,
! [SV163: $i] :
( ( ( ~ ( in @ ( sK42_SY416 @ SV163 ) @ SV163 ) )
= $false )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2828,plain,
! [SV163: $i,SV676: $i] :
( ( ( in @ SV676 @ omega )
= $false )
| ( ( in @ SV676 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( setadjoin @ ( sK42_SY416 @ SV163 ) @ ( sK42_SY416 @ SV163 ) ) @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2829,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| SV649 )
= $false )
| ( SV649 = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2830,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( SV649 = $true )
| ( SV649 = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2708]) ).
thf(2831,plain,
! [SV372: $i,SV166: $i,SV521: $i,SV649: $o] :
( ( SV649 = $false )
| ( SV649 = $true )
| ( SV649 = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2708]) ).
thf(2832,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2833,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2710]) ).
thf(2834,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2710]) ).
thf(2835,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2836,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2837,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2838,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2713]) ).
thf(2839,plain,
! [SV175: $i > $o,SV590: $i] :
( ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2713]) ).
thf(2840,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV529 )
| ( SV652 @ SV686 ) )
= $true )
| ( ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(2841,plain,
! [SV383: $i,SV652: $i > $o,SV529: $i,SV179: $i] :
( ( ( ~ ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2842,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
| ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2717]) ).
thf(2843,plain,
! [SV187: $i,SV533: $i,SV388: $i] :
( ( ( ! [SY1174: $i] :
~ ~ ( ~ ( in @ SY1174 @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ SY1174 ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2844,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2720]) ).
thf(2845,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2846,plain,
! [SV196: $i > $o,SV593: $i] :
( ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2847,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV687 )
| ~ ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2848,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2723]) ).
thf(2849,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2850,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV547 )
| ( SV655 @ SV688 ) )
= $true )
| ( ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2851,plain,
! [SV410: $i,SV655: $i > $o,SV547: $i,SV213: $i] :
( ( ( ~ ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2852,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
| ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2853,plain,
! [SV415: $i,SV656: $i > $o,SV595: $i > $o,SV218: $i] :
( ( ( ~ ( in @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2854,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
!= ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ~ ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
| ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2855,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2856,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( ~ ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 ) )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2857,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2858,plain,
! [SV224: $i,SV421: $i > $o,SV657: $i] :
( ( ( ~ ( in @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) @ SV224 )
| ~ ~ ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2859,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SV227 ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2860,plain,
! [SV227: $i,SV551: $i,SV658: $i,SV424: $i] :
( ( ( ! [SY1201: $i] :
( ~ ( in @ SY1201 @ SV424 )
| ~ ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SY1201 ) @ SV551 )
| ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SY1201 ) @ SV658 ) ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2861,plain,
! [SV659: $i,SV427: $i > $o,SV231: $i] :
( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV659 @ SV231 )
= $false )
| ( ( SV427 @ SV659 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2862,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( ~ ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(2863,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ( ~ ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) )
| ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2734]) ).
thf(2864,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ! [SY1176: $i] :
( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SY1176 )
| ( SV663 = SY1176 ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2865,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2736]) ).
thf(2866,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2867,plain,
! [SV18: $i,SV572: $i] :
( ( ( ~ ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2868,plain,
! [SV20: $i,SV573: $i,SV664: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV664 ) )
= $true )
| ( ( SV573 = SV664 )
= $true )
| ( ( SV246 @ SV573 )
= $false )
| ( ( in @ SV664 @ SV20 )
= $false )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2869,plain,
! [SV23: $i] :
( ( ! [SY933: $i] :
( ~ ( in @ SY933 @ ( sK4_SY65 @ SV23 ) )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SY933 )
| ( in @ SY67 @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2741]) ).
thf(2870,plain,
! [SV23: $i] :
( ( ! [SY935: $i,SY936: $i] :
( ~ ~ ( ~ ( in @ SY935 @ SV23 )
| ~ ( in @ SY936 @ SV23 ) )
| ~ ! [SY937: $i] :
( ~ ( in @ SY937 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SY935 @ SY937 )
| ( in @ SY936 @ SY937 ) )
| ~ ( ~ ( in @ SY936 @ SY937 )
| ( in @ SY935 @ SY937 ) ) ) )
| ( SY935 = SY936 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2871,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ( ~ ~ ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) ) )
= $true )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2872,plain,
! [SV23: $i,SV665: $i] :
( ( ( ! [SY1178: $i] :
( ~ ( in @ SY1178 @ SV665 )
| ( in @ SY1178 @ SV23 ) ) )
= $false )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2873,plain,
! [SV575: $i,SV27: $i > $o] :
( ( ( SV27 @ ( sK59_SY1102 @ SV575 @ SV27 ) )
= $true )
| ( ( SV27 @ SV575 )
= $false )
| ( ( SV27
@ ( descr
@ ^ [SY89: $i] : ( SV27 @ SY89 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(2874,plain,
! [SV30: $i,SV442: $i,SV252: $i > $o] :
( ( ( SV252 @ ( sK50_SY951 @ SV442 @ SV252 @ SV30 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV30
@ ^ [SY633: $i] : ( SV252 @ SY633 ) ) )
= $true )
| ( ( SV252 @ SV442 )
= $false )
| ( ( in @ SV442 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2875,plain,
! [SV33: $i,SV254: $i] :
( ( ( in @ SV254 @ ( sK44_SY634 @ SV33 @ SV254 ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2876,plain,
! [SV254: $i,SV33: $i] :
( ( ( in @ ( sK44_SY634 @ SV33 @ SV254 ) @ SV33 )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2877,plain,
! [SV33: $i,SV670: $i,SV254: $i] :
( ( ( in @ SV254 @ SV670 )
= $false )
| ( ( ~ ( in @ SV670 @ SV33 ) )
= $true )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2878,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2879,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2880,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
| ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2881,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2882,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2883,plain,
! [SV607: $i,SV268: $i > $o,SV48: $i] :
( ( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ SV48 )
| ( SV268 @ SY659 ) ) )
= $false )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( SV268 @ SV607 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2884,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( ~ ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2885,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2886,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( SV556 = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2887,plain,
! [SV272: $i,SV53: $i,SV453: $i,SV556: $o] :
( ( SV556 = $false )
| ( SV556 = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2760]) ).
thf(2888,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( SV556 = $true )
| ( SV556 = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2889,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2763]) ).
thf(2890,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2763]) ).
thf(2891,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2892,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV272 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2893,plain,
! [SV272: $i,SV53: $i,SV453: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2894,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2895,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2769]) ).
thf(2896,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2769]) ).
thf(2897,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 ) )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2898,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2899,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2771]) ).
thf(2900,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2901,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2902,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2903,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2904,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2905,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2906,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2907,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2908,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2909,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2910,plain,
! [SV287: $i > $o,SV68: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV68 ) )
= $true )
| ( ( ~ ( SV287 @ SV674 ) )
= $true )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2911,plain,
! [SV287: $i > $o,SV68: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV68 ) )
= $true )
| ( ( ~ ( SV287 @ SV675 ) )
= $true )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(2912,plain,
! [SV288: $i > $o,SV69: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV69 ) )
= $true )
| ( ( ~ ( SV288 @ SV682 ) )
= $true )
| ( ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(2913,plain,
! [SV288: $i > $o,SV69: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV69 ) )
= $true )
| ( ( ~ ( SV288 @ SV683 ) )
= $true )
| ( ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2914,plain,
! [SV292: $i,SV617: $i,SV74: $i,SV579: $i] :
( ( ( in @ SV579 @ SV74 )
= $false )
| ( ( in @ SV617 @ SV292 )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2915,plain,
! [SV74: $i,SV579: $i,SV292: $i,SV617: $i] :
( ( ( in @ SV617 @ SV292 )
= $false )
| ( ( in @ SV579 @ SV74 )
= $true )
| ( ( SV579 = SV617 )
= $false )
| ( ( SV74 = SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2916,plain,
! [SV76: $i,SV294: $i > $o,SV618: $i] :
( ( ( ~ ( in @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) @ SV76 ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2917,plain,
! [SV76: $i,SV618: $i,SV294: $i > $o] :
( ( ( ~ ~ ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2918,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i] :
( ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV77 )
| ! [SY1139: $i] :
( ~ ( in @ SY1139 @ SV295 )
| ~ ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV619 )
| ( in @ ( kpair @ SY1138 @ SY1139 ) @ SV471 ) ) ) )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2786]) ).
thf(2919,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV77 )
| ! [SY1205: $i] :
( ~ ( in @ SY1205 @ SV295 )
| ~ ( in @ ( kpair @ SV689 @ SY1205 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SY1205 ) @ SV471 ) ) )
= $true )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(2920,plain,
! [SV79: $i,SV580: $i,SV297: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV297 ) )
= $true )
| ( ( in @ SV667 @ SV580 )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV580 ) )
= $false )
| ( ( in @ SV667 @ SV79 )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2921,plain,
! [SV581: $i,SV80: $i > $o] :
( ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( ! [SY224: $i,SY225: $i] :
( ~ ( SV80 @ SY224 )
| ~ ( SV80 @ SY225 )
| ( SY224 = SY225 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2922,plain,
! [SV581: $i,SV690: $i,SV80: $i > $o] :
( ( ( ! [SY1206: $i] :
( ~ ( SV80 @ SV690 )
| ~ ( SV80 @ SY1206 )
| ( SV690 = SY1206 ) ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(2923,plain,
! [SV81: $i,SV298: $i,SV582: $i] :
( ( ( in @ ( sK53_SY1109 @ SV582 @ SV298 @ SV81 ) @ SV298 )
= $true )
| ( ( in @ SV298 @ ( powerset @ SV582 ) )
= $true )
| ( ( in @ SV582 @ ( powerset @ SV81 ) )
= $false )
| ( ( in @ SV298 @ ( powerset @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2924,plain,
! [SV82: $i,SV299: $i,SV473: $i,SV620: $i] :
( ( ( in @ ( sK63_SY1140 @ SV620 @ SV473 @ SV299 @ SV82 ) @ SV82 )
= $true )
| ( ( SV473 = SV620 )
= $true )
| ( ( in @ SV620 @ ( funcSet @ SV82 @ SV299 ) )
= $false )
| ( ( in @ SV473 @ ( funcSet @ SV82 @ SV299 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2794]) ).
thf(2925,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2926,plain,
! [SV301: $i,SV621: $i,SV474: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
| ~ ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
| ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2797]) ).
thf(2927,plain,
! [SV583: $i,SV91: $i > $o] :
( ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( ! [SY261: $i,SY262: $i] :
( ~ ( SV91 @ SY261 )
| ~ ( SV91 @ SY262 )
| ( SY261 = SY262 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2928,plain,
! [SV583: $i,SV691: $i,SV91: $i > $o] :
( ( ( ! [SY1207: $i] :
( ~ ( SV91 @ SV691 )
| ~ ( SV91 @ SY1207 )
| ( SV691 = SY1207 ) ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2929,plain,
! [SV309: $i > $o,SV96: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV96 ) )
= $true )
| ( ( ~ ( SV309 @ SV684 ) )
= $true )
| ( ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2930,plain,
! [SV309: $i > $o,SV96: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV96 ) )
= $true )
| ( ( ~ ( SV309 @ SV685 ) )
= $true )
| ( ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(2931,plain,
! [SV321: $i,SV108: $i,SV485: $i,SV672: $i,SV628: $i] :
( ( ( in @ ( kpair @ SV628 @ SV672 ) @ SV485 )
= $false )
| ( ( ( ap @ SV108 @ SV321 @ SV485 @ SV628 )
= SV672 )
= $true )
| ( ( in @ SV672 @ SV321 )
= $false )
| ( ( in @ SV628 @ SV108 )
= $false )
| ( ( func @ SV108 @ SV321 @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2932,plain,
! [SV109: $i,SV322: $i] :
( ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV322 )
= $true )
| ( ( in @ ( sK13_SY748 @ SV322 @ SV109 ) @ SV109 )
= $true )
| ( ( SV109 = SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2933,plain,
! [SV331: $i > $o,SV121: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV121 )
| ~ ( SV331 @ SV679 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2806]) ).
thf(2934,plain,
! [SV331: $i > $o,SV121: $i,SV692: $i] :
( ( ( ~ ~ ( ~ ( in @ SV692 @ SV121 )
| ~ ( SV331 @ SV692 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(2935,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2808]) ).
thf(2936,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ~ ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2937,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2810]) ).
thf(2938,plain,
! [SV351: $i > $o,SV139: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV139 )
| ~ ( SV351 @ SV680 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2939,plain,
! [SV351: $i > $o,SV139: $i,SV693: $i] :
( ( ( ~ ~ ( ~ ( in @ SV693 @ SV139 )
| ~ ( SV351 @ SV693 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(2940,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2941,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ~ ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2942,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2815]) ).
thf(2943,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) )
= $true )
| ( ( SV145 @ SV585 )
= $false )
| ( ( ~ ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2944,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV585
= ( sK66_SY1114 @ SV585 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2817]) ).
thf(2945,plain,
! [SV152: $i,SV361: $i,SV586: $i] :
( ( ( in @ ( sK54_SY1115 @ SV586 @ SV361 @ SV152 ) @ SV361 )
= $true )
| ( ( subset @ SV361 @ SV586 )
= $true )
| ( ( in @ SV586 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV361 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2946,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
| ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(2947,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2822]) ).
thf(2948,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2822]) ).
thf(2949,plain,
! [SV364: $i,SV156: $i,SV513: $i,SV673: $i,SV645: $i] :
( ( ( in @ ( kpair @ SV645 @ SV673 ) @ SV513 )
= $false )
| ( ( ( ap @ SV156 @ SV364 @ SV513 @ SV645 )
= SV673 )
= $true )
| ( ( in @ SV673 @ SV364 )
= $false )
| ( ( in @ SV645 @ SV156 )
= $false )
| ( ( in @ SV513 @ ( funcSet @ SV156 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2950,plain,
! [SV162: $i,SV369: $i,SV518: $i,SV647: $i] :
( ( ( in @ ( sK67_SY1156 @ SV647 @ SV518 @ SV369 @ SV162 ) @ SV162 )
= $true )
| ( ( SV518 = SV647 )
= $true )
| ( ( func @ SV162 @ SV369 @ SV647 )
= $false )
| ( ( func @ SV162 @ SV369 @ SV518 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2951,plain,
! [SV163: $i] :
( ( ( in @ ( sK42_SY416 @ SV163 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2952,plain,
! [SV163: $i] :
( ( ( in @ ( sK42_SY416 @ SV163 ) @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ omega )
| ( in @ SY417 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2827]) ).
thf(2953,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( SV649 = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(2954,plain,
! [SV372: $i,SV166: $i,SV521: $i,SV649: $o] :
( ( SV649 = $false )
| ( SV649 = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(2955,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( SV649 = $true )
| ( SV649 = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2830]) ).
thf(2956,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( $true = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2832]) ).
thf(2957,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2832]) ).
thf(2958,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(2959,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV372 ) )
= $false )
| ( $false = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2960,plain,
! [SV372: $i,SV166: $i,SV521: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2961,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2962,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2838]) ).
thf(2963,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2964,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV529 ) )
= $true )
| ( ( SV652 @ SV686 )
= $true )
| ( ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2965,plain,
! [SV383: $i,SV652: $i > $o,SV529: $i,SV179: $i] :
( ( ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 )
= $true )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(2966,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2967,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2968,plain,
! [SV388: $i,SV533: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2843]) ).
thf(2969,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $false )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2970,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( ~ ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2845]) ).
thf(2971,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $false )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2972,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV687 )
| ~ ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2973,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
| ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2974,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2975,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2976,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV547 ) )
= $true )
| ( ( SV655 @ SV688 )
= $true )
| ( ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(2977,plain,
! [SV410: $i,SV655: $i > $o,SV547: $i,SV213: $i] :
( ( ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 )
= $true )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2851]) ).
thf(2978,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(2979,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) )
= $false )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2852]) ).
thf(2980,plain,
! [SV415: $i,SV656: $i > $o,SV595: $i > $o,SV218: $i] :
( ( ( in @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) @ SV415 )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2853]) ).
thf(2981,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
!= ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2982,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
| ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2983,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2984,plain,
! [SV222: $i,SV419: $i,SV596: $i] :
( ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) )
| ( SV419 = SV596 ) )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2985,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(2986,plain,
! [SV224: $i,SV421: $i > $o,SV657: $i] :
( ( ( ~ ( in @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) @ SV224 ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2858]) ).
thf(2987,plain,
! [SV224: $i,SV657: $i,SV421: $i > $o] :
( ( ( ~ ~ ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2858]) ).
thf(2988,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( in @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ SV227 )
= $true )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2989,plain,
! [SV424: $i,SV658: $i,SV551: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) @ SV424 )
| ~ ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV551 )
| ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV658 ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2860]) ).
thf(2990,plain,
! [SV659: $i,SV427: $i > $o,SV231: $i] :
( ( ( ( dsetconstr @ SV231
@ ^ [SY911: $i] : ( SV427 @ SY911 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV659 @ SV231 )
= $false )
| ( ( SV427 @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(2991,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2862]) ).
thf(2992,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) )
| ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(2993,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
| ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2864]) ).
thf(2994,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ! [SY49: $i] :
~ ~ ( ~ ( SV16 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( SV16 @ SY50 )
| ( SY49 = SY50 ) ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2995,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK77_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1208: $i] :
( ~ ( SV16 @ SY1208 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SY1208 ) ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2866]) ).
thf(2996,plain,
! [SV18: $i,SV572: $i] :
( ( ( ! [SY1177: $i] :
~ ~ ( ~ ( in @ SY1177 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SY1177 @ SV18 ) ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2997,plain,
! [SV20: $i,SV573: $i,SV664: $i,SV246: $i > $o] :
( ( ( SV246 @ SV664 )
= $false )
| ( ( SV573 = SV664 )
= $true )
| ( ( SV246 @ SV573 )
= $false )
| ( ( in @ SV664 @ SV20 )
= $false )
| ( ( in @ SV573 @ SV20 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV20
@ ^ [SY621: $i] : ( SV246 @ SY621 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(2998,plain,
! [SV23: $i,SV694: $i] :
( ( ~ ( in @ SV694 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV694 )
| ( in @ SY1209 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(2999,plain,
! [SV23: $i,SV695: $i] :
( ( ! [SY1210: $i] :
( ~ ~ ( ~ ( in @ SV695 @ SV23 )
| ~ ( in @ SY1210 @ SV23 ) )
| ~ ! [SY1211: $i] :
( ~ ( in @ SY1211 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1211 )
| ( in @ SY1210 @ SY1211 ) )
| ~ ( ~ ( in @ SY1210 @ SY1211 )
| ( in @ SV695 @ SY1211 ) ) ) )
| ( SV695 = SY1210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3000,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ( ~ ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) ) )
= $false )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(3001,plain,
! [SV665: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
| ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 ) )
= $false )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2872]) ).
thf(3002,plain,
! [SV254: $i,SV33: $i,SV670: $i] :
( ( ( in @ SV670 @ SV33 )
= $false )
| ( ( in @ SV254 @ SV670 )
= $false )
| ( ( in @ SV254 @ ( setunion @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3003,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(3004,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(3005,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2880]) ).
thf(3006,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2880]) ).
thf(3007,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(3008,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3009,plain,
! [SV48: $i,SV268: $i > $o,SV607: $i] :
( ( ( ~ ( in @ ( sK79_SY659 @ SV607 @ SV268 @ SV48 ) @ SV48 )
| ( SV268 @ ( sK79_SY659 @ SV607 @ SV268 @ SV48 ) ) )
= $false )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( SV268 @ SV607 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2883]) ).
thf(3010,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ! [SY151: $i] :
~ ! [SY152: $i] :
~ ( ~ ( ~ ( SV51 @ SY152 )
| ( SY152 = SY151 ) )
| ~ ( ( SY152 != SY151 )
| ( SV51 @ SY152 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3011,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ! [SY1212: $i] :
~ ( ~ ( ~ ( SV51 @ SY1212 )
| ( SY1212
= ( sK80_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SY1212
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SY1212 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2885]) ).
thf(3012,plain,
! [SV53: $i,SV556: $o,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( SV556 = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(3013,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( $true = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(3014,plain,
! [SV53: $i,SV272: $i,SV453: $i] :
( ( ( in @ SV453 @ SV272 )
= $true )
| ( $false = $true )
| ( ( in @ SV453 @ SV53 )
= $true )
| ( ( in @ SV453 @ ( binunion @ SV53 @ SV272 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(3015,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2895]) ).
thf(3016,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(3017,plain,
! [SV277: $i,SV58: $i,SV456: $i,SV609: $o] :
( ( SV609 = $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(3018,plain,
! [SV609: $o,SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3019,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3020,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3021,plain,
! [SV277: $i,SV58: $i,SV456: $i,SV609: $o] :
( ( SV609 = $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3022,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2900]) ).
thf(3023,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2901]) ).
thf(3024,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2901]) ).
thf(3025,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3026,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3027,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3028,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3029,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2905]) ).
thf(3030,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3031,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3032,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 )
| ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3033,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2908]) ).
thf(3034,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3035,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3036,plain,
! [SV287: $i > $o,SV68: $i,SV674: $i] :
( ( ( in @ SV674 @ SV68 )
= $false )
| ( ( ~ ( SV287 @ SV674 ) )
= $true )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3037,plain,
! [SV287: $i > $o,SV68: $i,SV675: $i] :
( ( ( in @ SV675 @ SV68 )
= $false )
| ( ( ~ ( SV287 @ SV675 ) )
= $true )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(3038,plain,
! [SV288: $i > $o,SV69: $i,SV682: $i] :
( ( ( in @ SV682 @ SV69 )
= $false )
| ( ( ~ ( SV288 @ SV682 ) )
= $true )
| ( ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3039,plain,
! [SV288: $i > $o,SV69: $i,SV683: $i] :
( ( ( in @ SV683 @ SV69 )
= $false )
| ( ( ~ ( SV288 @ SV683 ) )
= $true )
| ( ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(3040,plain,
! [SV76: $i,SV294: $i > $o,SV618: $i] :
( ( ( in @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) @ SV76 )
= $true )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(3041,plain,
! [SV76: $i,SV618: $i,SV294: $i > $o] :
( ( ( ~ ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) ) )
= $true )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(3042,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV77 )
| ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV295 )
| ~ ( in @ ( kpair @ SV696 @ SY1213 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SY1213 ) @ SV471 ) ) )
= $true )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3043,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV77 ) )
= $true )
| ( ( ! [SY1205: $i] :
( ~ ( in @ SY1205 @ SV295 )
| ~ ( in @ ( kpair @ SV689 @ SY1205 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SY1205 ) @ SV471 ) ) )
= $true )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(3044,plain,
! [SV79: $i,SV580: $i,SV297: $i,SV667: $i] :
( ( ( in @ SV667 @ SV297 )
= $false )
| ( ( in @ SV667 @ SV580 )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV580 ) )
= $false )
| ( ( in @ SV667 @ SV79 )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV79 ) )
= $false )
| ( ( in @ SV297 @ ( powerset @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3045,plain,
! [SV581: $i,SV697: $i,SV80: $i > $o] :
( ( ( ! [SY1214: $i] :
( ~ ( SV80 @ SV697 )
| ~ ( SV80 @ SY1214 )
| ( SV697 = SY1214 ) ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3046,plain,
! [SV581: $i,SV698: $i,SV690: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV690 )
| ~ ( SV80 @ SV698 )
| ( SV690 = SV698 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3047,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3048,plain,
! [SV301: $i,SV621: $i,SV474: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2926]) ).
thf(3049,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
| ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2926]) ).
thf(3050,plain,
! [SV583: $i,SV699: $i,SV91: $i > $o] :
( ( ( ! [SY1215: $i] :
( ~ ( SV91 @ SV699 )
| ~ ( SV91 @ SY1215 )
| ( SV699 = SY1215 ) ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3051,plain,
! [SV583: $i,SV700: $i,SV691: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV691 )
| ~ ( SV91 @ SV700 )
| ( SV691 = SV700 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3052,plain,
! [SV309: $i > $o,SV96: $i,SV684: $i] :
( ( ( in @ SV684 @ SV96 )
= $false )
| ( ( ~ ( SV309 @ SV684 ) )
= $true )
| ( ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3053,plain,
! [SV309: $i > $o,SV96: $i,SV685: $i] :
( ( ( in @ SV685 @ SV96 )
= $false )
| ( ( ~ ( SV309 @ SV685 ) )
= $true )
| ( ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3054,plain,
! [SV331: $i > $o,SV121: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV121 ) )
= $true )
| ( ( ~ ( SV331 @ SV679 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(3055,plain,
! [SV331: $i > $o,SV121: $i,SV692: $i] :
( ( ( ~ ( ~ ( in @ SV692 @ SV121 )
| ~ ( SV331 @ SV692 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3056,plain,
! [SV331: $i > $o,SV121: $i,SV701: $i] :
( ( ( ~ ~ ( ~ ( in @ SV701 @ SV121 )
| ~ ( SV331 @ SV701 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3057,plain,
! [SV331: $i > $o,SV121: $i] :
( ( ( ! [SY762: $i] :
~ ~ ( ~ ( in @ SY762 @ SV121 )
| ~ ( SV331 @ SY762 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(3058,plain,
! [SV331: $i > $o,SV121: $i,SV702: $i] :
( ( ( ~ ~ ( ~ ( in @ SV702 @ SV121 )
| ~ ( SV331 @ SV702 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3059,plain,
! [SV351: $i > $o,SV139: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV139 ) )
= $true )
| ( ( ~ ( SV351 @ SV680 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3060,plain,
! [SV351: $i > $o,SV139: $i,SV693: $i] :
( ( ( ~ ( ~ ( in @ SV693 @ SV139 )
| ~ ( SV351 @ SV693 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3061,plain,
! [SV351: $i > $o,SV139: $i,SV703: $i] :
( ( ( ~ ~ ( ~ ( in @ SV703 @ SV139 )
| ~ ( SV351 @ SV703 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3062,plain,
! [SV351: $i > $o,SV139: $i] :
( ( ( ! [SY788: $i] :
~ ~ ( ~ ( in @ SY788 @ SV139 )
| ~ ( SV351 @ SY788 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2941]) ).
thf(3063,plain,
! [SV351: $i > $o,SV139: $i,SV704: $i] :
( ( ( ~ ~ ( ~ ( in @ SV704 @ SV139 )
| ~ ( SV351 @ SV704 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3064,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ! [SY380: $i] :
~ ( SV145 @ SY380 ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3065,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ ( sK81_SY380 @ SV585 @ SV145 ) ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV585
= ( sK66_SY1114 @ SV585 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2944]) ).
thf(3066,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
!= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2946]) ).
thf(3067,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2946]) ).
thf(3068,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(3069,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3070,plain,
! [SV163: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ omega )
| ( in @ SV705 @ SV163 ) )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3071,plain,
! [SV163: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ omega )
| ( in @ SV706 @ SV163 ) )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ SV163 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3072,plain,
! [SV166: $i,SV649: $o,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( SV649 = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3073,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( $true = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3074,plain,
! [SV166: $i,SV372: $i,SV521: $i] :
( ( ( in @ SV521 @ SV372 )
= $true )
| ( $false = $true )
| ( ( SV521 = SV166 )
= $true )
| ( ( in @ SV521 @ ( setadjoin @ SV166 @ SV372 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2959]) ).
thf(3075,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ! [SY449: $i] :
~ ~ ( ~ ( SV175 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV175 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3076,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ~ ( ~ ( SV175 @ ( sK82_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1216: $i] :
( ~ ( SV175 @ SY1216 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SY1216 ) ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2963]) ).
thf(3077,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV686: $i] :
( ( ( in @ SV686 @ SV529 )
= $false )
| ( ( SV652 @ SV686 )
= $true )
| ( ( in @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ SV179 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3078,plain,
! [SV383: $i,SV179: $i,SV652: $i > $o,SV529: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV529 )
| ( SV652 @ SV707 ) )
= $true )
| ( ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3079,plain,
! [SV179: $i,SV383: $i,SV529: $i,SV652: $i > $o] :
( ( ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
= $true )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV529 )
| ( SV652 @ SY1159 ) ) )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(3080,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ SV529 )
| ( SV652 @ SV708 ) )
= $true )
| ( ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) )
= $false )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3081,plain,
! [SV388: $i,SV533: $i,SV187: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) ) ) ) )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2968]) ).
thf(3082,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ ( sK83_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1217: $i] :
( ~ ( SV196 @ SY1217 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SY1217 ) ) ) )
= $false )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2969]) ).
thf(3083,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY500: $i] :
~ ~ ( ~ ( SV196 @ SY500 )
| ~ ! [SY501: $i] :
( ~ ( SV196 @ SY501 )
| ( SY500 = SY501 ) ) ) )
= $false )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3084,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ ( sK84_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1218: $i] :
( ~ ( SV196 @ SY1218 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SY1218 ) ) ) )
= $false )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2971]) ).
thf(3085,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV687 )
| ~ ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2972]) ).
thf(3086,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3087,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3088,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2974]) ).
thf(3089,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3090,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV688: $i] :
( ( ( in @ SV688 @ SV547 )
= $false )
| ( ( SV655 @ SV688 )
= $true )
| ( ( in @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ SV213 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3091,plain,
! [SV410: $i,SV213: $i,SV655: $i > $o,SV547: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV547 )
| ( SV655 @ SV709 ) )
= $true )
| ( ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3092,plain,
! [SV213: $i,SV410: $i,SV547: $i,SV655: $i > $o] :
( ( ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
= $true )
| ( ( ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV547 )
| ( SV655 @ SY1163 ) ) )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3093,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV547 )
| ( SV655 @ SV710 ) )
= $true )
| ( ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) )
= $false )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3094,plain,
! [SV218: $i,SV415: $i,SV595: $i > $o,SV656: $i > $o] :
( ( ( ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 )
= ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3095,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
| ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3096,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3097,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ~ ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3098,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3099,plain,
! [SV224: $i,SV421: $i > $o,SV657: $i] :
( ( ( in @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) @ SV224 )
= $true )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2986]) ).
thf(3100,plain,
! [SV224: $i,SV657: $i,SV421: $i > $o] :
( ( ( ~ ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) ) )
= $true )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3101,plain,
! [SV424: $i,SV658: $i,SV551: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3102,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV551 )
| ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV658 ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2989]) ).
thf(3103,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) ) )
= $true )
| ( ( ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3104,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3105,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2993]) ).
thf(3106,plain,
! [SV4: $i > $i > $o,SV236: $i,SV663: $i] :
( ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2993]) ).
thf(3107,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ~ ( ~ ( SV16 @ ( sK85_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1219: $i] :
( ~ ( SV16 @ SY1219 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SY1219 ) ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2994]) ).
thf(3108,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK77_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1208: $i] :
( ~ ( SV16 @ SY1208 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SY1208 ) ) ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3109,plain,
! [SV18: $i,SV572: $i,SV711: $i] :
( ( ( ~ ~ ( ~ ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SV711 @ SV18 ) ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3110,plain,
! [SV23: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV694 )
| ( in @ SY1209 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2998]) ).
thf(3111,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ~ ~ ( ~ ( in @ SV695 @ SV23 )
| ~ ( in @ SV712 @ SV23 ) )
| ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3112,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3113,plain,
! [SV665: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 ) )
= $false )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3114,plain,
! [SV665: $i,SV23: $i] :
( ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3115,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV713 )
| ~ ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3116,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ SV714 )
| ~ ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3117,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3118,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3119,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3120,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3121,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3008]) ).
thf(3122,plain,
! [SV48: $i,SV268: $i > $o,SV607: $i] :
( ( ( ~ ( in @ ( sK79_SY659 @ SV607 @ SV268 @ SV48 ) @ SV48 ) )
= $false )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( SV268 @ SV607 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3123,plain,
! [SV48: $i,SV607: $i,SV268: $i > $o] :
( ( ( SV268 @ ( sK79_SY659 @ SV607 @ SV268 @ SV48 ) )
= $false )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( SV268 @ SV607 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3124,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ~ ! [SY1223: $i] :
~ ( ~ ( ~ ( SV51 @ SY1223 )
| ( SY1223
= ( sK86_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SY1223
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SY1223 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3010]) ).
thf(3125,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ! [SY1212: $i] :
~ ( ~ ( ~ ( SV51 @ SY1212 )
| ( SY1212
= ( sK80_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SY1212
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SY1212 ) ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3126,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3127,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3128,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3129,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| SV609 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3130,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3131,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( SV609 = $true )
| ( SV609 = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3020]) ).
thf(3132,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3133,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3134,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3135,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3136,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3137,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3027]) ).
thf(3138,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3139,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV58 )
= $true )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3140,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ~ ( in @ SV456 @ SV58 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3141,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3142,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3143,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3144,plain,
! [SV68: $i,SV674: $i,SV287: $i > $o] :
( ( ( SV287 @ SV674 )
= $false )
| ( ( in @ SV674 @ SV68 )
= $false )
| ( ( in @ ( sK11_SY684 @ SV287 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3145,plain,
! [SV68: $i,SV675: $i,SV287: $i > $o] :
( ( ( SV287 @ SV675 )
= $false )
| ( ( in @ SV675 @ SV68 )
= $false )
| ( ( SV287 @ ( sK11_SY684 @ SV287 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3146,plain,
! [SV69: $i,SV682: $i,SV288: $i > $o] :
( ( ( SV288 @ SV682 )
= $false )
| ( ( in @ SV682 @ SV69 )
= $false )
| ( ( in @ ( sK30_SY686 @ SV288 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3147,plain,
! [SV69: $i,SV683: $i,SV288: $i > $o] :
( ( ( SV288 @ SV683 )
= $false )
| ( ( in @ SV683 @ SV69 )
= $false )
| ( ( SV288 @ ( sK30_SY686 @ SV288 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3148,plain,
! [SV76: $i,SV618: $i,SV294: $i > $o] :
( ( ( SV294 @ ( sK52_SY698 @ SV618 @ SV294 @ SV76 ) )
= $false )
| ( ( SV294 @ SV618 )
= $true )
| ( ( in @ SV618 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3149,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV77 ) )
= $true )
| ( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV295 )
| ~ ( in @ ( kpair @ SV696 @ SY1213 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SY1213 ) @ SV471 ) ) )
= $true )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3150,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV689: $i] :
( ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ! [SY1205: $i] :
( ~ ( in @ SY1205 @ SV295 )
| ~ ( in @ ( kpair @ SV689 @ SY1205 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SY1205 ) @ SV471 ) ) )
= $true )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3151,plain,
! [SV581: $i,SV715: $i,SV697: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV697 )
| ~ ( SV80 @ SV715 )
| ( SV697 = SV715 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3152,plain,
! [SV581: $i,SV698: $i,SV690: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV690 ) )
= $true )
| ( ( ~ ( SV80 @ SV698 )
| ( SV690 = SV698 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3046]) ).
thf(3153,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3154,plain,
! [SV301: $i,SV621: $i,SV474: $i,SV85: $i] :
( ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3155,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3156,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3157,plain,
! [SV583: $i,SV716: $i,SV699: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV699 )
| ~ ( SV91 @ SV716 )
| ( SV699 = SV716 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3158,plain,
! [SV583: $i,SV700: $i,SV691: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV691 ) )
= $true )
| ( ( ~ ( SV91 @ SV700 )
| ( SV691 = SV700 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3159,plain,
! [SV96: $i,SV684: $i,SV309: $i > $o] :
( ( ( SV309 @ SV684 )
= $false )
| ( ( in @ SV684 @ SV96 )
= $false )
| ( ( in @ ( sK31_SY733 @ SV309 @ SV96 ) @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3160,plain,
! [SV96: $i,SV685: $i,SV309: $i > $o] :
( ( ( SV309 @ SV685 )
= $false )
| ( ( in @ SV685 @ SV96 )
= $false )
| ( ( SV309 @ ( sK31_SY733 @ SV309 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3161,plain,
! [SV331: $i > $o,SV121: $i,SV679: $i] :
( ( ( in @ SV679 @ SV121 )
= $false )
| ( ( ~ ( SV331 @ SV679 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3162,plain,
! [SV331: $i > $o,SV121: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV121 )
| ~ ( SV331 @ SV692 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3163,plain,
! [SV331: $i > $o,SV121: $i,SV701: $i] :
( ( ( ~ ( ~ ( in @ SV701 @ SV121 )
| ~ ( SV331 @ SV701 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3164,plain,
! [SV331: $i > $o,SV121: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( in @ SV717 @ SV121 )
| ~ ( SV331 @ SV717 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3165,plain,
! [SV331: $i > $o,SV121: $i,SV702: $i] :
( ( ( ~ ( ~ ( in @ SV702 @ SV121 )
| ~ ( SV331 @ SV702 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3166,plain,
! [SV351: $i > $o,SV139: $i,SV680: $i] :
( ( ( in @ SV680 @ SV139 )
= $false )
| ( ( ~ ( SV351 @ SV680 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3167,plain,
! [SV351: $i > $o,SV139: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV139 )
| ~ ( SV351 @ SV693 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3168,plain,
! [SV351: $i > $o,SV139: $i,SV703: $i] :
( ( ( ~ ( ~ ( in @ SV703 @ SV139 )
| ~ ( SV351 @ SV703 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3169,plain,
! [SV351: $i > $o,SV139: $i,SV718: $i] :
( ( ( ~ ~ ( ~ ( in @ SV718 @ SV139 )
| ~ ( SV351 @ SV718 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3170,plain,
! [SV351: $i > $o,SV139: $i,SV704: $i] :
( ( ( ~ ( ~ ( in @ SV704 @ SV139 )
| ~ ( SV351 @ SV704 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3171,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( ~ ( SV145 @ ( sK87_SY380 @ SV585 @ SV145 ) ) )
= $false )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3064]) ).
thf(3172,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( SV145 @ ( sK81_SY380 @ SV585 @ SV145 ) )
= $true )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV585
= ( sK66_SY1114 @ SV585 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3173,plain,
! [SV153: $i > $o,SV587: $i] :
( ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ~ ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3174,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3175,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3176,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ~ ( ~ ( SV153 @ ( sK88_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1224: $i] :
( ~ ( SV153 @ SY1224 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SY1224 ) ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3069]) ).
thf(3177,plain,
! [SV163: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ omega ) )
= $true )
| ( ( in @ SV705 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3178,plain,
! [SV163: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ omega ) )
= $true )
| ( ( in @ SV706 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3179,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ~ ( ~ ( SV175 @ ( sK89_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1225: $i] :
( ~ ( SV175 @ SY1225 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SY1225 ) ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3075]) ).
thf(3180,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( ~ ( SV175 @ ( sK82_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1216: $i] :
( ~ ( SV175 @ SY1216 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SY1216 ) ) ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3076]) ).
thf(3181,plain,
! [SV383: $i,SV179: $i,SV652: $i > $o,SV529: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV529 ) )
= $true )
| ( ( SV652 @ SV707 )
= $true )
| ( ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3182,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV529 )
| ( SV652 @ SV719 ) )
= $true )
| ( ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3183,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ SV529 ) )
= $true )
| ( ( SV652 @ SV708 )
= $true )
| ( ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) )
= $false )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3184,plain,
! [SV388: $i,SV533: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) @ SV388 )
| ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3185,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ ( sK83_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1217: $i] :
( ~ ( SV196 @ SY1217 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SY1217 ) ) ) )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3186,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ~ ( ~ ( SV196 @ ( sK90_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1226: $i] :
( ~ ( SV196 @ SY1226 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SY1226 ) ) ) )
= $false )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3083]) ).
thf(3187,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ ( sK84_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1218: $i] :
( ~ ( SV196 @ SY1218 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SY1218 ) ) ) )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3188,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV687 ) )
= $true )
| ( ( ~ ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3189,plain,
! [SV197: $i > $o,SV396: $i > $o] :
( ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) )
| ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3190,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3191,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3192,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3193,plain,
! [SV410: $i,SV213: $i,SV655: $i > $o,SV547: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV547 ) )
= $true )
| ( ( SV655 @ SV709 )
= $true )
| ( ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3194,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV547 )
| ( SV655 @ SV720 ) )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3195,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV547 ) )
= $true )
| ( ( SV655 @ SV710 )
= $true )
| ( ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) )
= $false )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3196,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( ~ ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3197,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
| ~ ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3096]) ).
thf(3198,plain,
! [SV419: $i,SV596: $i,SV222: $i] :
( ( ( ! [SY1129: $i] :
( ~ ( in @ SY1129 @ SV222 )
| ~ ( in @ SY1129 @ SV596 )
| ( in @ SY1129 @ SV419 ) ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3199,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
| ~ ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3098]) ).
thf(3200,plain,
! [SV224: $i,SV657: $i,SV421: $i > $o] :
( ( ( SV421 @ ( sK57_SY899 @ SV657 @ SV421 @ SV224 ) )
= $false )
| ( ( SV421 @ SV657 )
= $true )
| ( ( in @ SV657 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3201,plain,
! [SV424: $i,SV658: $i,SV551: $i,SV227: $i] :
( ( ( in @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) @ SV424 )
= $true )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3202,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV551 ) )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3203,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV658 )
= $false )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3204,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( ~ ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3205,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3206,plain,
! [SV663: $i,SV236: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3207,plain,
! [SV663: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3208,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( ~ ( SV16 @ ( sK85_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1219: $i] :
( ~ ( SV16 @ SY1219 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SY1219 ) ) ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3209,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK77_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1208: $i] :
( ~ ( SV16 @ SY1208 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SY1208 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3108]) ).
thf(3210,plain,
! [SV18: $i,SV572: $i,SV711: $i] :
( ( ( ~ ( ~ ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SV711 @ SV18 ) ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3211,plain,
! [SV23: $i,SV694: $i] :
( ( ( in @ SV694 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV694 )
| ( in @ SY1209 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3212,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ( ~ ~ ( ~ ( in @ SV695 @ SV23 )
| ~ ( in @ SV712 @ SV23 ) ) )
= $true )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3213,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3214,plain,
! [SV665: $i,SV23: $i] :
( ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( ~ ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3215,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3216,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV713 )
| ~ ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3217,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ SV714 )
| ~ ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3218,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3219,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3220,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3118]) ).
thf(3221,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3222,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3223,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3224,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3225,plain,
! [SV48: $i,SV268: $i > $o,SV607: $i] :
( ( ( in @ ( sK79_SY659 @ SV607 @ SV268 @ SV48 ) @ SV48 )
= $true )
| ( ( in @ SV607 @ SV48 )
= $false )
| ( ( SV268 @ SV607 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3226,plain,
! [SV577: $i,SV51: $i > $o] :
( ( ( ! [SY1223: $i] :
~ ( ~ ( ~ ( SV51 @ SY1223 )
| ( SY1223
= ( sK86_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SY1223
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SY1223 ) ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3227,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV51 @ SV721 )
| ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SV721
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV721 ) ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3228,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3229,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3230,plain,
! [SV58: $i,SV277: $i,SV456: $i,SV609: $o] :
( ( SV609 = $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3231,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3232,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3233,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3135]) ).
thf(3234,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV58 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3140]) ).
thf(3235,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV277 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3236,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3237,plain,
! [SV471: $i,SV619: $i,SV295: $i,SV77: $i,SV696: $i] :
( ( ( in @ SV696 @ SV77 )
= $false )
| ( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV295 )
| ~ ( in @ ( kpair @ SV696 @ SY1213 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SY1213 ) @ SV471 ) ) )
= $true )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3238,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV689: $i,SV295: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV295 )
| ~ ( in @ ( kpair @ SV689 @ SV722 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SV722 ) @ SV471 ) )
= $true )
| ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3239,plain,
! [SV581: $i,SV715: $i,SV697: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV697 ) )
= $true )
| ( ( ~ ( SV80 @ SV715 )
| ( SV697 = SV715 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3240,plain,
! [SV581: $i,SV698: $i,SV690: $i,SV80: $i > $o] :
( ( ( SV80 @ SV690 )
= $false )
| ( ( ~ ( SV80 @ SV698 )
| ( SV690 = SV698 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3241,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
| ! [SY1227: $i] :
( ~ ( in @ SY1227 @ SV301 )
| ~ ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1227 ) @ SV621 )
| ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1227 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3153]) ).
thf(3242,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3243,plain,
! [SV85: $i,SV301: $i,SV474: $i,SV621: $i] :
( ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) )
| ( SV474 = SV621 ) )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3244,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3245,plain,
! [SV583: $i,SV716: $i,SV699: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV699 ) )
= $true )
| ( ( ~ ( SV91 @ SV716 )
| ( SV699 = SV716 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3157]) ).
thf(3246,plain,
! [SV583: $i,SV700: $i,SV691: $i,SV91: $i > $o] :
( ( ( SV91 @ SV691 )
= $false )
| ( ( ~ ( SV91 @ SV700 )
| ( SV691 = SV700 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3247,plain,
! [SV121: $i,SV679: $i,SV331: $i > $o] :
( ( ( SV331 @ SV679 )
= $false )
| ( ( in @ SV679 @ SV121 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK14_SY760 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3248,plain,
! [SV331: $i > $o,SV121: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV121 ) )
= $true )
| ( ( ~ ( SV331 @ SV692 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3249,plain,
! [SV331: $i > $o,SV121: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV121 )
| ~ ( SV331 @ SV701 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3250,plain,
! [SV331: $i > $o,SV121: $i,SV717: $i] :
( ( ( ~ ( ~ ( in @ SV717 @ SV121 )
| ~ ( SV331 @ SV717 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3251,plain,
! [SV331: $i > $o,SV121: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV121 )
| ~ ( SV331 @ SV702 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3165]) ).
thf(3252,plain,
! [SV139: $i,SV680: $i,SV351: $i > $o] :
( ( ( SV351 @ SV680 )
= $false )
| ( ( in @ SV680 @ SV139 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK15_SY786 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3253,plain,
! [SV351: $i > $o,SV139: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV139 ) )
= $true )
| ( ( ~ ( SV351 @ SV693 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3254,plain,
! [SV351: $i > $o,SV139: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV139 )
| ~ ( SV351 @ SV703 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3255,plain,
! [SV351: $i > $o,SV139: $i,SV718: $i] :
( ( ( ~ ( ~ ( in @ SV718 @ SV139 )
| ~ ( SV351 @ SV718 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3169]) ).
thf(3256,plain,
! [SV351: $i > $o,SV139: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV139 )
| ~ ( SV351 @ SV704 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3170]) ).
thf(3257,plain,
! [SV585: $i,SV145: $i > $o] :
( ( ( SV145 @ ( sK87_SY380 @ SV585 @ SV145 ) )
= $true )
| ( ( SV145 @ SV585 )
= $false )
| ( ( SV145 @ ( sK66_SY1114 @ SV585 @ SV145 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3258,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY394: $i] :
~ ~ ( ~ ( SV153 @ SY394 )
| ~ ! [SY395: $i] :
( ~ ( SV153 @ SY395 )
| ( SY394 = SY395 ) ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3259,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ~ ( ~ ( SV153 @ ( sK94_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1228: $i] :
( ~ ( SV153 @ SY1228 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SY1228 ) ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3174]) ).
thf(3260,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ~ ( ~ ( SV153 @ ( sK95_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1229: $i] :
( ~ ( SV153 @ SY1229 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SY1229 ) ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3175]) ).
thf(3261,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK88_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1224: $i] :
( ~ ( SV153 @ SY1224 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SY1224 ) ) ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3176]) ).
thf(3262,plain,
! [SV163: $i,SV705: $i] :
( ( ( in @ SV705 @ omega )
= $false )
| ( ( in @ SV705 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3263,plain,
! [SV163: $i,SV706: $i] :
( ( ( in @ SV706 @ omega )
= $false )
| ( ( in @ SV706 @ SV163 )
= $true )
| ( ( in @ emptyset @ SV163 )
= $false )
| ( ( in @ ( sK42_SY416 @ SV163 ) @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3264,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( ~ ( SV175 @ ( sK89_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1225: $i] :
( ~ ( SV175 @ SY1225 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SY1225 ) ) ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3265,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK82_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1216: $i] :
( ~ ( SV175 @ SY1216 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SY1216 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3266,plain,
! [SV383: $i,SV179: $i,SV652: $i > $o,SV529: $i,SV707: $i] :
( ( ( in @ SV707 @ SV529 )
= $false )
| ( ( SV652 @ SV707 )
= $true )
| ( ( in @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) @ SV383 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3267,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV529 ) )
= $true )
| ( ( SV652 @ SV719 )
= $true )
| ( ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3182]) ).
thf(3268,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV708: $i] :
( ( ( in @ SV708 @ SV529 )
= $false )
| ( ( SV652 @ SV708 )
= $true )
| ( ( SV652 @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) )
= $false )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3269,plain,
! [SV388: $i,SV533: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) @ SV388 ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3270,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( SV533
!= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) ) )
= $false )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3271,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK83_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1217: $i] :
( ~ ( SV196 @ SY1217 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SY1217 ) ) )
= $false )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3272,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( ~ ( SV196 @ ( sK90_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1226: $i] :
( ~ ( SV196 @ SY1226 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SY1226 ) ) ) )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3186]) ).
thf(3273,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK84_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1218: $i] :
( ~ ( SV196 @ SY1218 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SY1218 ) ) )
= $false )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3274,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3275,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3276,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3277,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3278,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3192]) ).
thf(3279,plain,
! [SV410: $i,SV213: $i,SV655: $i > $o,SV547: $i,SV709: $i] :
( ( ( in @ SV709 @ SV547 )
= $false )
| ( ( SV655 @ SV709 )
= $true )
| ( ( in @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) @ SV410 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3280,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV547 ) )
= $true )
| ( ( SV655 @ SV720 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3281,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV710: $i] :
( ( ( in @ SV710 @ SV547 )
= $false )
| ( ( SV655 @ SV710 )
= $true )
| ( ( SV655 @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) )
= $false )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3282,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
| ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
= $false )
| ( ( ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3283,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3284,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3197]) ).
thf(3285,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
| ~ ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3198]) ).
thf(3286,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3199]) ).
thf(3287,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3199]) ).
thf(3288,plain,
! [SV227: $i,SV424: $i,SV551: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK72_SY1168 @ SV658 @ SV551 @ SV424 @ SV227 ) @ ( sK75_SY1201 @ SV227 @ SV551 @ SV658 @ SV424 ) ) @ SV551 )
= $true )
| ( ( subset @ SV551 @ SV658 )
= $true )
| ( ( subset @ SV658 @ ( cartprod @ SV227 @ SV424 ) )
= $false )
| ( ( subset @ SV551 @ ( cartprod @ SV227 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3202]) ).
thf(3289,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1195: $i] :
~ ~ ( ~ ( in @ SY1195 @ SV236 )
| ~ ( SV4 @ SY1195 @ SV677 ) ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3290,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1196: $i] :
~ ~ ( ~ ( in @ SY1196 @ SV236 )
| ~ ( SV4 @ SY1196 @ SV677 ) ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3291,plain,
! [SV663: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY599: $i] :
~ ! [SY600: $i] :
~ ( ~ ( ~ ( in @ SY600 @ SY599 )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY600 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY600 ) )
| ( in @ SY600 @ SY599 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3292,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i] :
( ( ( ~ ! [SY1230: $i] :
~ ( ~ ( ~ ( in @ SY1230 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1230 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1230 ) )
| ( in @ SY1230 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3207]) ).
thf(3293,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK85_SY49 @ SV571 @ SV16 ) )
| ~ ! [SY1219: $i] :
( ~ ( SV16 @ SY1219 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SY1219 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3294,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK77_SY49 @ SV571 @ SV16 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3295,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ! [SY1208: $i] :
( ~ ( SV16 @ SY1208 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SY1208 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3209]) ).
thf(3296,plain,
! [SV18: $i,SV572: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) )
| ~ ( in @ SV711 @ SV18 ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3297,plain,
! [SV23: $i,SV694: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV694 )
| ( in @ SV723 @ SV23 ) )
= $true )
| ( ( in @ SV694 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3298,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ( ~ ( ~ ( in @ SV695 @ SV23 )
| ~ ( in @ SV712 @ SV23 ) ) )
= $false )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3299,plain,
! [SV681: $i,SV23: $i,SV678: $i] :
( ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV681 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3300,plain,
! [SV23: $i,SV665: $i] :
( ( ( ~ ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3301,plain,
! [SV23: $i,SV665: $i] :
( ( ( ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3215]) ).
thf(3302,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV713 )
| ~ ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3216]) ).
thf(3303,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV714 )
| ~ ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3304,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3218]) ).
thf(3305,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3218]) ).
thf(3306,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3219]) ).
thf(3307,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3220]) ).
thf(3308,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3221]) ).
thf(3309,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3222]) ).
thf(3310,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3311,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3312,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV51 @ SV724 )
| ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SV724
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV724 ) ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3313,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV721 )
| ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SV721
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV721 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3314,plain,
! [SV277: $i,SV609: $o,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3315,plain,
! [SV58: $i,SV609: $o,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( SV609 = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3229]) ).
thf(3316,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3317,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $true = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3232]) ).
thf(3318,plain,
! [SV277: $i,SV58: $i,SV456: $i] :
( ( ( in @ SV456 @ SV58 )
= $false )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3319,plain,
! [SV58: $i,SV277: $i,SV456: $i] :
( ( ( in @ SV456 @ SV277 )
= $true )
| ( $false = $true )
| ( ( in @ SV456 @ SV277 )
= $false )
| ( ( in @ SV456 @ ( symdiff @ SV58 @ SV277 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3320,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV696: $i,SV295: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV295 )
| ~ ( in @ ( kpair @ SV696 @ SV725 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SV725 ) @ SV471 ) )
= $true )
| ( ( in @ SV696 @ SV77 )
= $false )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3321,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV689: $i,SV295: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV295 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV689 @ SV722 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SV722 ) @ SV471 ) )
= $true )
| ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3322,plain,
! [SV581: $i,SV715: $i,SV697: $i,SV80: $i > $o] :
( ( ( SV80 @ SV697 )
= $false )
| ( ( ~ ( SV80 @ SV715 )
| ( SV697 = SV715 ) )
= $true )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3323,plain,
! [SV581: $i,SV690: $i,SV698: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV698 ) )
= $true )
| ( ( SV690 = SV698 )
= $true )
| ( ( SV80 @ SV690 )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3324,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3325,plain,
! [SV85: $i,SV621: $i,SV474: $i,SV301: $i] :
( ( ( ! [SY1227: $i] :
( ~ ( in @ SY1227 @ SV301 )
| ~ ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1227 ) @ SV621 )
| ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1227 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3326,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3327,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3243]) ).
thf(3328,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3329,plain,
! [SV583: $i,SV716: $i,SV699: $i,SV91: $i > $o] :
( ( ( SV91 @ SV699 )
= $false )
| ( ( ~ ( SV91 @ SV716 )
| ( SV699 = SV716 ) )
= $true )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3245]) ).
thf(3330,plain,
! [SV583: $i,SV691: $i,SV700: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV700 ) )
= $true )
| ( ( SV691 = SV700 )
= $true )
| ( ( SV91 @ SV691 )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3331,plain,
! [SV331: $i > $o,SV121: $i,SV692: $i] :
( ( ( in @ SV692 @ SV121 )
= $false )
| ( ( ~ ( SV331 @ SV692 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3332,plain,
! [SV331: $i > $o,SV121: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV121 ) )
= $true )
| ( ( ~ ( SV331 @ SV701 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3249]) ).
thf(3333,plain,
! [SV331: $i > $o,SV121: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV121 )
| ~ ( SV331 @ SV717 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3334,plain,
! [SV331: $i > $o,SV121: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV121 ) )
= $true )
| ( ( ~ ( SV331 @ SV702 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3335,plain,
! [SV351: $i > $o,SV139: $i,SV693: $i] :
( ( ( in @ SV693 @ SV139 )
= $false )
| ( ( ~ ( SV351 @ SV693 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3336,plain,
! [SV351: $i > $o,SV139: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV139 ) )
= $true )
| ( ( ~ ( SV351 @ SV703 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3337,plain,
! [SV351: $i > $o,SV139: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV139 )
| ~ ( SV351 @ SV718 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3255]) ).
thf(3338,plain,
! [SV351: $i > $o,SV139: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV139 ) )
= $true )
| ( ( ~ ( SV351 @ SV704 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3339,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ~ ( ~ ( SV153 @ ( sK98_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1233: $i] :
( ~ ( SV153 @ SY1233 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SY1233 ) ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3258]) ).
thf(3340,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK94_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1228: $i] :
( ~ ( SV153 @ SY1228 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SY1228 ) ) ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3259]) ).
thf(3341,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK95_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1229: $i] :
( ~ ( SV153 @ SY1229 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SY1229 ) ) ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3342,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK88_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1224: $i] :
( ~ ( SV153 @ SY1224 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SY1224 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3343,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK89_SY449 @ SV590 @ SV175 ) )
| ~ ! [SY1225: $i] :
( ~ ( SV175 @ SY1225 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SY1225 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3344,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK82_SY449 @ SV590 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3345,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ! [SY1216: $i] :
( ~ ( SV175 @ SY1216 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SY1216 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3346,plain,
! [SV179: $i,SV383: $i,SV652: $i > $o,SV529: $i,SV719: $i] :
( ( ( in @ SV719 @ SV529 )
= $false )
| ( ( SV652 @ SV719 )
= $true )
| ( ( in @ ( kpair @ ( sK46_SY1157 @ SV652 @ SV529 @ SV383 @ SV179 ) @ ( sK69_SY1191 @ SV179 @ SV529 @ SV652 @ SV383 ) ) @ SV529 )
= $true )
| ( ( subset @ SV529 @ ( cartprod @ SV179 @ SV383 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3347,plain,
! [SV388: $i,SV533: $i,SV187: $i] :
( ( ( in @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) @ SV388 )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3269]) ).
thf(3348,plain,
! [SV187: $i,SV388: $i,SV533: $i] :
( ( ( SV533
= ( kpair @ ( sK36_SY1059 @ SV533 @ SV388 @ SV187 ) @ ( sK74_SY1174 @ SV187 @ SV533 @ SV388 ) ) )
= $true )
| ( ( in @ SV533 @ ( cartprod @ SV187 @ SV388 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3349,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK83_SY500 @ SV593 @ SV196 ) ) )
= $false )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3350,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ! [SY1217: $i] :
( ~ ( SV196 @ SY1217 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SY1217 ) ) )
= $false )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3351,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK90_SY500 @ SV593 @ SV196 ) )
| ~ ! [SY1226: $i] :
( ~ ( SV196 @ SY1226 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SY1226 ) ) )
= $false )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3352,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK84_SY500 @ SV593 @ SV196 ) ) )
= $false )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3353,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ! [SY1218: $i] :
( ~ ( SV196 @ SY1218 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SY1218 ) ) )
= $false )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3273]) ).
thf(3354,plain,
! [SV396: $i > $o,SV687: $i,SV197: $i > $o] :
( ( ( ! [SY1204: $i] :
( ~ ( SV197 @ SY1204 )
| ( SV687 = SY1204 ) ) )
= $false )
| ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3355,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3356,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3276]) ).
thf(3357,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3277]) ).
thf(3358,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV726 )
| ~ ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3359,plain,
! [SV213: $i,SV410: $i,SV655: $i > $o,SV547: $i,SV720: $i] :
( ( ( in @ SV720 @ SV547 )
= $false )
| ( ( SV655 @ SV720 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1161 @ SV655 @ SV547 @ SV410 @ SV213 ) @ ( sK70_SY1193 @ SV213 @ SV547 @ SV655 @ SV410 ) ) @ SV547 )
= $true )
| ( ( subset @ SV547 @ ( cartprod @ SV213 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3360,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( ~ ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) )
= $false )
| ( ( ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3361,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3282]) ).
thf(3362,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3283]) ).
thf(3363,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3364,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3365,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3366,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
| ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3367,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3286]) ).
thf(3368,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3369,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3287]) ).
thf(3370,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV677 ) ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3289]) ).
thf(3371,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i,SV727: $i] :
( ( ( ~ ~ ( ~ ( in @ SV727 @ SV236 )
| ~ ( SV4 @ SV727 @ SV677 ) ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3372,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i] :
( ( ( ~ ! [SY1235: $i] :
~ ( ~ ( ~ ( in @ SY1235 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1235 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1235 ) )
| ( in @ SY1235 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3291]) ).
thf(3373,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i] :
( ( ( ! [SY1230: $i] :
~ ( ~ ( ~ ( in @ SY1230 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1230 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1230 ) )
| ( in @ SY1230 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3292]) ).
thf(3374,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ ( sK85_SY49 @ SV571 @ SV16 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3293]) ).
thf(3375,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ~ ! [SY1219: $i] :
( ~ ( SV16 @ SY1219 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SY1219 ) ) )
= $false )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3293]) ).
thf(3376,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( SV16 @ ( sK77_SY49 @ SV571 @ SV16 ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3377,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ! [SY1208: $i] :
( ~ ( SV16 @ SY1208 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SY1208 ) ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3378,plain,
! [SV18: $i,SV572: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) ) )
= $true )
| ( ( ~ ( in @ SV711 @ SV18 ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3379,plain,
! [SV23: $i,SV694: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV694 ) )
= $true )
| ( ( in @ SV723 @ SV23 )
= $true )
| ( ( in @ SV694 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3380,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV23 )
| ~ ( in @ SV712 @ SV23 ) )
= $true )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3298]) ).
thf(3381,plain,
! [SV678: $i,SV23: $i,SV681: $i] :
( ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3382,plain,
! [SV23: $i,SV665: $i] :
( ( ( ! [SY1179: $i] :
~ ( in @ SY1179 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3300]) ).
thf(3383,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3384,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV713 ) )
= $true )
| ( ( ~ ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3385,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV714 ) )
= $true )
| ( ( ~ ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3386,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) )
| ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3304]) ).
thf(3387,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) )
| ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3305]) ).
thf(3388,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3389,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3390,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3391,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3392,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3393,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3394,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV724 )
| ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) ) )
| ~ ( ( SV724
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV724 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3395,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV721 )
| ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3396,plain,
! [SV51: $i > $o,SV577: $i,SV721: $i] :
( ( ( ~ ( ( SV721
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV721 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3397,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV696: $i,SV295: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV295 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV696 @ SV725 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SV725 ) @ SV471 ) )
= $true )
| ( ( in @ SV696 @ SV77 )
= $false )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3320]) ).
thf(3398,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV689: $i,SV295: $i,SV722: $i] :
( ( ( in @ SV722 @ SV295 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV689 @ SV722 ) @ SV619 )
| ( in @ ( kpair @ SV689 @ SV722 ) @ SV471 ) )
= $true )
| ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3399,plain,
! [SV581: $i,SV697: $i,SV715: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV715 ) )
= $true )
| ( ( SV697 = SV715 )
= $true )
| ( ( SV80 @ SV697 )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3400,plain,
! [SV581: $i,SV690: $i,SV698: $i,SV80: $i > $o] :
( ( ( SV80 @ SV698 )
= $false )
| ( ( SV690 = SV698 )
= $true )
| ( ( SV80 @ SV690 )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV581
= ( sK62_SY1108 @ SV581 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3401,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3402,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
| ~ ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3325]) ).
thf(3403,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
| ! [SY1238: $i] :
( ~ ( in @ SY1238 @ SV301 )
| ~ ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1238 ) @ SV621 )
| ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1238 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3326]) ).
thf(3404,plain,
! [SV474: $i,SV621: $i,SV301: $i,SV85: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SV85 )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ SV301 )
| ~ ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV621 )
| ( in @ ( kpair @ SY1143 @ SY1144 ) @ SV474 ) ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3405,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
| ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV301 )
| ~ ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1239 ) @ SV621 )
| ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1239 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3328]) ).
thf(3406,plain,
! [SV583: $i,SV699: $i,SV716: $i,SV91: $i > $o] :
( ( ( ~ ( SV91 @ SV716 ) )
= $true )
| ( ( SV699 = SV716 )
= $true )
| ( ( SV91 @ SV699 )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3407,plain,
! [SV583: $i,SV691: $i,SV700: $i,SV91: $i > $o] :
( ( ( SV91 @ SV700 )
= $false )
| ( ( SV691 = SV700 )
= $true )
| ( ( SV91 @ SV691 )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV583
= ( sK65_SY1110 @ SV583 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3408,plain,
! [SV121: $i,SV692: $i,SV331: $i > $o] :
( ( ( SV331 @ SV692 )
= $false )
| ( ( in @ SV692 @ SV121 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( in @ ( sK32_SY1112 @ SV331 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3409,plain,
! [SV331: $i > $o,SV121: $i,SV701: $i] :
( ( ( in @ SV701 @ SV121 )
= $false )
| ( ( ~ ( SV331 @ SV701 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3410,plain,
! [SV331: $i > $o,SV121: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV121 ) )
= $true )
| ( ( ~ ( SV331 @ SV717 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3411,plain,
! [SV331: $i > $o,SV121: $i,SV702: $i] :
( ( ( in @ SV702 @ SV121 )
= $false )
| ( ( ~ ( SV331 @ SV702 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3412,plain,
! [SV139: $i,SV693: $i,SV351: $i > $o] :
( ( ( SV351 @ SV693 )
= $false )
| ( ( in @ SV693 @ SV139 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( in @ ( sK33_SY1113 @ SV351 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3413,plain,
! [SV351: $i > $o,SV139: $i,SV703: $i] :
( ( ( in @ SV703 @ SV139 )
= $false )
| ( ( ~ ( SV351 @ SV703 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3414,plain,
! [SV351: $i > $o,SV139: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV139 ) )
= $true )
| ( ( ~ ( SV351 @ SV718 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3415,plain,
! [SV351: $i > $o,SV139: $i,SV704: $i] :
( ( ( in @ SV704 @ SV139 )
= $false )
| ( ( ~ ( SV351 @ SV704 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3416,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK98_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1233: $i] :
( ~ ( SV153 @ SY1233 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SY1233 ) ) ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3339]) ).
thf(3417,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK94_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1228: $i] :
( ~ ( SV153 @ SY1228 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SY1228 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3418,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK95_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1229: $i] :
( ~ ( SV153 @ SY1229 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SY1229 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3419,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK88_SY394 @ SV587 @ SV153 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3342]) ).
thf(3420,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ! [SY1224: $i] :
( ~ ( SV153 @ SY1224 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SY1224 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3342]) ).
thf(3421,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ ( sK89_SY449 @ SV590 @ SV175 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3343]) ).
thf(3422,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ~ ! [SY1225: $i] :
( ~ ( SV175 @ SY1225 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SY1225 ) ) )
= $false )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3343]) ).
thf(3423,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( SV175 @ ( sK82_SY449 @ SV590 @ SV175 ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3344]) ).
thf(3424,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ! [SY1216: $i] :
( ~ ( SV175 @ SY1216 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SY1216 ) ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3345]) ).
thf(3425,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK83_SY500 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3349]) ).
thf(3426,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY1217: $i] :
( ~ ( SV196 @ SY1217 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SY1217 ) ) )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3350]) ).
thf(3427,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ ( sK90_SY500 @ SV593 @ SV196 ) ) )
= $false )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3351]) ).
thf(3428,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ~ ! [SY1226: $i] :
( ~ ( SV196 @ SY1226 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SY1226 ) ) )
= $false )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3351]) ).
thf(3429,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK84_SY500 @ SV593 @ SV196 ) )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3352]) ).
thf(3430,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY1218: $i] :
( ~ ( SV196 @ SY1218 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SY1218 ) ) )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3353]) ).
thf(3431,plain,
! [SV687: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
| ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3354]) ).
thf(3432,plain,
! [SV396: $i > $o,SV197: $i > $o] :
( ( ( ! [SY505: $i] :
~ ~ ( ~ ( SV197 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( SV197 @ SY506 )
| ( SY505 = SY506 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3433,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV729 )
| ~ ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3434,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV730 )
| ~ ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3435,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV726 )
| ~ ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3436,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $true )
| ( ( ~ ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3360]) ).
thf(3437,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) )
= $false )
| ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3438,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK91_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV222 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3363]) ).
thf(3439,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV222 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3365]) ).
thf(3440,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 ) )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3366]) ).
thf(3441,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV419 )
= $false )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3366]) ).
thf(3442,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK92_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV596 )
= $false )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3368]) ).
thf(3443,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( ~ ( in @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV677 ) ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3370]) ).
thf(3444,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i,SV727: $i] :
( ( ( ~ ( ~ ( in @ SV727 @ SV236 )
| ~ ( SV4 @ SV727 @ SV677 ) ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3445,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i] :
( ( ( ! [SY1235: $i] :
~ ( ~ ( ~ ( in @ SY1235 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY601: $i] :
~ ~ ( ~ ( in @ SY601 @ SV236 )
| ~ ( SV4 @ SY601 @ SY1235 ) ) )
| ~ ( ~ ~ ! [SY602: $i] :
~ ~ ( ~ ( in @ SY602 @ SV236 )
| ~ ( SV4 @ SY602 @ SY1235 ) )
| ( in @ SY1235 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3372]) ).
thf(3446,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
| ~ ( ~ ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) )
| ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3447,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( SV16 @ ( sK85_SY49 @ SV571 @ SV16 ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3374]) ).
thf(3448,plain,
! [SV571: $i,SV16: $i > $o] :
( ( ( ! [SY1219: $i] :
( ~ ( SV16 @ SY1219 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SY1219 ) ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3375]) ).
thf(3449,plain,
! [SV571: $i,SV732: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV732 )
| ( ( sK77_SY49 @ SV571 @ SV16 )
= SV732 ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(3450,plain,
! [SV18: $i,SV572: $i,SV711: $i] :
( ( ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) )
= $false )
| ( ( ~ ( in @ SV711 @ SV18 ) )
= $true )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(3451,plain,
! [SV23: $i,SV694: $i,SV723: $i] :
( ( ( in @ SV723 @ SV694 )
= $false )
| ( ( in @ SV723 @ SV23 )
= $true )
| ( ( in @ SV694 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3452,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV712 @ SV23 ) )
= $true )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3453,plain,
! [SV23: $i,SV681: $i,SV678: $i] :
( ( ( ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV678 )
| ( in @ SY1202 @ SV681 ) ) )
= $true )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3454,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3455,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( in @ SV728 @ SV665 )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3456,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3457,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3458,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3459,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3460,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3388]) ).
thf(3461,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3462,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3463,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3464,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3392]) ).
thf(3465,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3393]) ).
thf(3466,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( ~ ( ~ ( SV51 @ SV724 )
| ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3467,plain,
! [SV51: $i > $o,SV577: $i,SV724: $i] :
( ( ( ~ ( ( SV724
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV724 ) ) )
= $false )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3468,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV721 )
| ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3395]) ).
thf(3469,plain,
! [SV51: $i > $o,SV577: $i,SV721: $i] :
( ( ( ( SV721
!= ( sK80_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV721 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3396]) ).
thf(3470,plain,
! [SV77: $i,SV471: $i,SV619: $i,SV696: $i,SV295: $i,SV725: $i] :
( ( ( in @ SV725 @ SV295 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV696 @ SV725 ) @ SV619 )
| ( in @ ( kpair @ SV696 @ SV725 ) @ SV471 ) )
= $true )
| ( ( in @ SV696 @ SV77 )
= $false )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3471,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i,SV722: $i,SV689: $i] :
( ( ( ~ ( in @ ( kpair @ SV689 @ SV722 ) @ SV619 ) )
= $true )
| ( ( in @ ( kpair @ SV689 @ SV722 ) @ SV471 )
= $true )
| ( ( in @ SV722 @ SV295 )
= $false )
| ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3472,plain,
! [SV581: $i,SV697: $i,SV715: $i,SV80: $i > $o] :
( ( ( SV80 @ SV715 )
= $false )
| ( ( SV697 = SV715 )
= $true )
| ( ( SV80 @ SV697 )
= $false )
| ( ( SV80 @ SV581 )
= $false )
| ( ( SV80 @ ( sK62_SY1108 @ SV581 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3473,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3474,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3475,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3403]) ).
thf(3476,plain,
! [SV85: $i,SV621: $i,SV474: $i,SV301: $i] :
( ( ( ! [SY1238: $i] :
( ~ ( in @ SY1238 @ SV301 )
| ~ ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1238 ) @ SV621 )
| ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1238 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3403]) ).
thf(3477,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
| ! [SY1244: $i] :
( ~ ( in @ SY1244 @ SV301 )
| ~ ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1244 ) @ SV621 )
| ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1244 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3404]) ).
thf(3478,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3479,plain,
! [SV85: $i,SV621: $i,SV474: $i,SV301: $i] :
( ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ SV301 )
| ~ ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1239 ) @ SV621 )
| ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1239 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3480,plain,
! [SV583: $i,SV699: $i,SV716: $i,SV91: $i > $o] :
( ( ( SV91 @ SV716 )
= $false )
| ( ( SV699 = SV716 )
= $true )
| ( ( SV91 @ SV699 )
= $false )
| ( ( SV91 @ SV583 )
= $false )
| ( ( SV91 @ ( sK65_SY1110 @ SV583 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(3481,plain,
! [SV121: $i,SV701: $i,SV331: $i > $o] :
( ( ( SV331 @ SV701 )
= $false )
| ( ( in @ SV701 @ SV121 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK14_SY760 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3482,plain,
! [SV331: $i > $o,SV121: $i,SV717: $i] :
( ( ( in @ SV717 @ SV121 )
= $false )
| ( ( ~ ( SV331 @ SV717 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3483,plain,
! [SV121: $i,SV702: $i,SV331: $i > $o] :
( ( ( SV331 @ SV702 )
= $false )
| ( ( in @ SV702 @ SV121 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( ( sK14_SY760 @ SV331 @ SV121 )
= ( sK32_SY1112 @ SV331 @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3484,plain,
! [SV139: $i,SV703: $i,SV351: $i > $o] :
( ( ( SV351 @ SV703 )
= $false )
| ( ( in @ SV703 @ SV139 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK15_SY786 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3485,plain,
! [SV351: $i > $o,SV139: $i,SV718: $i] :
( ( ( in @ SV718 @ SV139 )
= $false )
| ( ( ~ ( SV351 @ SV718 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3486,plain,
! [SV139: $i,SV704: $i,SV351: $i > $o] :
( ( ( SV351 @ SV704 )
= $false )
| ( ( in @ SV704 @ SV139 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( ( sK15_SY786 @ SV351 @ SV139 )
= ( sK33_SY1113 @ SV351 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3487,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK98_SY394 @ SV587 @ SV153 ) )
| ~ ! [SY1233: $i] :
( ~ ( SV153 @ SY1233 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SY1233 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3488,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK94_SY394 @ SV587 @ SV153 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3417]) ).
thf(3489,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ! [SY1228: $i] :
( ~ ( SV153 @ SY1228 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SY1228 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3417]) ).
thf(3490,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK95_SY394 @ SV587 @ SV153 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3491,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ! [SY1229: $i] :
( ~ ( SV153 @ SY1229 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SY1229 ) ) )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3492,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK88_SY394 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3493,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY1224: $i] :
( ~ ( SV153 @ SY1224 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SY1224 ) ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3420]) ).
thf(3494,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( SV175 @ ( sK89_SY449 @ SV590 @ SV175 ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3421]) ).
thf(3495,plain,
! [SV590: $i,SV175: $i > $o] :
( ( ( ! [SY1225: $i] :
( ~ ( SV175 @ SY1225 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SY1225 ) ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3422]) ).
thf(3496,plain,
! [SV590: $i,SV734: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV734 )
| ( ( sK82_SY449 @ SV590 @ SV175 )
= SV734 ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3497,plain,
! [SV593: $i,SV735: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV735 )
| ( ( sK83_SY500 @ SV593 @ SV196 )
= SV735 ) )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(3498,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( SV196 @ ( sK90_SY500 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3427]) ).
thf(3499,plain,
! [SV593: $i,SV196: $i > $o] :
( ( ( ! [SY1226: $i] :
( ~ ( SV196 @ SY1226 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SY1226 ) ) )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3500,plain,
! [SV593: $i,SV736: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV736 )
| ( ( sK84_SY500 @ SV593 @ SV196 )
= SV736 ) )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3501,plain,
! [SV687: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3431]) ).
thf(3502,plain,
! [SV197: $i > $o,SV396: $i > $o,SV687: $i] :
( ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3431]) ).
thf(3503,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( ~ ~ ( ~ ( SV197 @ SV737 )
| ~ ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(3504,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV729 )
| ~ ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3505,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV730 )
| ~ ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3506,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV726 )
| ~ ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3435]) ).
thf(3507,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
| ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) ) )
= $false )
| ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3508,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
= $false )
| ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3509,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $false )
| ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3510,plain,
! [SV222: $i,SV596: $i,SV419: $i] :
( ( ( in @ ( sK96_SY1129 @ SV419 @ SV596 @ SV222 ) @ SV596 )
= $true )
| ( ( SV419 = SV596 )
= $true )
| ( ( in @ ( sK56_SY1128 @ SV596 @ SV419 @ SV222 ) @ SV419 )
= $true )
| ( ( in @ SV596 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV419 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3440]) ).
thf(3511,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( in @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV677 ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3512,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV236 )
| ~ ( SV4 @ SV727 @ SV677 ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3444]) ).
thf(3513,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
| ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) )
| ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3514,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( ~ ( ~ ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
| ~ ( ~ ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) )
| ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3515,plain,
! [SV571: $i,SV739: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV739 )
| ( ( sK85_SY49 @ SV571 @ SV16 )
= SV739 ) )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(3516,plain,
! [SV571: $i,SV732: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV732 ) )
= $true )
| ( ( ( sK77_SY49 @ SV571 @ SV16 )
= SV732 )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3517,plain,
! [SV572: $i,SV18: $i,SV711: $i] :
( ( ( in @ SV711 @ SV18 )
= $false )
| ( ( in @ SV711 @ ( sK37_SY55 @ SV572 @ SV18 ) )
= $false )
| ( ( in @ SV572 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(3518,plain,
! [SV712: $i,SV23: $i,SV695: $i] :
( ( ( in @ SV695 @ SV23 )
= $false )
| ( ( ~ ( in @ SV712 @ SV23 ) )
= $true )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3519,plain,
! [SV23: $i,SV681: $i,SV678: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ SV678 )
| ( in @ SV740 @ SV681 ) )
= $true )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3520,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( in @ SV733 @ SV665 )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( ~ ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3521,plain,
! [SV728: $i,SV665: $i,SV23: $i] :
( ( ( ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3522,plain,
! [SV262: $i > $o,SV713: $i,SV42: $i > $o] :
( ( ( ! [SY1221: $i] :
( ~ ( SV42 @ SY1221 )
| ( SV713 = SY1221 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3523,plain,
! [SV42: $i > $o,SV714: $i,SV262: $i > $o] :
( ( ( ! [SY1222: $i] :
( ~ ( SV262 @ SY1222 )
| ( SV714 = SY1222 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3524,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3525,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3526,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3460]) ).
thf(3527,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3528,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3462]) ).
thf(3529,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3463]) ).
thf(3530,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV741 )
| ~ ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(3531,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ SV742 )
| ~ ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3532,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV724 )
| ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3466]) ).
thf(3533,plain,
! [SV51: $i > $o,SV577: $i,SV724: $i] :
( ( ( ( SV724
!= ( sK86_SY151 @ SV577 @ SV51 ) )
| ( SV51 @ SV724 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3467]) ).
thf(3534,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV721 ) )
= $true )
| ( ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3468]) ).
thf(3535,plain,
! [SV51: $i > $o,SV577: $i,SV721: $i] :
( ( ( SV721
!= ( sK80_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV721 )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(3536,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i,SV725: $i,SV696: $i] :
( ( ( ~ ( in @ ( kpair @ SV696 @ SV725 ) @ SV619 ) )
= $true )
| ( ( in @ ( kpair @ SV696 @ SV725 ) @ SV471 )
= $true )
| ( ( in @ SV725 @ SV295 )
= $false )
| ( ( in @ SV696 @ SV77 )
= $false )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3537,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i,SV722: $i,SV689: $i] :
( ( ( in @ ( kpair @ SV689 @ SV722 ) @ SV619 )
= $false )
| ( ( in @ ( kpair @ SV689 @ SV722 ) @ SV471 )
= $true )
| ( ( in @ SV722 @ SV295 )
= $false )
| ( ( in @ SV689 @ SV77 )
= $false )
| ( ( ( ap @ SV77 @ SV295 @ SV471 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) )
= ( ap @ SV77 @ SV295 @ SV619 @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) ) )
= $false )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3538,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( in @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3473]) ).
thf(3539,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3474]) ).
thf(3540,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3474]) ).
thf(3541,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3475]) ).
thf(3542,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
| ~ ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3476]) ).
thf(3543,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3544,plain,
! [SV85: $i,SV621: $i,SV474: $i,SV301: $i] :
( ( ( ! [SY1244: $i] :
( ~ ( in @ SY1244 @ SV301 )
| ~ ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1244 ) @ SV621 )
| ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SY1244 ) @ SV474 ) ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3545,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3478]) ).
thf(3546,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
| ~ ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3479]) ).
thf(3547,plain,
! [SV121: $i,SV717: $i,SV331: $i > $o] :
( ( ( SV331 @ SV717 )
= $false )
| ( ( in @ SV717 @ SV121 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV121
@ ^ [SY763: $i] : ( SV331 @ SY763 ) ) )
= $true )
| ( ( SV331 @ ( sK32_SY1112 @ SV331 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3548,plain,
! [SV139: $i,SV718: $i,SV351: $i > $o] :
( ( ( SV351 @ SV718 )
= $false )
| ( ( in @ SV718 @ SV139 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV139
@ ^ [SY789: $i] : ( SV351 @ SY789 ) ) )
= $true )
| ( ( SV351 @ ( sK33_SY1113 @ SV351 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3549,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK98_SY394 @ SV587 @ SV153 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3550,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ~ ! [SY1233: $i] :
( ~ ( SV153 @ SY1233 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SY1233 ) ) )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3551,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK94_SY394 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3552,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY1228: $i] :
( ~ ( SV153 @ SY1228 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SY1228 ) ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3489]) ).
thf(3553,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK95_SY394 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3490]) ).
thf(3554,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY1229: $i] :
( ~ ( SV153 @ SY1229 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SY1229 ) ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3491]) ).
thf(3555,plain,
! [SV587: $i,SV743: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV743 )
| ( ( sK88_SY394 @ SV587 @ SV153 )
= SV743 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(3556,plain,
! [SV590: $i,SV744: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV744 )
| ( ( sK89_SY449 @ SV590 @ SV175 )
= SV744 ) )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3557,plain,
! [SV590: $i,SV734: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV734 ) )
= $true )
| ( ( ( sK82_SY449 @ SV590 @ SV175 )
= SV734 )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(3558,plain,
! [SV593: $i,SV735: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV735 ) )
= $true )
| ( ( ( sK83_SY500 @ SV593 @ SV196 )
= SV735 )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(3559,plain,
! [SV593: $i,SV745: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV745 )
| ( ( sK90_SY500 @ SV593 @ SV196 )
= SV745 ) )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3560,plain,
! [SV593: $i,SV736: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV736 ) )
= $true )
| ( ( ( sK84_SY500 @ SV593 @ SV196 )
= SV736 )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3561,plain,
! [SV687: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3501]) ).
thf(3562,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3563,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( ~ ( ~ ( SV197 @ SV737 )
| ~ ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3564,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV729 )
| ~ ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3504]) ).
thf(3565,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV730 )
| ~ ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3505]) ).
thf(3566,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV726 ) )
= $true )
| ( ( ~ ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3567,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( ~ ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) ) )
= $false )
| ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3507]) ).
thf(3568,plain,
! [SV218: $i,SV415: $i,SV656: $i > $o,SV595: $i > $o] :
( ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $false )
| ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3507]) ).
thf(3569,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $true )
| ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $false )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3508]) ).
thf(3570,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( ~ ( in @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV236 ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3511]) ).
thf(3571,plain,
! [SV236: $i,SV677: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV677 ) )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3511]) ).
thf(3572,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV236 ) )
= $true )
| ( ( ~ ( SV4 @ SV727 @ SV677 ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3573,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( ~ ( ~ ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
| ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) )
| ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3574,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( ~ ( ~ ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3575,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ( ~ ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) )
| ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3514]) ).
thf(3576,plain,
! [SV571: $i,SV739: $i,SV16: $i > $o] :
( ( ( ~ ( SV16 @ SV739 ) )
= $true )
| ( ( ( sK85_SY49 @ SV571 @ SV16 )
= SV739 )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3577,plain,
! [SV571: $i,SV732: $i,SV16: $i > $o] :
( ( ( SV16 @ SV732 )
= $false )
| ( ( ( sK77_SY49 @ SV571 @ SV16 )
= SV732 )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV571
= ( sK58_SY1099 @ SV571 @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3578,plain,
! [SV695: $i,SV23: $i,SV712: $i] :
( ( ( in @ SV712 @ SV23 )
= $false )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) )
| ( SV695 = SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3579,plain,
! [SV23: $i,SV681: $i,SV678: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ SV678 ) )
= $true )
| ( ( in @ SV740 @ SV681 )
= $true )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3580,plain,
! [SV733: $i,SV665: $i,SV23: $i] :
( ( ( ! [SY1180: $i] :
~ ~ ! [SY1181: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1180 @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1181 @ SV665 ) )
| ~ ~ ~ ! [SY1182: $i] :
~ ~ ( ~ ( in @ SY1182 @ SY1180 )
| ~ ( in @ SY1182 @ SV665 ) ) )
| ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ ( sK4_SY65 @ SV23 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY948 )
| ( in @ SX6 @ SY1180 ) )
| ( in @ SY1181 @ SY948 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3581,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ! [SY1250: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1250 @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1252: $i] :
( ~ ( in @ SY1252 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ SY1250 @ SY1252 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3521]) ).
thf(3582,plain,
! [SV713: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
| ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3522]) ).
thf(3583,plain,
! [SV714: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
| ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3523]) ).
thf(3584,plain,
! [SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY120: $i] :
~ ~ ( ~ ( SV42 @ SY120 )
| ~ ! [SY121: $i] :
( ~ ( SV42 @ SY121 )
| ( SY120 = SY121 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3524]) ).
thf(3585,plain,
! [SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( SV262 @ SY648 )
| ~ ! [SY649: $i] :
( ~ ( SV262 @ SY649 )
| ( SY648 = SY649 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3586,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV746 )
| ~ ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3587,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ SV747 )
| ~ ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3588,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV748 )
| ~ ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(3589,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ SV749 )
| ~ ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(3590,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV741 )
| ~ ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3591,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ SV742 )
| ~ ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3531]) ).
thf(3592,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( ~ ( SV51 @ SV724 ) )
= $true )
| ( ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3593,plain,
! [SV51: $i > $o,SV577: $i,SV724: $i] :
( ( ( SV724
!= ( sK86_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV724 )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(3594,plain,
! [SV577: $i,SV721: $i,SV51: $i > $o] :
( ( ( SV51 @ SV721 )
= $false )
| ( ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3595,plain,
! [SV51: $i > $o,SV577: $i,SV721: $i] :
( ( ( SV721
= ( sK80_SY151 @ SV577 @ SV51 ) )
= $false )
| ( ( SV51 @ SV721 )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV577
= ( sK60_SY1104 @ SV577 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3596,plain,
! [SV77: $i,SV295: $i,SV471: $i,SV619: $i,SV725: $i,SV696: $i] :
( ( ( in @ ( kpair @ SV696 @ SV725 ) @ SV619 )
= $false )
| ( ( in @ ( kpair @ SV696 @ SV725 ) @ SV471 )
= $true )
| ( ( in @ SV725 @ SV295 )
= $false )
| ( ( in @ SV696 @ SV77 )
= $false )
| ( ( in @ ( sK61_SY1137 @ SV619 @ SV471 @ SV295 @ SV77 ) @ SV77 )
= $true )
| ( ( func @ SV77 @ SV295 @ SV619 )
= $false )
| ( ( func @ SV77 @ SV295 @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3597,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK93_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK101_SY1227 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3539]) ).
thf(3598,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3599,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3600,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ SV85 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3543]) ).
thf(3601,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
| ~ ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3544]) ).
thf(3602,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3603,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3604,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK98_SY394 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3605,plain,
! [SV587: $i,SV153: $i > $o] :
( ( ( ! [SY1233: $i] :
( ~ ( SV153 @ SY1233 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SY1233 ) ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3550]) ).
thf(3606,plain,
! [SV587: $i,SV750: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV750 )
| ( ( sK94_SY394 @ SV587 @ SV153 )
= SV750 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(3607,plain,
! [SV587: $i,SV751: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV751 )
| ( ( sK95_SY394 @ SV587 @ SV153 )
= SV751 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3608,plain,
! [SV587: $i,SV743: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV743 ) )
= $true )
| ( ( ( sK88_SY394 @ SV587 @ SV153 )
= SV743 )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3609,plain,
! [SV590: $i,SV744: $i,SV175: $i > $o] :
( ( ( ~ ( SV175 @ SV744 ) )
= $true )
| ( ( ( sK89_SY449 @ SV590 @ SV175 )
= SV744 )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3610,plain,
! [SV590: $i,SV734: $i,SV175: $i > $o] :
( ( ( SV175 @ SV734 )
= $false )
| ( ( ( sK82_SY449 @ SV590 @ SV175 )
= SV734 )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV590
= ( sK68_SY1119 @ SV590 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3611,plain,
! [SV593: $i,SV735: $i,SV196: $i > $o] :
( ( ( SV196 @ SV735 )
= $false )
| ( ( ( sK83_SY500 @ SV593 @ SV196 )
= SV735 )
= $true )
| ( ( SV196 @ ( sK47_SY498 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3612,plain,
! [SV593: $i,SV745: $i,SV196: $i > $o] :
( ( ( ~ ( SV196 @ SV745 ) )
= $true )
| ( ( ( sK90_SY500 @ SV593 @ SV196 )
= SV745 )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3613,plain,
! [SV593: $i,SV736: $i,SV196: $i > $o] :
( ( ( SV196 @ SV736 )
= $false )
| ( ( ( sK84_SY500 @ SV593 @ SV196 )
= SV736 )
= $true )
| ( ( ( sK47_SY498 @ SV593 @ SV196 )
= ( sK55_SY1192 @ SV593 @ SV196 ) )
= $false )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3560]) ).
thf(3614,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(3615,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3616,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV737 )
| ~ ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3563]) ).
thf(3617,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV729 ) )
= $true )
| ( ( ~ ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3618,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV730 ) )
= $true )
| ( ( ~ ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(3619,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3566]) ).
thf(3620,plain,
! [SV415: $i,SV595: $i > $o,SV218: $i,SV656: $i > $o] :
( ( ( SV656 @ ( sK71_SY1194 @ SV218 @ SV595 @ SV656 @ SV415 ) )
= $true )
| ( ( SV595 @ ( sK49_SY1164 @ SV656 @ SV595 @ SV415 @ SV218 ) )
= $true )
| ( ( ( dsetconstr @ SV218
@ ^ [SY1126: $i] : ( SV595 @ SY1126 ) )
= ( dsetconstr @ SV415
@ ^ [SY1167: $i] : ( SV656 @ SY1167 ) ) )
= $true )
| ( ( SV218 = SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3621,plain,
! [SV236: $i,SV4: $i > $i > $o,SV677: $i] :
( ( ( in @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV236 )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3570]) ).
thf(3622,plain,
! [SV236: $i,SV677: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK99_SY1195 @ SV677 @ SV4 @ SV236 ) @ SV677 )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $false )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3571]) ).
thf(3623,plain,
! [SV677: $i,SV4: $i > $i > $o,SV236: $i,SV727: $i] :
( ( ( in @ SV727 @ SV236 )
= $false )
| ( ( ~ ( SV4 @ SV727 @ SV677 ) )
= $true )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3624,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( ~ ( ~ ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3625,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) )
| ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3626,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3574]) ).
thf(3627,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) )
| ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3575]) ).
thf(3628,plain,
! [SV571: $i,SV739: $i,SV16: $i > $o] :
( ( ( SV16 @ SV739 )
= $false )
| ( ( ( sK85_SY49 @ SV571 @ SV16 )
= SV739 )
= $true )
| ( ( SV16 @ SV571 )
= $false )
| ( ( SV16 @ ( sK58_SY1099 @ SV571 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3629,plain,
! [SV712: $i,SV695: $i,SV23: $i] :
( ( ( ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3578]) ).
thf(3630,plain,
! [SV23: $i,SV681: $i,SV678: $i,SV740: $i] :
( ( ( in @ SV740 @ SV678 )
= $false )
| ( ( in @ SV740 @ SV681 )
= $true )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV681 )
| ( in @ SY1203 @ SV678 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3631,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ! [SY1258: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1258 @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1260: $i] :
( ~ ( in @ SY1260 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1260 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ SY1258 @ SY1260 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3580]) ).
thf(3632,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ! [SY1250: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1250 @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1252: $i] :
( ~ ( in @ SY1252 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ SY1250 @ SY1252 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3581]) ).
thf(3633,plain,
! [SV713: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3582]) ).
thf(3634,plain,
! [SV42: $i > $o,SV262: $i > $o,SV713: $i] :
( ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3582]) ).
thf(3635,plain,
! [SV714: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3636,plain,
! [SV262: $i > $o,SV42: $i > $o,SV714: $i] :
( ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3637,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ SV752 )
| ~ ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(3638,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ SV753 )
| ~ ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3639,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV746 )
| ~ ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3640,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ SV747 )
| ~ ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3641,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV748 )
| ~ ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(3642,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ SV749 )
| ~ ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3643,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV741 )
| ~ ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3590]) ).
thf(3644,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV742 )
| ~ ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3591]) ).
thf(3645,plain,
! [SV577: $i,SV724: $i,SV51: $i > $o] :
( ( ( SV51 @ SV724 )
= $false )
| ( ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3646,plain,
! [SV51: $i > $o,SV577: $i,SV724: $i] :
( ( ( SV724
= ( sK86_SY151 @ SV577 @ SV51 ) )
= $false )
| ( ( SV51 @ SV724 )
= $true )
| ( ( SV51 @ SV577 )
= $false )
| ( ( SV51 @ ( sK60_SY1104 @ SV577 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3647,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( in @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(3648,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3599]) ).
thf(3649,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3599]) ).
thf(3650,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( ~ ( in @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3651,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
| ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3652,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( in @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3653,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3654,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3655,plain,
! [SV587: $i,SV754: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV754 )
| ( ( sK98_SY394 @ SV587 @ SV153 )
= SV754 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(3656,plain,
! [SV587: $i,SV750: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV750 ) )
= $true )
| ( ( ( sK94_SY394 @ SV587 @ SV153 )
= SV750 )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(3657,plain,
! [SV587: $i,SV751: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV751 ) )
= $true )
| ( ( ( sK95_SY394 @ SV587 @ SV153 )
= SV751 )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3658,plain,
! [SV587: $i,SV743: $i,SV153: $i > $o] :
( ( ( SV153 @ SV743 )
= $false )
| ( ( ( sK88_SY394 @ SV587 @ SV153 )
= SV743 )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3659,plain,
! [SV590: $i,SV744: $i,SV175: $i > $o] :
( ( ( SV175 @ SV744 )
= $false )
| ( ( ( sK89_SY449 @ SV590 @ SV175 )
= SV744 )
= $true )
| ( ( SV175 @ SV590 )
= $false )
| ( ( SV175 @ ( sK68_SY1119 @ SV590 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3660,plain,
! [SV593: $i,SV745: $i,SV196: $i > $o] :
( ( ( SV196 @ SV745 )
= $false )
| ( ( ( sK90_SY500 @ SV593 @ SV196 )
= SV745 )
= $true )
| ( ( SV196 @ ( sK55_SY1192 @ SV593 @ SV196 ) )
= $true )
| ( ( SV196 @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3661,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3662,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3615]) ).
thf(3663,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( ~ ( SV197 @ SV737 ) )
= $true )
| ( ( ~ ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3664,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3617]) ).
thf(3665,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3666,plain,
! [SV396: $i > $o,SV726: $i,SV197: $i > $o] :
( ( ( ! [SY1234: $i] :
( ~ ( SV197 @ SY1234 )
| ( SV726 = SY1234 ) ) )
= $false )
| ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3667,plain,
! [SV236: $i,SV677: $i,SV727: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV727 @ SV677 )
= $false )
| ( ( in @ SV727 @ SV236 )
= $false )
| ( ( in @ SV677 @ ( sK43_SY599 @ SV4 @ SV236 ) )
= $true )
| ( ( in @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(3668,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
| ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3624]) ).
thf(3669,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) )
| ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3625]) ).
thf(3670,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) ) )
= $true )
| ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3671,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(3672,plain,
! [SV712: $i,SV695: $i,SV23: $i] :
( ( ( ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ SY1220 )
| ( in @ SV712 @ SY1220 ) )
| ~ ( ~ ( in @ SV712 @ SY1220 )
| ( in @ SV695 @ SY1220 ) ) ) ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3673,plain,
! [SV23: $i,SV740: $i,SV678: $i,SV681: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV681 )
| ( in @ SV755 @ SV678 ) )
= $true )
| ( ( in @ SV740 @ SV681 )
= $true )
| ( ( in @ SV740 @ SV678 )
= $false )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3674,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ! [SY1258: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1258 @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1260: $i] :
( ~ ( in @ SY1260 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1260 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ SY1258 @ SY1260 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3631]) ).
thf(3675,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ! [SY1250: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1250 @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1252: $i] :
( ~ ( in @ SY1252 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1252 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ SY1250 @ SY1252 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(3676,plain,
! [SV713: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3677,plain,
! [SV713: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(3678,plain,
! [SV714: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3635]) ).
thf(3679,plain,
! [SV714: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3636]) ).
thf(3680,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ SV752 )
| ~ ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) ) )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3681,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ SV753 )
| ~ ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) ) )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3638]) ).
thf(3682,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV746 )
| ~ ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3639]) ).
thf(3683,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV747 )
| ~ ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3640]) ).
thf(3684,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV748 )
| ~ ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3641]) ).
thf(3685,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV749 )
| ~ ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3642]) ).
thf(3686,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV741 ) )
= $true )
| ( ( ~ ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3687,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV742 ) )
= $true )
| ( ( ~ ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3688,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK102_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK106_SY1238 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) @ SV301 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(3689,plain,
! [SV301: $i,SV474: $i,SV621: $i,SV85: $i] :
( ( ( in @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) @ SV301 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3650]) ).
thf(3690,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 ) )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3651]) ).
thf(3691,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV474 )
= $false )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3651]) ).
thf(3692,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK103_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK107_SY1239 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV621 )
= $false )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(3693,plain,
! [SV587: $i,SV754: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ SV754 ) )
= $true )
| ( ( ( sK98_SY394 @ SV587 @ SV153 )
= SV754 )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3694,plain,
! [SV587: $i,SV750: $i,SV153: $i > $o] :
( ( ( SV153 @ SV750 )
= $false )
| ( ( ( sK94_SY394 @ SV587 @ SV153 )
= SV750 )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(3695,plain,
! [SV587: $i,SV751: $i,SV153: $i > $o] :
( ( ( SV153 @ SV751 )
= $false )
| ( ( ( sK95_SY394 @ SV587 @ SV153 )
= SV751 )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $false )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3696,plain,
! [SV687: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(3697,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV756 )
| ~ ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3698,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) )
= $true )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3699,plain,
! [SV396: $i > $o,SV729: $i,SV197: $i > $o] :
( ( ( ! [SY1240: $i] :
( ~ ( SV197 @ SY1240 )
| ( SV729 = SY1240 ) ) )
= $false )
| ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(3700,plain,
! [SV396: $i > $o,SV730: $i,SV197: $i > $o] :
( ( ( ! [SY1241: $i] :
( ~ ( SV197 @ SY1241 )
| ( SV730 = SY1241 ) ) )
= $false )
| ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3701,plain,
! [SV726: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
| ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3666]) ).
thf(3702,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) ) )
= $true )
| ( ( ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3703,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(3704,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV731: $i] :
( ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3705,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(3706,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( ~ ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
| ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3672]) ).
thf(3707,plain,
! [SV23: $i,SV740: $i,SV678: $i,SV681: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV681 ) )
= $true )
| ( ( in @ SV755 @ SV678 )
= $true )
| ( ( in @ SV740 @ SV681 )
= $true )
| ( ( in @ SV740 @ SV678 )
= $false )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3673]) ).
thf(3708,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ! [SY1258: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ SY1258 @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1260: $i] :
( ~ ( in @ SY1260 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1260 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ SY1258 @ SY1260 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(3709,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1266: $i] :
( ~ ( in @ SY1266 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1266 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SY1266 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3675]) ).
thf(3710,plain,
! [SV713: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3711,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK116_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1268: $i] :
( ~ ( SV262 @ SY1268 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SY1268 ) ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3677]) ).
thf(3712,plain,
! [SV714: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3713,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK117_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1269: $i] :
( ~ ( SV42 @ SY1269 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SY1269 ) ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3679]) ).
thf(3714,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV752 )
| ~ ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3680]) ).
thf(3715,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV753 )
| ~ ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3681]) ).
thf(3716,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV746 ) )
= $true )
| ( ( ~ ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3717,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV747 ) )
= $true )
| ( ( ~ ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3718,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV748 ) )
= $true )
| ( ( ~ ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(3719,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV749 ) )
= $true )
| ( ( ~ ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3720,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(3721,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(3722,plain,
! [SV85: $i,SV301: $i,SV621: $i,SV474: $i] :
( ( ( in @ ( kpair @ ( sK105_SY1143 @ SV474 @ SV621 @ SV301 @ SV85 ) @ ( sK111_SY1244 @ SV85 @ SV621 @ SV474 @ SV301 ) ) @ SV621 )
= $true )
| ( ( SV474 = SV621 )
= $true )
| ( ( in @ ( kpair @ ( sK64_SY1141 @ SV621 @ SV474 @ SV301 @ SV85 ) @ ( sK73_SY1200 @ SV85 @ SV474 @ SV621 @ SV301 ) ) @ SV474 )
= $true )
| ( ( subset @ SV621 @ ( cartprod @ SV85 @ SV301 ) )
= $false )
| ( ( subset @ SV474 @ ( cartprod @ SV85 @ SV301 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3690]) ).
thf(3723,plain,
! [SV587: $i,SV754: $i,SV153: $i > $o] :
( ( ( SV153 @ SV754 )
= $false )
| ( ( ( sK98_SY394 @ SV587 @ SV153 )
= SV754 )
= $true )
| ( ( SV153 @ ( sK34_SY1116 @ SV587 @ SV153 ) )
= $true )
| ( ( ( sK34_SY1116 @ SV587 @ SV153 )
= SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(3724,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV757 )
| ~ ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(3725,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV756 )
| ~ ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3726,plain,
! [SV396: $i > $o,SV737: $i,SV197: $i > $o] :
( ( ( ! [SY1245: $i] :
( ~ ( SV197 @ SY1245 )
| ( SV737 = SY1245 ) ) )
= $false )
| ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3727,plain,
! [SV729: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
| ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3699]) ).
thf(3728,plain,
! [SV730: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
| ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3700]) ).
thf(3729,plain,
! [SV726: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3701]) ).
thf(3730,plain,
! [SV197: $i > $o,SV396: $i > $o,SV726: $i] :
( ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3701]) ).
thf(3731,plain,
! [SV236: $i,SV4: $i > $i > $o,SV663: $i,SV738: $i] :
( ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( ~ ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3732,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ~ ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3733,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV236 )
| ~ ( SV4 @ SY1242 @ SV731 ) ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3734,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1243: $i] :
~ ~ ( ~ ( in @ SY1243 @ SV236 )
| ~ ( SV4 @ SY1243 @ SV731 ) ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3735,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) @ ( sK4_SY65 @ SV23 ) ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3706]) ).
thf(3736,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
| ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3706]) ).
thf(3737,plain,
! [SV23: $i,SV740: $i,SV678: $i,SV681: $i,SV755: $i] :
( ( ( in @ SV755 @ SV681 )
= $false )
| ( ( in @ SV755 @ SV678 )
= $true )
| ( ( in @ SV740 @ SV681 )
= $true )
| ( ( in @ SV740 @ SV678 )
= $false )
| ( ( in @ SV678 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ SV681 @ ( sK4_SY65 @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3738,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1272 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SY1272 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3708]) ).
thf(3739,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1266: $i] :
( ~ ( in @ SY1266 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1266 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SY1266 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3740,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK121_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1274: $i] :
( ~ ( SV262 @ SY1274 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SY1274 ) ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3710]) ).
thf(3741,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK116_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1268: $i] :
( ~ ( SV262 @ SY1268 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SY1268 ) ) ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3711]) ).
thf(3742,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK122_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1275: $i] :
( ~ ( SV42 @ SY1275 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SY1275 ) ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3712]) ).
thf(3743,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK117_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1269: $i] :
( ~ ( SV42 @ SY1269 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SY1269 ) ) ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3744,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV752 ) )
= $true )
| ( ( ~ ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(3745,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV753 ) )
= $true )
| ( ( ~ ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(3746,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(3747,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(3748,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3749,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(3750,plain,
! [SV262: $i > $o,SV741: $i,SV42: $i > $o] :
( ( ( ! [SY1248: $i] :
( ~ ( SV42 @ SY1248 )
| ( SV741 = SY1248 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3720]) ).
thf(3751,plain,
! [SV42: $i > $o,SV742: $i,SV262: $i > $o] :
( ( ( ! [SY1249: $i] :
( ~ ( SV262 @ SY1249 )
| ( SV742 = SY1249 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3752,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV757 )
| ~ ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(3753,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV756 )
| ~ ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3725]) ).
thf(3754,plain,
! [SV737: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
| ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3726]) ).
thf(3755,plain,
! [SV729: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3756,plain,
! [SV197: $i > $o,SV396: $i > $o,SV729: $i] :
( ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3757,plain,
! [SV730: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3728]) ).
thf(3758,plain,
! [SV197: $i > $o,SV396: $i > $o,SV730: $i] :
( ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3728]) ).
thf(3759,plain,
! [SV726: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3760,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(3761,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1246: $i] :
~ ~ ( ~ ( in @ SY1246 @ SV236 )
| ~ ( SV4 @ SY1246 @ SV738 ) ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3762,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i] :
( ( ( ! [SY1247: $i] :
~ ~ ( ~ ( in @ SY1247 @ SV236 )
| ~ ( SV4 @ SY1247 @ SV738 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(3763,plain,
! [SV236: $i,SV4: $i > $i > $o,SV731: $i,SV663: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV731 ) ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3733]) ).
thf(3764,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i,SV758: $i] :
( ( ( ~ ~ ( ~ ( in @ SV758 @ SV236 )
| ~ ( SV4 @ SV758 @ SV731 ) ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(3765,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( in @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3735]) ).
thf(3766,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( ~ ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
| ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3736]) ).
thf(3767,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1272 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SY1272 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3738]) ).
thf(3768,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
| ~ ! [SY1266: $i] :
( ~ ( in @ SY1266 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1266 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SY1266 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3769,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK121_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1274: $i] :
( ~ ( SV262 @ SY1274 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SY1274 ) ) ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(3770,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK116_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1268: $i] :
( ~ ( SV262 @ SY1268 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SY1268 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3771,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK122_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1275: $i] :
( ~ ( SV42 @ SY1275 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SY1275 ) ) ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3742]) ).
thf(3772,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK117_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1269: $i] :
( ~ ( SV42 @ SY1269 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SY1269 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3773,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) )
= $true )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3774,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) )
= $true )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3775,plain,
! [SV262: $i > $o,SV746: $i,SV42: $i > $o] :
( ( ( ! [SY1254: $i] :
( ~ ( SV42 @ SY1254 )
| ( SV746 = SY1254 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(3776,plain,
! [SV42: $i > $o,SV747: $i,SV262: $i > $o] :
( ( ( ! [SY1255: $i] :
( ~ ( SV262 @ SY1255 )
| ( SV747 = SY1255 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(3777,plain,
! [SV262: $i > $o,SV748: $i,SV42: $i > $o] :
( ( ( ! [SY1256: $i] :
( ~ ( SV42 @ SY1256 )
| ( SV748 = SY1256 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(3778,plain,
! [SV42: $i > $o,SV749: $i,SV262: $i > $o] :
( ( ( ! [SY1257: $i] :
( ~ ( SV262 @ SY1257 )
| ( SV749 = SY1257 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(3779,plain,
! [SV741: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
| ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3750]) ).
thf(3780,plain,
! [SV742: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
| ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3751]) ).
thf(3781,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV757 )
| ~ ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3752]) ).
thf(3782,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV756 ) )
= $true )
| ( ( ~ ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(3783,plain,
! [SV737: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( ~ ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) ) )
= $false )
| ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3754]) ).
thf(3784,plain,
! [SV197: $i > $o,SV396: $i > $o,SV737: $i] :
( ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3754]) ).
thf(3785,plain,
! [SV729: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(3786,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(3787,plain,
! [SV730: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3757]) ).
thf(3788,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3789,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3759]) ).
thf(3790,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3760]) ).
thf(3791,plain,
! [SV236: $i,SV4: $i > $i > $o,SV738: $i,SV663: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV738 ) ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3761]) ).
thf(3792,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i,SV759: $i] :
( ( ( ~ ~ ( ~ ( in @ SV759 @ SV236 )
| ~ ( SV4 @ SV759 @ SV738 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3793,plain,
! [SV236: $i,SV4: $i > $i > $o,SV731: $i,SV663: $i] :
( ( ( ~ ( ~ ( in @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV731 ) ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3763]) ).
thf(3794,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i,SV758: $i] :
( ( ( ~ ( ~ ( in @ SV758 @ SV236 )
| ~ ( SV4 @ SV758 @ SV731 ) ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3795,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( ~ ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3796,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
| ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1272 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SY1272 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(3797,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3768]) ).
thf(3798,plain,
! [SV665: $i,SV728: $i,SV23: $i] :
( ( ( ~ ! [SY1266: $i] :
( ~ ( in @ SY1266 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1266 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SY1266 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3768]) ).
thf(3799,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK121_SY646 @ SV713 @ SV42 @ SV262 ) )
| ~ ! [SY1274: $i] :
( ~ ( SV262 @ SY1274 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SY1274 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3800,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK116_SY646 @ SV713 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3770]) ).
thf(3801,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1268: $i] :
( ~ ( SV262 @ SY1268 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SY1268 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3770]) ).
thf(3802,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK122_SY126 @ SV714 @ SV262 @ SV42 ) )
| ~ ! [SY1275: $i] :
( ~ ( SV42 @ SY1275 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SY1275 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3803,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK117_SY126 @ SV714 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3772]) ).
thf(3804,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1269: $i] :
( ~ ( SV42 @ SY1269 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SY1269 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3772]) ).
thf(3805,plain,
! [SV262: $i > $o,SV752: $i,SV42: $i > $o] :
( ( ( ! [SY1262: $i] :
( ~ ( SV42 @ SY1262 )
| ( SV752 = SY1262 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3806,plain,
! [SV42: $i > $o,SV753: $i,SV262: $i > $o] :
( ( ( ! [SY1263: $i] :
( ~ ( SV262 @ SY1263 )
| ( SV753 = SY1263 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3807,plain,
! [SV746: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
| ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3775]) ).
thf(3808,plain,
! [SV747: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
| ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3776]) ).
thf(3809,plain,
! [SV748: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
| ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3777]) ).
thf(3810,plain,
! [SV749: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
| ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3778]) ).
thf(3811,plain,
! [SV741: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3812,plain,
! [SV42: $i > $o,SV262: $i > $o,SV741: $i] :
( ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3779]) ).
thf(3813,plain,
! [SV742: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3780]) ).
thf(3814,plain,
! [SV262: $i > $o,SV42: $i > $o,SV742: $i] :
( ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3780]) ).
thf(3815,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV757 ) )
= $true )
| ( ( ~ ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(3816,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( SV396 @ SV756 )
= $false )
| ( ( ~ ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3817,plain,
! [SV737: $i,SV396: $i > $o,SV197: $i > $o] :
( ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) )
| ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3783]) ).
thf(3818,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(3819,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(3820,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3821,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(3822,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3823,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3824,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3790]) ).
thf(3825,plain,
! [SV236: $i,SV4: $i > $i > $o,SV738: $i,SV663: $i] :
( ( ( ~ ( ~ ( in @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV738 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3791]) ).
thf(3826,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i,SV759: $i] :
( ( ( ~ ( ~ ( in @ SV759 @ SV236 )
| ~ ( SV4 @ SV759 @ SV738 ) ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3792]) ).
thf(3827,plain,
! [SV236: $i,SV4: $i > $i > $o,SV731: $i,SV663: $i] :
( ( ( ~ ( in @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV731 ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3828,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ SV236 )
| ~ ( SV4 @ SV758 @ SV731 ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3794]) ).
thf(3829,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3830,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3796]) ).
thf(3831,plain,
! [SV665: $i,SV733: $i,SV23: $i] :
( ( ( ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1272 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SY1272 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3796]) ).
thf(3832,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3797]) ).
thf(3833,plain,
! [SV665: $i,SV728: $i,SV23: $i] :
( ( ( ! [SY1266: $i] :
( ~ ( in @ SY1266 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SY1266 )
| ( in @ SY1253 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SY1266 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3798]) ).
thf(3834,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK121_SY646 @ SV713 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3799]) ).
thf(3835,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1274: $i] :
( ~ ( SV262 @ SY1274 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SY1274 ) ) )
= $false )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3799]) ).
thf(3836,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK116_SY646 @ SV713 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3800]) ).
thf(3837,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ! [SY1268: $i] :
( ~ ( SV262 @ SY1268 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SY1268 ) ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3838,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK122_SY126 @ SV714 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3802]) ).
thf(3839,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1275: $i] :
( ~ ( SV42 @ SY1275 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SY1275 ) ) )
= $false )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3802]) ).
thf(3840,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK117_SY126 @ SV714 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3803]) ).
thf(3841,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ! [SY1269: $i] :
( ~ ( SV42 @ SY1269 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SY1269 ) ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3804]) ).
thf(3842,plain,
! [SV752: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
| ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3805]) ).
thf(3843,plain,
! [SV753: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
| ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3806]) ).
thf(3844,plain,
! [SV746: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3845,plain,
! [SV42: $i > $o,SV262: $i > $o,SV746: $i] :
( ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3846,plain,
! [SV747: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3847,plain,
! [SV262: $i > $o,SV42: $i > $o,SV747: $i] :
( ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3848,plain,
! [SV748: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3849,plain,
! [SV42: $i > $o,SV262: $i > $o,SV748: $i] :
( ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3850,plain,
! [SV749: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(3851,plain,
! [SV262: $i > $o,SV42: $i > $o,SV749: $i] :
( ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(3852,plain,
! [SV741: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3811]) ).
thf(3853,plain,
! [SV741: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3854,plain,
! [SV742: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3813]) ).
thf(3855,plain,
! [SV742: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3856,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( SV396 @ SV757 )
= $false )
| ( ( ~ ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(3857,plain,
! [SV687: $i,SV197: $i > $o,SV756: $i,SV396: $i > $o] :
( ( ( ! [SY1264: $i] :
( ~ ( SV396 @ SY1264 )
| ( SV756 = SY1264 ) ) )
= $false )
| ( ( SV396 @ SV756 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(3858,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(3859,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(3860,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(3861,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3820]) ).
thf(3862,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3863,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3822]) ).
thf(3864,plain,
! [SV726: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3823]) ).
thf(3865,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV760 )
| ~ ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(3866,plain,
! [SV236: $i,SV4: $i > $i > $o,SV738: $i,SV663: $i] :
( ( ( ~ ( in @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV236 )
| ~ ( SV4 @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV738 ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3867,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV236 )
| ~ ( SV4 @ SV759 @ SV738 ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3826]) ).
thf(3868,plain,
! [SV236: $i,SV4: $i > $i > $o,SV731: $i,SV663: $i] :
( ( ( ~ ( in @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV236 ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3827]) ).
thf(3869,plain,
! [SV236: $i,SV731: $i,SV663: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV731 ) )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3827]) ).
thf(3870,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ SV236 ) )
= $true )
| ( ( ~ ( SV4 @ SV758 @ SV731 ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(3871,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3829]) ).
thf(3872,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3829]) ).
thf(3873,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(3874,plain,
! [SV665: $i,SV733: $i,SV23: $i] :
( ( ( ! [SY1272: $i] :
( ~ ( in @ SY1272 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SY1272 )
| ( in @ SY1261 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SY1272 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3831]) ).
thf(3875,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
| ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(3876,plain,
! [SV665: $i,SV728: $i,SV23: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV761 )
| ( in @ SY1277 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(3877,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK121_SY646 @ SV713 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3834]) ).
thf(3878,plain,
! [SV42: $i > $o,SV713: $i,SV262: $i > $o] :
( ( ( ! [SY1274: $i] :
( ~ ( SV262 @ SY1274 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SY1274 ) ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3835]) ).
thf(3879,plain,
! [SV42: $i > $o,SV713: $i,SV762: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV762 )
| ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SV762 ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(3880,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK122_SY126 @ SV714 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3838]) ).
thf(3881,plain,
! [SV262: $i > $o,SV714: $i,SV42: $i > $o] :
( ( ( ! [SY1275: $i] :
( ~ ( SV42 @ SY1275 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SY1275 ) ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3839]) ).
thf(3882,plain,
! [SV262: $i > $o,SV714: $i,SV763: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV763 )
| ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SV763 ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(3883,plain,
! [SV752: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3842]) ).
thf(3884,plain,
! [SV42: $i > $o,SV262: $i > $o,SV752: $i] :
( ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3842]) ).
thf(3885,plain,
! [SV753: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3843]) ).
thf(3886,plain,
! [SV262: $i > $o,SV42: $i > $o,SV753: $i] :
( ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3843]) ).
thf(3887,plain,
! [SV746: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3844]) ).
thf(3888,plain,
! [SV746: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3889,plain,
! [SV747: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3846]) ).
thf(3890,plain,
! [SV747: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(3891,plain,
! [SV748: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(3892,plain,
! [SV748: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3893,plain,
! [SV749: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3850]) ).
thf(3894,plain,
! [SV749: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3851]) ).
thf(3895,plain,
! [SV741: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3896,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK134_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1278: $i] :
( ~ ( SV262 @ SY1278 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SY1278 ) ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3853]) ).
thf(3897,plain,
! [SV742: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3898,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK135_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1279: $i] :
( ~ ( SV42 @ SY1279 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SY1279 ) ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3855]) ).
thf(3899,plain,
! [SV687: $i,SV197: $i > $o,SV757: $i,SV396: $i > $o] :
( ( ( ! [SY1270: $i] :
( ~ ( SV396 @ SY1270 )
| ( SV757 = SY1270 ) ) )
= $false )
| ( ( SV396 @ SV757 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3900,plain,
! [SV756: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK136_SY1264 @ SV687 @ SV197 @ SV756 @ SV396 ) )
| ( SV756
= ( sK136_SY1264 @ SV687 @ SV197 @ SV756 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV756 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3857]) ).
thf(3901,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ~ ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(3902,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3859]) ).
thf(3903,plain,
! [SV729: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3860]) ).
thf(3904,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV764 )
| ~ ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(3905,plain,
! [SV730: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3862]) ).
thf(3906,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV765 )
| ~ ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(3907,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV766 )
| ~ ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(3908,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV760 )
| ~ ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(3909,plain,
! [SV236: $i,SV4: $i > $i > $o,SV738: $i,SV663: $i] :
( ( ( ~ ( in @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV236 ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(3910,plain,
! [SV236: $i,SV738: $i,SV663: $i,SV4: $i > $i > $o] :
( ( ( ~ ( SV4 @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV738 ) )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3866]) ).
thf(3911,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV236 ) )
= $true )
| ( ( ~ ( SV4 @ SV759 @ SV738 ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(3912,plain,
! [SV236: $i,SV4: $i > $i > $o,SV731: $i,SV663: $i] :
( ( ( in @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV236 )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3868]) ).
thf(3913,plain,
! [SV236: $i,SV731: $i,SV663: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK124_SY1242 @ SV663 @ SV731 @ SV4 @ SV236 ) @ SV731 )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3869]) ).
thf(3914,plain,
! [SV663: $i,SV731: $i,SV4: $i > $i > $o,SV236: $i,SV758: $i] :
( ( ( in @ SV758 @ SV236 )
= $false )
| ( ( ~ ( SV4 @ SV758 @ SV731 ) )
= $true )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(3915,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3871]) ).
thf(3916,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(3917,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
| ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(3918,plain,
! [SV665: $i,SV733: $i,SV23: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
| ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV767 )
| ( in @ SY1283 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(3919,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3875]) ).
thf(3920,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3875]) ).
thf(3921,plain,
! [SV665: $i,SV728: $i,SV23: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV761 )
| ( in @ SY1277 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3876]) ).
thf(3922,plain,
! [SV42: $i > $o,SV713: $i,SV768: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV768 )
| ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SV768 ) )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(3923,plain,
! [SV42: $i > $o,SV713: $i,SV762: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV762 ) )
= $true )
| ( ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SV762 )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(3924,plain,
! [SV262: $i > $o,SV714: $i,SV769: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV769 )
| ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SV769 ) )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3881]) ).
thf(3925,plain,
! [SV262: $i > $o,SV714: $i,SV763: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV763 ) )
= $true )
| ( ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SV763 )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(3926,plain,
! [SV752: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( ~ ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3883]) ).
thf(3927,plain,
! [SV752: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(3928,plain,
! [SV753: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( ~ ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3885]) ).
thf(3929,plain,
! [SV753: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(3930,plain,
! [SV746: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(3931,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK137_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1284: $i] :
( ~ ( SV262 @ SY1284 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SY1284 ) ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3888]) ).
thf(3932,plain,
! [SV747: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3889]) ).
thf(3933,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK138_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1285: $i] :
( ~ ( SV42 @ SY1285 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SY1285 ) ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3890]) ).
thf(3934,plain,
! [SV748: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(3935,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK139_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1286: $i] :
( ~ ( SV262 @ SY1286 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SY1286 ) ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3892]) ).
thf(3936,plain,
! [SV749: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(3937,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK140_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1287: $i] :
( ~ ( SV42 @ SY1287 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SY1287 ) ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3894]) ).
thf(3938,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK141_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1288: $i] :
( ~ ( SV262 @ SY1288 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SY1288 ) ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3895]) ).
thf(3939,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK134_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1278: $i] :
( ~ ( SV262 @ SY1278 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SY1278 ) ) ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(3940,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK142_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1289: $i] :
( ~ ( SV42 @ SY1289 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SY1289 ) ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3897]) ).
thf(3941,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK135_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1279: $i] :
( ~ ( SV42 @ SY1279 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SY1279 ) ) ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3898]) ).
thf(3942,plain,
! [SV757: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK143_SY1270 @ SV687 @ SV197 @ SV757 @ SV396 ) )
| ( SV757
= ( sK143_SY1270 @ SV687 @ SV197 @ SV757 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV757 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3899]) ).
thf(3943,plain,
! [SV756: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK136_SY1264 @ SV687 @ SV197 @ SV756 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV756 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3900]) ).
thf(3944,plain,
! [SV396: $i > $o,SV197: $i > $o,SV687: $i,SV756: $i] :
( ( ( SV756
= ( sK136_SY1264 @ SV687 @ SV197 @ SV756 @ SV396 ) )
= $false )
| ( ( SV396 @ SV756 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3900]) ).
thf(3945,plain,
! [SV737: $i,SV197: $i > $o,SV396: $i > $o] :
( ( ( ! [SY862: $i] :
~ ~ ( ~ ( SV396 @ SY862 )
| ~ ! [SY863: $i] :
( ~ ( SV396 @ SY863 )
| ( SY862 = SY863 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3901]) ).
thf(3946,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV770 )
| ~ ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(3947,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV771 )
| ~ ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(3948,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV764 )
| ~ ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3904]) ).
thf(3949,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV772 )
| ~ ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3905]) ).
thf(3950,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV765 )
| ~ ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(3951,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV766 )
| ~ ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(3952,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV760 )
| ~ ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3908]) ).
thf(3953,plain,
! [SV236: $i,SV4: $i > $i > $o,SV738: $i,SV663: $i] :
( ( ( in @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV236 )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3909]) ).
thf(3954,plain,
! [SV236: $i,SV738: $i,SV663: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ ( sK127_SY1246 @ SV663 @ SV738 @ SV4 @ SV236 ) @ SV738 )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3910]) ).
thf(3955,plain,
! [SV663: $i,SV738: $i,SV4: $i > $i > $o,SV236: $i,SV759: $i] :
( ( ( in @ SV759 @ SV236 )
= $false )
| ( ( ~ ( SV4 @ SV759 @ SV738 ) )
= $true )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(3956,plain,
! [SV663: $i,SV236: $i,SV731: $i,SV758: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV758 @ SV731 )
= $false )
| ( ( in @ SV758 @ SV236 )
= $false )
| ( ( in @ SV731 @ ( sK97_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV663
= ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3914]) ).
thf(3957,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
| ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3915]) ).
thf(3958,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(3959,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(3960,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3917]) ).
thf(3961,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3917]) ).
thf(3962,plain,
! [SV665: $i,SV733: $i,SV23: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ ( sK4_SY65 @ SV23 ) ) )
= $true )
| ( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV767 )
| ( in @ SY1283 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3918]) ).
thf(3963,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3919]) ).
thf(3964,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3920]) ).
thf(3965,plain,
! [SV665: $i,SV728: $i,SV23: $i,SV761: $i] :
( ( ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV761 )
| ( in @ SY1277 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
| ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(3966,plain,
! [SV42: $i > $o,SV713: $i,SV768: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV768 ) )
= $true )
| ( ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SV768 )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(3967,plain,
! [SV42: $i > $o,SV713: $i,SV762: $i,SV262: $i > $o] :
( ( ( SV262 @ SV762 )
= $false )
| ( ( ( sK116_SY646 @ SV713 @ SV42 @ SV262 )
= SV762 )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV713
= ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(3968,plain,
! [SV262: $i > $o,SV714: $i,SV769: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV769 ) )
= $true )
| ( ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SV769 )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(3969,plain,
! [SV262: $i > $o,SV714: $i,SV763: $i,SV42: $i > $o] :
( ( ( SV42 @ SV763 )
= $false )
| ( ( ( sK117_SY126 @ SV714 @ SV262 @ SV42 )
= SV763 )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV714
= ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $false )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3925]) ).
thf(3970,plain,
! [SV752: $i,SV42: $i > $o,SV262: $i > $o] :
( ( ( ! [SY646: $i] :
~ ~ ( ~ ( SV262 @ SY646 )
| ~ ! [SY647: $i] :
( ~ ( SV262 @ SY647 )
| ( SY646 = SY647 ) ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3926]) ).
thf(3971,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK144_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1293: $i] :
( ~ ( SV262 @ SY1293 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SY1293 ) ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3927]) ).
thf(3972,plain,
! [SV753: $i,SV262: $i > $o,SV42: $i > $o] :
( ( ( ! [SY126: $i] :
~ ~ ( ~ ( SV42 @ SY126 )
| ~ ! [SY127: $i] :
( ~ ( SV42 @ SY127 )
| ( SY126 = SY127 ) ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(3973,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK145_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1294: $i] :
( ~ ( SV42 @ SY1294 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SY1294 ) ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3929]) ).
thf(3974,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK146_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1295: $i] :
( ~ ( SV262 @ SY1295 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SY1295 ) ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3930]) ).
thf(3975,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK137_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1284: $i] :
( ~ ( SV262 @ SY1284 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SY1284 ) ) ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3931]) ).
thf(3976,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK147_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1296: $i] :
( ~ ( SV42 @ SY1296 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SY1296 ) ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3932]) ).
thf(3977,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK138_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1285: $i] :
( ~ ( SV42 @ SY1285 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SY1285 ) ) ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3933]) ).
thf(3978,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK148_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1297: $i] :
( ~ ( SV262 @ SY1297 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SY1297 ) ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3934]) ).
thf(3979,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK139_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1286: $i] :
( ~ ( SV262 @ SY1286 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SY1286 ) ) ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3935]) ).
thf(3980,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK149_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1298: $i] :
( ~ ( SV42 @ SY1298 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SY1298 ) ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3936]) ).
thf(3981,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK140_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1287: $i] :
( ~ ( SV42 @ SY1287 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SY1287 ) ) ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3937]) ).
thf(3982,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK141_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1288: $i] :
( ~ ( SV262 @ SY1288 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SY1288 ) ) ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3938]) ).
thf(3983,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK134_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1278: $i] :
( ~ ( SV262 @ SY1278 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SY1278 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(3984,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK142_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1289: $i] :
( ~ ( SV42 @ SY1289 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SY1289 ) ) ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3940]) ).
thf(3985,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK135_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1279: $i] :
( ~ ( SV42 @ SY1279 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SY1279 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(3986,plain,
! [SV757: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK143_SY1270 @ SV687 @ SV197 @ SV757 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV757 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3942]) ).
thf(3987,plain,
! [SV396: $i > $o,SV197: $i > $o,SV687: $i,SV757: $i] :
( ( ( SV757
= ( sK143_SY1270 @ SV687 @ SV197 @ SV757 @ SV396 ) )
= $false )
| ( ( SV396 @ SV757 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3942]) ).
thf(3988,plain,
! [SV756: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK136_SY1264 @ SV687 @ SV197 @ SV756 @ SV396 ) )
= $true )
| ( ( SV396 @ SV756 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV687
= ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $false )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3943]) ).
thf(3989,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( ~ ~ ( ~ ( SV396 @ SV773 )
| ~ ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(3990,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV770 )
| ~ ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(3991,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV771 )
| ~ ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(3992,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV764 )
| ~ ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3948]) ).
thf(3993,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV772 )
| ~ ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3949]) ).
thf(3994,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV765 )
| ~ ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(3995,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV766 )
| ~ ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(3996,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV760 ) )
= $true )
| ( ( ~ ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(3997,plain,
! [SV663: $i,SV236: $i,SV738: $i,SV759: $i,SV4: $i > $i > $o] :
( ( ( SV4 @ SV759 @ SV738 )
= $false )
| ( ( in @ SV759 @ SV236 )
= $false )
| ( ( in @ SV738 @ ( sK100_SY599 @ SV663 @ SV4 @ SV236 ) )
= $true )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ SV663 )
= $false )
| ( ( SV4 @ ( sK7_SY596 @ SV4 @ SV236 ) @ ( sK76_SY1176 @ SV663 @ SV236 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(3998,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) ) )
= $false )
| ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3957]) ).
thf(3999,plain,
! [SV23: $i,SV712: $i,SV695: $i] :
( ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3957]) ).
thf(4000,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $false )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3958]) ).
thf(4001,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3960]) ).
thf(4002,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3961]) ).
thf(4003,plain,
! [SV665: $i,SV733: $i,SV23: $i,SV767: $i] :
( ( ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV767 )
| ( in @ SY1283 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
| ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4004,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3963]) ).
thf(4005,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4006,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV761: $i] :
( ( ( ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV761 )
| ( in @ SY1277 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) ) )
= $true )
| ( ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 )
= $true )
| ( ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3965]) ).
thf(4007,plain,
! [SV42: $i > $o,SV713: $i,SV768: $i,SV262: $i > $o] :
( ( ( SV262 @ SV768 )
= $false )
| ( ( ( sK121_SY646 @ SV713 @ SV42 @ SV262 )
= SV768 )
= $true )
| ( ( SV42 @ SV713 )
= $false )
| ( ( SV42 @ ( sK109_SY1221 @ SV262 @ SV713 @ SV42 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4008,plain,
! [SV262: $i > $o,SV714: $i,SV769: $i,SV42: $i > $o] :
( ( ( SV42 @ SV769 )
= $false )
| ( ( ( sK122_SY126 @ SV714 @ SV262 @ SV42 )
= SV769 )
= $true )
| ( ( SV262 @ SV714 )
= $false )
| ( ( SV262 @ ( sK110_SY1222 @ SV42 @ SV714 @ SV262 ) )
= $true )
| ( ( ( sK8_SY642 @ SV262 @ SV42 )
= ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3968]) ).
thf(4009,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ~ ( ~ ( SV262 @ ( sK150_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1300: $i] :
( ~ ( SV262 @ SY1300 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SY1300 ) ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3970]) ).
thf(4010,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK144_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1293: $i] :
( ~ ( SV262 @ SY1293 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SY1293 ) ) ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3971]) ).
thf(4011,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ~ ( ~ ( SV42 @ ( sK151_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1301: $i] :
( ~ ( SV42 @ SY1301 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SY1301 ) ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3972]) ).
thf(4012,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK145_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1294: $i] :
( ~ ( SV42 @ SY1294 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SY1294 ) ) ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3973]) ).
thf(4013,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK146_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1295: $i] :
( ~ ( SV262 @ SY1295 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SY1295 ) ) ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3974]) ).
thf(4014,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK137_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1284: $i] :
( ~ ( SV262 @ SY1284 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SY1284 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3975]) ).
thf(4015,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK147_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1296: $i] :
( ~ ( SV42 @ SY1296 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SY1296 ) ) ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3976]) ).
thf(4016,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK138_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1285: $i] :
( ~ ( SV42 @ SY1285 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SY1285 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4017,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK148_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1297: $i] :
( ~ ( SV262 @ SY1297 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SY1297 ) ) ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3978]) ).
thf(4018,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK139_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1286: $i] :
( ~ ( SV262 @ SY1286 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SY1286 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4019,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK149_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1298: $i] :
( ~ ( SV42 @ SY1298 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SY1298 ) ) ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3980]) ).
thf(4020,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK140_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1287: $i] :
( ~ ( SV42 @ SY1287 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SY1287 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4021,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK141_SY646 @ SV741 @ SV42 @ SV262 ) )
| ~ ! [SY1288: $i] :
( ~ ( SV262 @ SY1288 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SY1288 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4022,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK134_SY646 @ SV741 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4023,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1278: $i] :
( ~ ( SV262 @ SY1278 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SY1278 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4024,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK142_SY126 @ SV742 @ SV262 @ SV42 ) )
| ~ ! [SY1289: $i] :
( ~ ( SV42 @ SY1289 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SY1289 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4025,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK135_SY126 @ SV742 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3985]) ).
thf(4026,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1279: $i] :
( ~ ( SV42 @ SY1279 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SY1279 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3985]) ).
thf(4027,plain,
! [SV757: $i,SV197: $i > $o,SV687: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK143_SY1270 @ SV687 @ SV197 @ SV757 @ SV396 ) )
= $true )
| ( ( SV396 @ SV757 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV687 )
= $false )
| ( ( SV197 @ ( sK104_SY1204 @ SV396 @ SV687 @ SV197 ) )
= $true )
| ( ( ( sK17_SY858 @ SV396 @ SV197 )
= ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4028,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( ~ ( ~ ( SV396 @ SV773 )
| ~ ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4029,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV770 )
| ~ ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3990]) ).
thf(4030,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV771 )
| ~ ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3991]) ).
thf(4031,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV764 ) )
= $true )
| ( ( ~ ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4032,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV772 )
| ~ ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3993]) ).
thf(4033,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV765 ) )
= $true )
| ( ( ~ ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4034,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV766 ) )
= $true )
| ( ( ~ ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4035,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( SV396 @ SV760 )
= $false )
| ( ( ~ ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4036,plain,
! [SV23: $i,SV695: $i,SV712: $i] :
( ( ( in @ SV712 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( in @ SV695 @ ( sK114_SY1220 @ SV712 @ SV695 @ SV23 ) )
= $true )
| ( ( SV695 = SV712 )
= $true )
| ( ( in @ SV695 @ SV23 )
= $false )
| ( ( in @ SV712 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3998]) ).
thf(4037,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
| ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4038,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4039,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV767: $i] :
( ( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV767 )
| ( in @ SY1283 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) ) )
= $true )
| ( ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 )
= $true )
| ( ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4003]) ).
thf(4040,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ~ ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4004]) ).
thf(4041,plain,
! [SV728: $i,SV665: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4004]) ).
thf(4042,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( ! [SY1251: $i] :
~ ~ ( ~ ( in @ SY1251 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SY1251 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4005]) ).
thf(4043,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV761: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV761 )
| ( in @ SV774 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
= $true )
| ( ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 )
= $true )
| ( ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4044,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( ~ ( SV262 @ ( sK150_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1300: $i] :
( ~ ( SV262 @ SY1300 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SY1300 ) ) ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4009]) ).
thf(4045,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK144_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1293: $i] :
( ~ ( SV262 @ SY1293 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SY1293 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4046,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( ~ ( SV42 @ ( sK151_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1301: $i] :
( ~ ( SV42 @ SY1301 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SY1301 ) ) ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4011]) ).
thf(4047,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK145_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1294: $i] :
( ~ ( SV42 @ SY1294 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SY1294 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4012]) ).
thf(4048,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK146_SY646 @ SV746 @ SV42 @ SV262 ) )
| ~ ! [SY1295: $i] :
( ~ ( SV262 @ SY1295 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SY1295 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4013]) ).
thf(4049,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK137_SY646 @ SV746 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4014]) ).
thf(4050,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1284: $i] :
( ~ ( SV262 @ SY1284 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SY1284 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4014]) ).
thf(4051,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK147_SY126 @ SV747 @ SV262 @ SV42 ) )
| ~ ! [SY1296: $i] :
( ~ ( SV42 @ SY1296 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SY1296 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4052,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK138_SY126 @ SV747 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4016]) ).
thf(4053,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1285: $i] :
( ~ ( SV42 @ SY1285 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SY1285 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4016]) ).
thf(4054,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK148_SY646 @ SV748 @ SV42 @ SV262 ) )
| ~ ! [SY1297: $i] :
( ~ ( SV262 @ SY1297 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SY1297 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4017]) ).
thf(4055,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK139_SY646 @ SV748 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4018]) ).
thf(4056,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1286: $i] :
( ~ ( SV262 @ SY1286 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SY1286 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4018]) ).
thf(4057,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK149_SY126 @ SV749 @ SV262 @ SV42 ) )
| ~ ! [SY1298: $i] :
( ~ ( SV42 @ SY1298 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SY1298 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4058,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK140_SY126 @ SV749 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4020]) ).
thf(4059,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1287: $i] :
( ~ ( SV42 @ SY1287 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SY1287 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4020]) ).
thf(4060,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK141_SY646 @ SV741 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4021]) ).
thf(4061,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1288: $i] :
( ~ ( SV262 @ SY1288 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SY1288 ) ) )
= $false )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4021]) ).
thf(4062,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK134_SY646 @ SV741 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4022]) ).
thf(4063,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ! [SY1278: $i] :
( ~ ( SV262 @ SY1278 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SY1278 ) ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4023]) ).
thf(4064,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK142_SY126 @ SV742 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4024]) ).
thf(4065,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1289: $i] :
( ~ ( SV42 @ SY1289 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SY1289 ) ) )
= $false )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4024]) ).
thf(4066,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK135_SY126 @ SV742 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4025]) ).
thf(4067,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ! [SY1279: $i] :
( ~ ( SV42 @ SY1279 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SY1279 ) ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4026]) ).
thf(4068,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV773 )
| ~ ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4028]) ).
thf(4069,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV770 ) )
= $true )
| ( ( ~ ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4070,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV771 ) )
= $true )
| ( ( ~ ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4071,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( SV396 @ SV764 )
= $false )
| ( ( ~ ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4072,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV772 ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4073,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( SV396 @ SV765 )
= $false )
| ( ( ~ ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4074,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( SV396 @ SV766 )
= $false )
| ( ( ~ ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4075,plain,
! [SV726: $i,SV197: $i > $o,SV760: $i,SV396: $i > $o] :
( ( ( ! [SY1276: $i] :
( ~ ( SV396 @ SY1276 )
| ( SV760 = SY1276 ) ) )
= $false )
| ( ( SV396 @ SV760 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4076,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ~ ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4037]) ).
thf(4077,plain,
! [SV733: $i,SV665: $i,SV23: $i] :
( ( ( ~ ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4037]) ).
thf(4078,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( ! [SY1259: $i] :
~ ~ ( ~ ( in @ SY1259 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SY1259 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4038]) ).
thf(4079,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV767: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV767 )
| ( in @ SV775 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
= $true )
| ( ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 )
= $true )
| ( ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4080,plain,
! [SV23: $i,SV665: $i,SV728: $i] :
( ( ( in @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4040]) ).
thf(4081,plain,
! [SV728: $i,SV665: $i,SV23: $i] :
( ( ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV665 )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4041]) ).
thf(4082,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV776: $i] :
( ( ( ~ ~ ( ~ ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SV776 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4083,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV761: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV761 ) )
= $true )
| ( ( in @ SV774 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
= $true )
| ( ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 )
= $true )
| ( ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4043]) ).
thf(4084,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK150_SY646 @ SV752 @ SV42 @ SV262 ) )
| ~ ! [SY1300: $i] :
( ~ ( SV262 @ SY1300 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SY1300 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4085,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK144_SY646 @ SV752 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4045]) ).
thf(4086,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1293: $i] :
( ~ ( SV262 @ SY1293 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SY1293 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4045]) ).
thf(4087,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK151_SY126 @ SV753 @ SV262 @ SV42 ) )
| ~ ! [SY1301: $i] :
( ~ ( SV42 @ SY1301 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SY1301 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4088,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK145_SY126 @ SV753 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4047]) ).
thf(4089,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1294: $i] :
( ~ ( SV42 @ SY1294 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SY1294 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4047]) ).
thf(4090,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK146_SY646 @ SV746 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4048]) ).
thf(4091,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1295: $i] :
( ~ ( SV262 @ SY1295 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SY1295 ) ) )
= $false )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4048]) ).
thf(4092,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK137_SY646 @ SV746 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4049]) ).
thf(4093,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ! [SY1284: $i] :
( ~ ( SV262 @ SY1284 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SY1284 ) ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4050]) ).
thf(4094,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK147_SY126 @ SV747 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4051]) ).
thf(4095,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1296: $i] :
( ~ ( SV42 @ SY1296 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SY1296 ) ) )
= $false )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4051]) ).
thf(4096,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK138_SY126 @ SV747 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4052]) ).
thf(4097,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ! [SY1285: $i] :
( ~ ( SV42 @ SY1285 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SY1285 ) ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4053]) ).
thf(4098,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK148_SY646 @ SV748 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4054]) ).
thf(4099,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1297: $i] :
( ~ ( SV262 @ SY1297 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SY1297 ) ) )
= $false )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4054]) ).
thf(4100,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK139_SY646 @ SV748 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4055]) ).
thf(4101,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ! [SY1286: $i] :
( ~ ( SV262 @ SY1286 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SY1286 ) ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4102,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK149_SY126 @ SV749 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4057]) ).
thf(4103,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1298: $i] :
( ~ ( SV42 @ SY1298 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SY1298 ) ) )
= $false )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4057]) ).
thf(4104,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK140_SY126 @ SV749 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4058]) ).
thf(4105,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ! [SY1287: $i] :
( ~ ( SV42 @ SY1287 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SY1287 ) ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4106,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK141_SY646 @ SV741 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4060]) ).
thf(4107,plain,
! [SV42: $i > $o,SV741: $i,SV262: $i > $o] :
( ( ( ! [SY1288: $i] :
( ~ ( SV262 @ SY1288 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SY1288 ) ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4061]) ).
thf(4108,plain,
! [SV42: $i > $o,SV741: $i,SV777: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV777 )
| ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SV777 ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4109,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK142_SY126 @ SV742 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4064]) ).
thf(4110,plain,
! [SV262: $i > $o,SV742: $i,SV42: $i > $o] :
( ( ( ! [SY1289: $i] :
( ~ ( SV42 @ SY1289 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SY1289 ) ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4065]) ).
thf(4111,plain,
! [SV262: $i > $o,SV742: $i,SV778: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV778 )
| ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SV778 ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4112,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ SV773 ) )
= $true )
| ( ( ~ ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4113,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( SV396 @ SV770 )
= $false )
| ( ( ~ ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4069]) ).
thf(4114,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( SV396 @ SV771 )
= $false )
| ( ( ~ ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4070]) ).
thf(4115,plain,
! [SV729: $i,SV197: $i > $o,SV764: $i,SV396: $i > $o] :
( ( ( ! [SY1280: $i] :
( ~ ( SV396 @ SY1280 )
| ( SV764 = SY1280 ) ) )
= $false )
| ( ( SV396 @ SV764 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4116,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( SV396 @ SV772 )
= $false )
| ( ( ~ ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4072]) ).
thf(4117,plain,
! [SV730: $i,SV197: $i > $o,SV765: $i,SV396: $i > $o] :
( ( ( ! [SY1281: $i] :
( ~ ( SV396 @ SY1281 )
| ( SV765 = SY1281 ) ) )
= $false )
| ( ( SV396 @ SV765 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4118,plain,
! [SV726: $i,SV197: $i > $o,SV766: $i,SV396: $i > $o] :
( ( ( ! [SY1282: $i] :
( ~ ( SV396 @ SY1282 )
| ( SV766 = SY1282 ) ) )
= $false )
| ( ( SV396 @ SV766 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4119,plain,
! [SV760: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK152_SY1276 @ SV726 @ SV197 @ SV760 @ SV396 ) )
| ( SV760
= ( sK152_SY1276 @ SV726 @ SV197 @ SV760 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV760 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4075]) ).
thf(4120,plain,
! [SV23: $i,SV665: $i,SV733: $i] :
( ( ( in @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) @ ( sK4_SY65 @ SV23 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4076]) ).
thf(4121,plain,
! [SV733: $i,SV665: $i,SV23: $i] :
( ( ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV665 )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4077]) ).
thf(4122,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV779: $i] :
( ( ( ~ ~ ( ~ ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SV779 @ SV665 ) ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4123,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV767: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV767 ) )
= $true )
| ( ( in @ SV775 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
= $true )
| ( ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 )
= $true )
| ( ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4124,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV776: $i] :
( ( ( ~ ( ~ ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SV776 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4125,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV761: $i,SV774: $i] :
( ( ( in @ SV774 @ SV761 )
= $false )
| ( ( in @ SV774 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
= $true )
| ( ( in @ ( sK115_SY1250 @ SV23 @ SV665 @ SV728 ) @ SV761 )
= $true )
| ( ( in @ SV761 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4126,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ ( sK150_SY646 @ SV752 @ SV42 @ SV262 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4084]) ).
thf(4127,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ~ ! [SY1300: $i] :
( ~ ( SV262 @ SY1300 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SY1300 ) ) )
= $false )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4084]) ).
thf(4128,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK144_SY646 @ SV752 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4085]) ).
thf(4129,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ! [SY1293: $i] :
( ~ ( SV262 @ SY1293 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SY1293 ) ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4086]) ).
thf(4130,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ ( sK151_SY126 @ SV753 @ SV262 @ SV42 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4131,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ~ ! [SY1301: $i] :
( ~ ( SV42 @ SY1301 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SY1301 ) ) )
= $false )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4132,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK145_SY126 @ SV753 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4088]) ).
thf(4133,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ! [SY1294: $i] :
( ~ ( SV42 @ SY1294 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SY1294 ) ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4089]) ).
thf(4134,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK146_SY646 @ SV746 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4090]) ).
thf(4135,plain,
! [SV42: $i > $o,SV746: $i,SV262: $i > $o] :
( ( ( ! [SY1295: $i] :
( ~ ( SV262 @ SY1295 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SY1295 ) ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4091]) ).
thf(4136,plain,
! [SV42: $i > $o,SV746: $i,SV780: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV780 )
| ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SV780 ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4137,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK147_SY126 @ SV747 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4094]) ).
thf(4138,plain,
! [SV262: $i > $o,SV747: $i,SV42: $i > $o] :
( ( ( ! [SY1296: $i] :
( ~ ( SV42 @ SY1296 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SY1296 ) ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4095]) ).
thf(4139,plain,
! [SV262: $i > $o,SV747: $i,SV781: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV781 )
| ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SV781 ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4140,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK148_SY646 @ SV748 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4098]) ).
thf(4141,plain,
! [SV42: $i > $o,SV748: $i,SV262: $i > $o] :
( ( ( ! [SY1297: $i] :
( ~ ( SV262 @ SY1297 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SY1297 ) ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4099]) ).
thf(4142,plain,
! [SV42: $i > $o,SV748: $i,SV782: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV782 )
| ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SV782 ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4143,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK149_SY126 @ SV749 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4102]) ).
thf(4144,plain,
! [SV262: $i > $o,SV749: $i,SV42: $i > $o] :
( ( ( ! [SY1298: $i] :
( ~ ( SV42 @ SY1298 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SY1298 ) ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4103]) ).
thf(4145,plain,
! [SV262: $i > $o,SV749: $i,SV783: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV783 )
| ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SV783 ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4146,plain,
! [SV42: $i > $o,SV741: $i,SV784: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV784 )
| ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SV784 ) )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(4147,plain,
! [SV42: $i > $o,SV741: $i,SV777: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV777 ) )
= $true )
| ( ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SV777 )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4148,plain,
! [SV262: $i > $o,SV742: $i,SV785: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV785 )
| ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SV785 ) )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4149,plain,
! [SV262: $i > $o,SV742: $i,SV778: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV778 ) )
= $true )
| ( ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SV778 )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4150,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( SV396 @ SV773 )
= $false )
| ( ( ~ ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4151,plain,
! [SV737: $i,SV197: $i > $o,SV770: $i,SV396: $i > $o] :
( ( ( ! [SY1290: $i] :
( ~ ( SV396 @ SY1290 )
| ( SV770 = SY1290 ) ) )
= $false )
| ( ( SV396 @ SV770 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4152,plain,
! [SV729: $i,SV197: $i > $o,SV771: $i,SV396: $i > $o] :
( ( ( ! [SY1291: $i] :
( ~ ( SV396 @ SY1291 )
| ( SV771 = SY1291 ) ) )
= $false )
| ( ( SV396 @ SV771 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4153,plain,
! [SV764: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK153_SY1280 @ SV729 @ SV197 @ SV764 @ SV396 ) )
| ( SV764
= ( sK153_SY1280 @ SV729 @ SV197 @ SV764 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV764 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4115]) ).
thf(4154,plain,
! [SV730: $i,SV197: $i > $o,SV772: $i,SV396: $i > $o] :
( ( ( ! [SY1292: $i] :
( ~ ( SV396 @ SY1292 )
| ( SV772 = SY1292 ) ) )
= $false )
| ( ( SV396 @ SV772 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4155,plain,
! [SV765: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK154_SY1281 @ SV730 @ SV197 @ SV765 @ SV396 ) )
| ( SV765
= ( sK154_SY1281 @ SV730 @ SV197 @ SV765 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV765 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4117]) ).
thf(4156,plain,
! [SV766: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK155_SY1282 @ SV726 @ SV197 @ SV766 @ SV396 ) )
| ( SV766
= ( sK155_SY1282 @ SV726 @ SV197 @ SV766 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV766 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4118]) ).
thf(4157,plain,
! [SV760: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK152_SY1276 @ SV726 @ SV197 @ SV760 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV760 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4119]) ).
thf(4158,plain,
! [SV396: $i > $o,SV197: $i > $o,SV726: $i,SV760: $i] :
( ( ( SV760
= ( sK152_SY1276 @ SV726 @ SV197 @ SV760 @ SV396 ) )
= $false )
| ( ( SV396 @ SV760 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4119]) ).
thf(4159,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV779: $i] :
( ( ( ~ ( ~ ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SV779 @ SV665 ) ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4122]) ).
thf(4160,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV767: $i,SV775: $i] :
( ( ( in @ SV775 @ SV767 )
= $false )
| ( ( in @ SV775 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
= $true )
| ( ( in @ ( sK120_SY1258 @ SV23 @ SV665 @ SV733 ) @ SV767 )
= $true )
| ( ( in @ SV767 @ ( sK4_SY65 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4123]) ).
thf(4161,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
| ~ ( in @ SV776 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4124]) ).
thf(4162,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( SV262 @ ( sK150_SY646 @ SV752 @ SV42 @ SV262 ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4126]) ).
thf(4163,plain,
! [SV42: $i > $o,SV752: $i,SV262: $i > $o] :
( ( ( ! [SY1300: $i] :
( ~ ( SV262 @ SY1300 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SY1300 ) ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4127]) ).
thf(4164,plain,
! [SV42: $i > $o,SV752: $i,SV786: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV786 )
| ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SV786 ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4165,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( SV42 @ ( sK151_SY126 @ SV753 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4130]) ).
thf(4166,plain,
! [SV262: $i > $o,SV753: $i,SV42: $i > $o] :
( ( ( ! [SY1301: $i] :
( ~ ( SV42 @ SY1301 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SY1301 ) ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4131]) ).
thf(4167,plain,
! [SV262: $i > $o,SV753: $i,SV787: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV787 )
| ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SV787 ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4133]) ).
thf(4168,plain,
! [SV42: $i > $o,SV746: $i,SV788: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV788 )
| ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SV788 ) )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4169,plain,
! [SV42: $i > $o,SV746: $i,SV780: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV780 ) )
= $true )
| ( ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SV780 )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4170,plain,
! [SV262: $i > $o,SV747: $i,SV789: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV789 )
| ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SV789 ) )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4171,plain,
! [SV262: $i > $o,SV747: $i,SV781: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV781 ) )
= $true )
| ( ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SV781 )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4172,plain,
! [SV42: $i > $o,SV748: $i,SV790: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV790 )
| ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SV790 ) )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4173,plain,
! [SV42: $i > $o,SV748: $i,SV782: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV782 ) )
= $true )
| ( ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SV782 )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4142]) ).
thf(4174,plain,
! [SV262: $i > $o,SV749: $i,SV791: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV791 )
| ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SV791 ) )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4175,plain,
! [SV262: $i > $o,SV749: $i,SV783: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV783 ) )
= $true )
| ( ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SV783 )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4145]) ).
thf(4176,plain,
! [SV42: $i > $o,SV741: $i,SV784: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV784 ) )
= $true )
| ( ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SV784 )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4177,plain,
! [SV42: $i > $o,SV741: $i,SV777: $i,SV262: $i > $o] :
( ( ( SV262 @ SV777 )
= $false )
| ( ( ( sK134_SY646 @ SV741 @ SV42 @ SV262 )
= SV777 )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV741
= ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4178,plain,
! [SV262: $i > $o,SV742: $i,SV785: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV785 ) )
= $true )
| ( ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SV785 )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4148]) ).
thf(4179,plain,
! [SV262: $i > $o,SV742: $i,SV778: $i,SV42: $i > $o] :
( ( ( SV42 @ SV778 )
= $false )
| ( ( ( sK135_SY126 @ SV742 @ SV262 @ SV42 )
= SV778 )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV742
= ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4180,plain,
! [SV737: $i,SV197: $i > $o,SV773: $i,SV396: $i > $o] :
( ( ( ! [SY1299: $i] :
( ~ ( SV396 @ SY1299 )
| ( SV773 = SY1299 ) ) )
= $false )
| ( ( SV396 @ SV773 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4181,plain,
! [SV770: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK156_SY1290 @ SV737 @ SV197 @ SV770 @ SV396 ) )
| ( SV770
= ( sK156_SY1290 @ SV737 @ SV197 @ SV770 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV770 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4151]) ).
thf(4182,plain,
! [SV771: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK157_SY1291 @ SV729 @ SV197 @ SV771 @ SV396 ) )
| ( SV771
= ( sK157_SY1291 @ SV729 @ SV197 @ SV771 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV771 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4152]) ).
thf(4183,plain,
! [SV764: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK153_SY1280 @ SV729 @ SV197 @ SV764 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV764 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4153]) ).
thf(4184,plain,
! [SV396: $i > $o,SV197: $i > $o,SV729: $i,SV764: $i] :
( ( ( SV764
= ( sK153_SY1280 @ SV729 @ SV197 @ SV764 @ SV396 ) )
= $false )
| ( ( SV396 @ SV764 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4153]) ).
thf(4185,plain,
! [SV772: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK158_SY1292 @ SV730 @ SV197 @ SV772 @ SV396 ) )
| ( SV772
= ( sK158_SY1292 @ SV730 @ SV197 @ SV772 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV772 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4154]) ).
thf(4186,plain,
! [SV765: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK154_SY1281 @ SV730 @ SV197 @ SV765 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV765 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4187,plain,
! [SV396: $i > $o,SV197: $i > $o,SV730: $i,SV765: $i] :
( ( ( SV765
= ( sK154_SY1281 @ SV730 @ SV197 @ SV765 @ SV396 ) )
= $false )
| ( ( SV396 @ SV765 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4188,plain,
! [SV766: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK155_SY1282 @ SV726 @ SV197 @ SV766 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV766 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4156]) ).
thf(4189,plain,
! [SV396: $i > $o,SV197: $i > $o,SV726: $i,SV766: $i] :
( ( ( SV766
= ( sK155_SY1282 @ SV726 @ SV197 @ SV766 @ SV396 ) )
= $false )
| ( ( SV396 @ SV766 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4156]) ).
thf(4190,plain,
! [SV760: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK152_SY1276 @ SV726 @ SV197 @ SV760 @ SV396 ) )
= $true )
| ( ( SV396 @ SV760 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV726
= ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4157]) ).
thf(4191,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
| ~ ( in @ SV779 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4159]) ).
thf(4192,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV776 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4193,plain,
! [SV42: $i > $o,SV752: $i,SV792: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV792 )
| ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SV792 ) )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4194,plain,
! [SV42: $i > $o,SV752: $i,SV786: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV786 ) )
= $true )
| ( ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SV786 )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4195,plain,
! [SV262: $i > $o,SV753: $i,SV793: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV793 )
| ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SV793 ) )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4166]) ).
thf(4196,plain,
! [SV262: $i > $o,SV753: $i,SV787: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV787 ) )
= $true )
| ( ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SV787 )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4197,plain,
! [SV42: $i > $o,SV746: $i,SV788: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV788 ) )
= $true )
| ( ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SV788 )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4198,plain,
! [SV42: $i > $o,SV746: $i,SV780: $i,SV262: $i > $o] :
( ( ( SV262 @ SV780 )
= $false )
| ( ( ( sK137_SY646 @ SV746 @ SV42 @ SV262 )
= SV780 )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV746
= ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4199,plain,
! [SV262: $i > $o,SV747: $i,SV789: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV789 ) )
= $true )
| ( ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SV789 )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4200,plain,
! [SV262: $i > $o,SV747: $i,SV781: $i,SV42: $i > $o] :
( ( ( SV42 @ SV781 )
= $false )
| ( ( ( sK138_SY126 @ SV747 @ SV262 @ SV42 )
= SV781 )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV747
= ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4201,plain,
! [SV42: $i > $o,SV748: $i,SV790: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV790 ) )
= $true )
| ( ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SV790 )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4172]) ).
thf(4202,plain,
! [SV42: $i > $o,SV748: $i,SV782: $i,SV262: $i > $o] :
( ( ( SV262 @ SV782 )
= $false )
| ( ( ( sK139_SY646 @ SV748 @ SV42 @ SV262 )
= SV782 )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV748
= ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4203,plain,
! [SV262: $i > $o,SV749: $i,SV791: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV791 ) )
= $true )
| ( ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SV791 )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4174]) ).
thf(4204,plain,
! [SV262: $i > $o,SV749: $i,SV783: $i,SV42: $i > $o] :
( ( ( SV42 @ SV783 )
= $false )
| ( ( ( sK140_SY126 @ SV749 @ SV262 @ SV42 )
= SV783 )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV749
= ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4205,plain,
! [SV42: $i > $o,SV741: $i,SV784: $i,SV262: $i > $o] :
( ( ( SV262 @ SV784 )
= $false )
| ( ( ( sK141_SY646 @ SV741 @ SV42 @ SV262 )
= SV784 )
= $true )
| ( ( SV42 @ SV741 )
= $false )
| ( ( SV42 @ ( sK125_SY1248 @ SV262 @ SV741 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4206,plain,
! [SV262: $i > $o,SV742: $i,SV785: $i,SV42: $i > $o] :
( ( ( SV42 @ SV785 )
= $false )
| ( ( ( sK142_SY126 @ SV742 @ SV262 @ SV42 )
= SV785 )
= $true )
| ( ( SV262 @ SV742 )
= $false )
| ( ( SV262 @ ( sK126_SY1249 @ SV42 @ SV742 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4207,plain,
! [SV773: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK159_SY1299 @ SV737 @ SV197 @ SV773 @ SV396 ) )
| ( SV773
= ( sK159_SY1299 @ SV737 @ SV197 @ SV773 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV773 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4180]) ).
thf(4208,plain,
! [SV770: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK156_SY1290 @ SV737 @ SV197 @ SV770 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV770 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4181]) ).
thf(4209,plain,
! [SV396: $i > $o,SV197: $i > $o,SV737: $i,SV770: $i] :
( ( ( SV770
= ( sK156_SY1290 @ SV737 @ SV197 @ SV770 @ SV396 ) )
= $false )
| ( ( SV396 @ SV770 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4181]) ).
thf(4210,plain,
! [SV771: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK157_SY1291 @ SV729 @ SV197 @ SV771 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV771 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4182]) ).
thf(4211,plain,
! [SV396: $i > $o,SV197: $i > $o,SV729: $i,SV771: $i] :
( ( ( SV771
= ( sK157_SY1291 @ SV729 @ SV197 @ SV771 @ SV396 ) )
= $false )
| ( ( SV396 @ SV771 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4182]) ).
thf(4212,plain,
! [SV764: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK153_SY1280 @ SV729 @ SV197 @ SV764 @ SV396 ) )
= $true )
| ( ( SV396 @ SV764 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV729
= ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4183]) ).
thf(4213,plain,
! [SV772: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK158_SY1292 @ SV730 @ SV197 @ SV772 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV772 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4185]) ).
thf(4214,plain,
! [SV396: $i > $o,SV197: $i > $o,SV730: $i,SV772: $i] :
( ( ( SV772
= ( sK158_SY1292 @ SV730 @ SV197 @ SV772 @ SV396 ) )
= $false )
| ( ( SV396 @ SV772 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4185]) ).
thf(4215,plain,
! [SV765: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK154_SY1281 @ SV730 @ SV197 @ SV765 @ SV396 ) )
= $true )
| ( ( SV396 @ SV765 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV730
= ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4186]) ).
thf(4216,plain,
! [SV766: $i,SV197: $i > $o,SV726: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK155_SY1282 @ SV726 @ SV197 @ SV766 @ SV396 ) )
= $true )
| ( ( SV396 @ SV766 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV726 )
= $false )
| ( ( SV197 @ ( sK113_SY1234 @ SV396 @ SV726 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4188]) ).
thf(4217,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ SV779 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4218,plain,
! [SV23: $i,SV665: $i,SV728: $i,SV776: $i] :
( ( ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV776 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4219,plain,
! [SV42: $i > $o,SV752: $i,SV792: $i,SV262: $i > $o] :
( ( ( ~ ( SV262 @ SV792 ) )
= $true )
| ( ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SV792 )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4193]) ).
thf(4220,plain,
! [SV42: $i > $o,SV752: $i,SV786: $i,SV262: $i > $o] :
( ( ( SV262 @ SV786 )
= $false )
| ( ( ( sK144_SY646 @ SV752 @ SV42 @ SV262 )
= SV786 )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV752
= ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4221,plain,
! [SV262: $i > $o,SV753: $i,SV793: $i,SV42: $i > $o] :
( ( ( ~ ( SV42 @ SV793 ) )
= $true )
| ( ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SV793 )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4222,plain,
! [SV262: $i > $o,SV753: $i,SV787: $i,SV42: $i > $o] :
( ( ( SV42 @ SV787 )
= $false )
| ( ( ( sK145_SY126 @ SV753 @ SV262 @ SV42 )
= SV787 )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV753
= ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $false )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4223,plain,
! [SV42: $i > $o,SV746: $i,SV788: $i,SV262: $i > $o] :
( ( ( SV262 @ SV788 )
= $false )
| ( ( ( sK146_SY646 @ SV746 @ SV42 @ SV262 )
= SV788 )
= $true )
| ( ( SV42 @ SV746 )
= $false )
| ( ( SV42 @ ( sK128_SY1254 @ SV262 @ SV746 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4224,plain,
! [SV262: $i > $o,SV747: $i,SV789: $i,SV42: $i > $o] :
( ( ( SV42 @ SV789 )
= $false )
| ( ( ( sK147_SY126 @ SV747 @ SV262 @ SV42 )
= SV789 )
= $true )
| ( ( SV262 @ SV747 )
= $false )
| ( ( SV262 @ ( sK129_SY1255 @ SV42 @ SV747 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4225,plain,
! [SV42: $i > $o,SV748: $i,SV790: $i,SV262: $i > $o] :
( ( ( SV262 @ SV790 )
= $false )
| ( ( ( sK148_SY646 @ SV748 @ SV42 @ SV262 )
= SV790 )
= $true )
| ( ( SV42 @ SV748 )
= $false )
| ( ( SV42 @ ( sK130_SY1256 @ SV262 @ SV748 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4226,plain,
! [SV262: $i > $o,SV749: $i,SV791: $i,SV42: $i > $o] :
( ( ( SV42 @ SV791 )
= $false )
| ( ( ( sK149_SY126 @ SV749 @ SV262 @ SV42 )
= SV791 )
= $true )
| ( ( SV262 @ SV749 )
= $false )
| ( ( SV262 @ ( sK131_SY1257 @ SV42 @ SV749 @ SV262 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $false )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4203]) ).
thf(4227,plain,
! [SV773: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( ~ ( SV396 @ ( sK159_SY1299 @ SV737 @ SV197 @ SV773 @ SV396 ) ) )
= $false )
| ( ( SV396 @ SV773 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4228,plain,
! [SV396: $i > $o,SV197: $i > $o,SV737: $i,SV773: $i] :
( ( ( SV773
= ( sK159_SY1299 @ SV737 @ SV197 @ SV773 @ SV396 ) )
= $false )
| ( ( SV396 @ SV773 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4229,plain,
! [SV770: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK156_SY1290 @ SV737 @ SV197 @ SV770 @ SV396 ) )
= $true )
| ( ( SV396 @ SV770 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV737
= ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $false )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4208]) ).
thf(4230,plain,
! [SV771: $i,SV197: $i > $o,SV729: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK157_SY1291 @ SV729 @ SV197 @ SV771 @ SV396 ) )
= $true )
| ( ( SV396 @ SV771 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV729 )
= $false )
| ( ( SV197 @ ( sK118_SY1240 @ SV396 @ SV729 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4210]) ).
thf(4231,plain,
! [SV772: $i,SV197: $i > $o,SV730: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK158_SY1292 @ SV730 @ SV197 @ SV772 @ SV396 ) )
= $true )
| ( ( SV396 @ SV772 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV730 )
= $false )
| ( ( SV197 @ ( sK119_SY1241 @ SV396 @ SV730 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $false )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4213]) ).
thf(4232,plain,
! [SV23: $i,SV665: $i,SV733: $i,SV779: $i] :
( ( ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
= $false )
| ( ( ~ ( in @ SV779 @ SV665 ) )
= $true )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4233,plain,
! [SV23: $i,SV728: $i,SV665: $i,SV776: $i] :
( ( ( in @ SV776 @ SV665 )
= $false )
| ( ( in @ SV776 @ ( sK108_SY1180 @ SV728 @ SV665 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV23 )
= $false )
| ( ( in @ SV728 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4234,plain,
! [SV42: $i > $o,SV752: $i,SV792: $i,SV262: $i > $o] :
( ( ( SV262 @ SV792 )
= $false )
| ( ( ( sK150_SY646 @ SV752 @ SV42 @ SV262 )
= SV792 )
= $true )
| ( ( SV42 @ SV752 )
= $false )
| ( ( SV42 @ ( sK132_SY1262 @ SV262 @ SV752 @ SV42 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4235,plain,
! [SV262: $i > $o,SV753: $i,SV793: $i,SV42: $i > $o] :
( ( ( SV42 @ SV793 )
= $false )
| ( ( ( sK151_SY126 @ SV753 @ SV262 @ SV42 )
= SV793 )
= $true )
| ( ( SV262 @ SV753 )
= $false )
| ( ( SV262 @ ( sK133_SY1263 @ SV42 @ SV753 @ SV262 ) )
= $true )
| ( ( SV42 @ ( sK8_SY642 @ SV262 @ SV42 ) )
= $true )
| ( ( SV262 @ ( sK20_SY1103 @ SV42 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4236,plain,
! [SV773: $i,SV197: $i > $o,SV737: $i,SV396: $i > $o] :
( ( ( SV396 @ ( sK159_SY1299 @ SV737 @ SV197 @ SV773 @ SV396 ) )
= $true )
| ( ( SV396 @ SV773 )
= $false )
| ( ( ( descr
@ ^ [SY509: $i] : ( SV197 @ SY509 ) )
= ( descr
@ ^ [SY865: $i] : ( SV396 @ SY865 ) ) )
= $true )
| ( ( SV197 @ SV737 )
= $false )
| ( ( SV197 @ ( sK123_SY1245 @ SV396 @ SV737 @ SV197 ) )
= $true )
| ( ( SV197 @ ( sK17_SY858 @ SV396 @ SV197 ) )
= $true )
| ( ( SV396 @ ( sK27_SY1122 @ SV197 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4227]) ).
thf(4237,plain,
! [SV23: $i,SV733: $i,SV665: $i,SV779: $i] :
( ( ( in @ SV779 @ SV665 )
= $false )
| ( ( in @ SV779 @ ( sK112_SY1180 @ SV733 @ SV665 @ SV23 ) )
= $false )
| ( ( in @ ( sK78_SY1178 @ SV23 @ SV665 ) @ SV665 )
= $true )
| ( ( in @ SV733 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4238,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[500,4237,4236,4235,4234,4233,4231,4230,4229,4228,4226,4225,4224,4223,4222,4220,4216,4215,4214,4212,4211,4209,4206,4205,4204,4202,4200,4198,4190,4189,4187,4184,4179,4177,4165,4162,4160,4158,4143,4140,4137,4134,4132,4128,4125,4121,4120,4109,4106,4104,4100,4096,4092,4081,4080,4066,4062,4036,4027,4008,4007,4000,3999,3997,3988,3987,3969,3967,3959,3956,3954,3953,3944,3913,3912,3880,3877,3840,3836,3765,3737,3723,3722,3695,3694,3692,3691,3689,3688,3667,3660,3659,3658,3654,3652,3649,3647,3646,3645,3628,3622,3621,3620,3613,3611,3610,3604,3600,3597,3596,3595,3594,3577,3569,3568,3553,3551,3548,3547,3545,3541,3540,3538,3537,3517,3510,3509,3498,3494,3492,3486,3484,3483,3481,3480,3472,3451,3447,3442,3441,3439,3438,3429,3425,3423,3412,3408,3407,3401,3400,3376,3369,3367,3364,3362,3359,3348,3347,3346,3319,3318,3317,3316,3315,3314,3288,3281,3279,3268,3266,3263,3262,3257,3252,3247,3236,3233,3230,3225,3203,3201,3200,3172,3160,3159,3148,3147,3146,3145,3144,3143,3142,3139,3138,3137,3136,3133,3132,3131,3130,3127,3126,3123,3099,3094,3090,3077,3074,3073,3072,3044,3040,3035,3031,3028,3024,3021,3017,3014,3013,3012,3002,2997,2990,2988,2980,2961,2960,2958,2957,2955,2954,2950,2949,2945,2932,2931,2924,2923,2915,2914,2894,2893,2891,2890,2888,2887,2876,2875,2874,2873,2837,2834,2831,2828,2825,2820,2818,2805,2804,2795,2793,2791,2778,2768,2765,2762,2749,2747,2746,2738,2727,2718,2715,2714,2692,2691,2690,2689,2683,2676,2661,2660,2659,2658,2657,2639,2628,2627,2626,2618,2617,2616,2613,2606,2603,2602,2596,2563,2562,2561,2560,2559,2556,2555,2553,2552,2551,2548,2547,2544,2543,2542,2541,2540,2523,2522,2521,2520,2501,2498,2490,2488,2487,2485,2484,2482,2470,2456,2414,2413,2412,2411,2362,2359,2328,2327,2322,2321,2315,2313,2312,2308,2305,2304,2300,2299,2298,2296,2292,2291,2290,2289,2287,2286,2285,2284,2267,2262,2246,2244,2229,2220,2215,2214,2213,2209,2202,2199,2194,2193,2188,2187,2185,2183,2182,2176,2174,2165,2160,2156,2154,2149,2143,2128,2124,2117,2099,2085,2081,2065,2057,2048,2028,2026,2025,2016,2006,2005,2002,1999,1985,1970,1963,1958,1957,1941,1933,1922,1917,1896,1885,1878,1872,1862,1853,1827,1825,1814,1813,1807,1806,1798,1788,1787,1757,1756,1741,1730,1725,1720,1714,1706,1705,1700,1691,1658,1656,1641,1639,1636,1633,1627,1615,1614,1613,1610,1584,1576,1574,1573,1568,1564,1561,1557,1556,1555,1548,1547,1536,1533,1532,1524,1513,1487,1468,1463,1455,1442,1440,1431,1427,1405,1390,1380,1361,1360,1359,1355,1354,1353,1320,1310,1297,1263,1233,1224,1192,1190,1188,1171,1162,1154,1135,1117,1115,1109,1105,1099,1095,1094,1070,1064,1055,1010,1005,999,985,931,930,902,895,826,787,740,730,722,578,505,501]) ).
thf(4239,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU720^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n008.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 15:33:39 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.05/10.07 .
% 59.05/10.07
% 59.05/10.07 No.of.Axioms: 0
% 59.05/10.07
% 59.05/10.07 Length.of.Defs: 53330
% 59.05/10.07
% 59.05/10.07 Contains.Choice.Funs: true
% 59.05/10.07 .......................................................................................................................................................
% 59.05/10.07
% 59.05/10.07 ********************************
% 59.05/10.07 * All subproblems solved! *
% 59.05/10.07 ********************************
% 59.05/10.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:236,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4238,loop_count:0,foatp_calls:1,translation:fof_full)
% 59.05/10.07
% 59.05/10.07 %**** Beginning of derivation protocol ****
% 59.05/10.07 % SZS output start CNFRefutation
% See solution above
% 59.05/10.10
% 59.05/10.10 %**** End of derivation protocol ****
% 59.05/10.10 %**** no. of clauses in derivation: 4239 ****
% 59.05/10.10 %**** clause counter: 4238 ****
% 59.05/10.10
% 59.05/10.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:236,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4238,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------