%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU713^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10:46:34 AM UTC 2026
% Result : Theorem 71.03s 12.09s
% Output : CNFRefutation 71.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 234
% Syntax : Number of formulae : 3858 (1606 unt; 0 typ; 233 def)
% Number of atoms : 30708 (11826 equ; 0 cnn)
% Maximal formula atoms : 232 ( 7 avg)
% Number of connectives : 73790 (11319 ~;11416 |; 428 &;48713 @)
% ( 42 <=>;1872 =>; 0 <=; 0 <~>)
% Maximal formula depth : 239 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1939 (1939 >; 0 *; 0 +; 0 <<)
% Number of symbols : 362 ( 359 usr; 236 con; 0-4 aty)
% Number of variables : 14916 (1129 ^;13656 !; 131 ?;14916 :)
% 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_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_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_sK10_SY22,type,
sK10_SY22: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_SY1632,type,
sK11_SY1632: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_SY1650,type,
sK14_SY1650: $i > $i > $i > $i ).
thf(tp_sK15_SY1637,type,
sK15_SY1637: $i > $i > $i ).
thf(tp_sK16_SY1651,type,
sK16_SY1651: $i > $i > $i ).
thf(tp_sK17_Xx,type,
sK17_Xx: $i > $i > $i ).
thf(tp_sK18_SY55,type,
sK18_SY55: $i > ( $i > $o ) > $i ).
thf(tp_sK19_Xx,type,
sK19_Xx: ( $i > $o ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY72,type,
sK20_SY72: $i > ( $i > $o ) > $i ).
thf(tp_sK21_Xx,type,
sK21_Xx: ( $i > $o ) > $i ).
thf(tp_sK22_SY84,type,
sK22_SY84: $i > ( $i > $o ) > $i ).
thf(tp_sK23_Xx,type,
sK23_Xx: $i > $i > $i ).
thf(tp_sK24_Xx,type,
sK24_Xx: $i > $i > $i ).
thf(tp_sK25_Xx,type,
sK25_Xx: $i > $i ).
thf(tp_sK26_Xx,type,
sK26_Xx: $i > $i ).
thf(tp_sK27_Xx,type,
sK27_Xx: $i > $i ).
thf(tp_sK28_Xx,type,
sK28_Xx: $i > $i > $i ).
thf(tp_sK29_B,type,
sK29_B: $o > $i > $i > $i ).
thf(tp_sK2_SY1624,type,
sK2_SY1624: $i ).
thf(tp_sK30_Xx,type,
sK30_Xx: ( $i > $o ) > $i ).
thf(tp_sK31_SY140,type,
sK31_SY140: $i > ( $i > $o ) > $i ).
thf(tp_sK32_Xx,type,
sK32_Xx: $i > $i ).
thf(tp_sK33_Xx,type,
sK33_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK34_Xx,type,
sK34_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK35_Xx,type,
sK35_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK36_Xx,type,
sK36_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK37_Xx,type,
sK37_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK38_Xx,type,
sK38_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK39_SY196,type,
sK39_SY196: ( $i > $o ) > $i ).
thf(tp_sK3_SY1626,type,
sK3_SY1626: $i ).
thf(tp_sK40_Xy,type,
sK40_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK41_SY203,type,
sK41_SY203: ( $i > $o ) > $i ).
thf(tp_sK42_Xx,type,
sK42_Xx: ( $i > $o ) > $i ).
thf(tp_sK43_SY1663,type,
sK43_SY1663: ( $i > $o ) > $i ).
thf(tp_sK44_SY209,type,
sK44_SY209: ( $i > $o ) > $i ).
thf(tp_sK45_Xy,type,
sK45_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY222,type,
sK46_SY222: $i > ( $i > $o ) > $i ).
thf(tp_sK47_SY230,type,
sK47_SY230: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK48_SY234,type,
sK48_SY234: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK49_Xx,type,
sK49_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i > $i > $i ).
thf(tp_sK50_SY1666,type,
sK50_SY1666: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK51_SY233,type,
sK51_SY233: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK52_SY231,type,
sK52_SY231: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK53_Xx,type,
sK53_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK54_SY1668,type,
sK54_SY1668: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK55_SY246,type,
sK55_SY246: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY258,type,
sK56_SY258: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK57_SY255,type,
sK57_SY255: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK58_Xx,type,
sK58_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK59_SY1669,type,
sK59_SY1669: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i > $i ).
thf(tp_sK60_Xx,type,
sK60_Xx: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK61_SY1670,type,
sK61_SY1670: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK62_Xx,type,
sK62_Xx: $i > $i > $i ).
thf(tp_sK63_Xx,type,
sK63_Xx: $i > $i > $i ).
thf(tp_sK64_Xx,type,
sK64_Xx: $i > $i > $i ).
thf(tp_sK65_Xx,type,
sK65_Xx: $i > $i > $i > $i ).
thf(tp_sK66_SY1671,type,
sK66_SY1671: $i > $i > $i > $i ).
thf(tp_sK67_X,type,
sK67_X: $i > $i > $i ).
thf(tp_sK68_Xx,type,
sK68_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK69_SY1672,type,
sK69_SY1672: ( $i > $o ) > $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i > $i ).
thf(tp_sK70_Xx,type,
sK70_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK71_Xy,type,
sK71_Xy: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK72_Xx,type,
sK72_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK73_SY1673,type,
sK73_SY1673: ( $i > $o ) > $i > $i ).
thf(tp_sK74_Xx,type,
sK74_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK75_Xx,type,
sK75_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK76_Xx,type,
sK76_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK77_Xx,type,
sK77_Xx: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK78_SY1674,type,
sK78_SY1674: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK79_Xx,type,
sK79_Xx: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK7_Xx,type,
sK7_Xx: $i > $i ).
thf(tp_sK80_SY1675,type,
sK80_SY1675: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK81_Xx,type,
sK81_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK82_Xx,type,
sK82_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK83_SY1676,type,
sK83_SY1676: $i > $i > $i > $i > $i ).
thf(tp_sK84_Xx,type,
sK84_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK85_SY1677,type,
sK85_SY1677: $i > $i > $i > $i > $i ).
thf(tp_sK86_Xx,type,
sK86_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK87_SY1678,type,
sK87_SY1678: $i > $i > $i > $i > $i ).
thf(tp_sK88_Xx,type,
sK88_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK89_Xx,type,
sK89_Xx: $i > $i > $i > $i > $i ).
thf(tp_sK8_B,type,
sK8_B: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK90_Xx,type,
sK90_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK91_Xx,type,
sK91_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK92_Xx,type,
sK92_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK9_Xy,type,
sK9_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_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_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_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_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theeq,type,
theeq: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,definition,
( ap2apEq2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).
thf(beta1,definition,
( beta1
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1) ).
thf(beta2,definition,
( beta2
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta2) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(binunionT_lem,definition,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,definition,
( brelnall2
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairsurjEq,definition,
( cartprodpairsurjEq
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dpsetconstrEL1,definition,
( dpsetconstrEL1
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,definition,
( dpsetconstrEL2
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrERa,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,definition,
( dpsetconstrSub
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqbreln,definition,
( eqbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(eta1,definition,
( eta1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta1) ).
thf(eta2,definition,
( eta2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta2) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1E2,definition,
( ex1E2
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(funcGraphProp1,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcGraphProp3,definition,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp4,definition,
( funcGraphProp4
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,definition,
( funcext2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).
thf(funcextLem,definition,
( funcextLem
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcextLem) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).
thf(ifSingleton,definition,
( ifSingleton
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).
thf(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).
thf(iffalseProp1,definition,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,definition,
( iffalseProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp2) ).
thf(ifp,definition,
( ifp
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifp) ).
thf(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).
thf(iftrueProp1,definition,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,definition,
( iftrueProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp2) ).
thf(iftrueorfalse,definition,
( iftrueorfalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam2lamEq,definition,
( lam2lamEq
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2lamEq) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetT_lem,definition,
( powersetT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(subbreln,definition,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theeq,definition,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).
thf(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
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY98: $i] :
( ( SY98 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY98 ) )
=> ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ( in @ SY102 @ SY100 )
=> ( ( SY101 @ SY102 )
=> ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY104: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY104 )
=> ( SY104 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY137: $i > $o] :
( ? [SY139: $i] :
( ( SY137 @ SY139 )
& ! [SY140: $i] :
( ( SY137 @ SY140 )
=> ( SY139 = SY140 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY137 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY143: $i] :
( ( SY143 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY143 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY192: $i > $o] :
( ? [Xx: $i] :
( ( SY192 @ Xx )
& ! [Xy: $i] :
( ( SY192 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY196: $i] :
( ( SY192 @ SY196 )
& ! [SY197: $i] :
( ( SY192 @ SY197 )
=> ( SY196 = SY197 ) ) ) )
=> ( ! [SY198: $i > $o] :
( ? [Xx: $i] : ( SY198 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY198 @ Xx )
=> ( ( SY198 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY198 @ SY203 )
& ! [SY204: $i] :
( ( SY198 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) )
=> ( ! [SY205: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY205 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY209: $i] :
( ( SY205 @ SY209 )
& ! [SY210: $i] :
( ( SY205 @ SY210 )
=> ( SY209 = SY210 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY219: $i > $o] :
( ? [SY221: $i] :
( ( SY219 @ SY221 )
& ! [SY222: $i] :
( ( SY219 @ SY222 )
=> ( SY221 = SY222 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY219 @ Xx )
=> ( ( SY219 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY225: $i > $o,SY226: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY225 @ Xx )
<=> ( SY226 @ Xy ) ) )
=> ( ? [SY230: $i] :
( ( SY225 @ SY230 )
& ! [SY231: $i] :
( ( SY225 @ SY231 )
=> ( SY230 = SY231 ) ) )
<=> ? [SY233: $i] :
( ( SY226 @ SY233 )
& ! [SY234: $i] :
( ( SY226 @ SY234 )
=> ( SY233 = SY234 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY243: $i > $o] :
( ? [SY245: $i] :
( ( SY243 @ SY245 )
& ! [SY246: $i] :
( ( SY243 @ SY246 )
=> ( SY245 = SY246 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY243 @ Xx )
=> ( ( SY243 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY249: $i > $o,SY250: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY249 @ Xx )
<=> ( SY250 @ Xy ) ) )
=> ( ? [SY254: $i] :
( ( SY249 @ SY254 )
& ! [SY255: $i] :
( ( SY249 @ SY255 )
=> ( SY254 = SY255 ) ) )
=> ( ? [SY257: $i] :
( ( SY250 @ SY257 )
& ! [SY258: $i] :
( ( SY250 @ SY258 )
=> ( SY257 = SY258 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
=> ( ! [SY477: $i,SY478: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY477
@ ^ [SY482: $i] : ( SY478 @ SY482 ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY477 )
& ( SY478 @ Xx ) ) )
=> ( ! [SY484: $i,SY485: $i > $o,SY486: $i] :
( ( in @ SY486 @ SY484 )
=> ( ( SY485 @ SY486 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY484 )
=> ( ( SY485 @ Xy )
=> ( Xy = SY486 ) ) )
=> ( singleton
@ ( dsetconstr @ SY484
@ ^ [SY491: $i] : ( SY485 @ SY491 ) ) ) ) ) )
=> ( ! [SY492: $i,SY493: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY492 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY492 )
=> ( ( SY493 @ Xx )
=> ( ( SY493 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY492 )
& ( SY493 @ Xx ) )
=> ( singleton
@ ( dsetconstr @ SY492
@ ^ [SY500: $i] : ( SY493 @ SY500 ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) )
=> ( ! [SY584: $i,SY585: $i,SY586: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY584 @ SY585
@ ^ [Xx: $i,Xy: $i] : ( SY586 @ Xx @ Xy ) )
@ ( cartprod @ SY584 @ SY585 ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) )
=> ( ! [SY660: $i,SY661: $i,SY662: $i] :
( ( subset @ SY662 @ ( cartprod @ SY660 @ SY661 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY660 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY661 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY662 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY662 )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [SY670: $i,SY671: $i,SY672: $i] :
( ( subset @ SY672 @ ( cartprod @ SY670 @ SY671 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY670 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY671 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY672 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY672 )
=> ( Xphi @ Xx ) ) ) )
=> ( ! [SY680: $i,SY681: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY680
@ ^ [SY685: $i] : ( SY681 @ SY685 ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY680 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY680 )
=> ( ( SY681 @ Xx )
=> ( ( SY681 @ Xy )
=> ( Xx = Xy ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
=> ( ! [SY713: $i,SY714: $i,SY715: $i] :
( ( subset @ SY715 @ ( cartprod @ SY713 @ SY714 ) )
=> ! [SY719: $i] :
( ( subset @ SY719 @ ( cartprod @ SY713 @ SY714 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY713 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY714 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY715 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY719 ) ) ) )
=> ( subset @ SY715 @ SY719 ) ) ) )
=> ( ! [SY725: $i,SY726: $i,SY727: $i] :
( ( subset @ SY727 @ ( cartprod @ SY725 @ SY726 ) )
=> ! [SY731: $i] :
( ( subset @ SY731 @ ( cartprod @ SY725 @ SY726 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY725 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY726 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY727 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY731 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY725 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY726 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY731 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY727 ) ) ) )
=> ( SY727 = SY731 ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ! [SY22: $i] :
( ( in @ SY22 @ SY21 )
=> ? [SY24: $i] :
( ( SY20 @ SY22 @ SY24 )
& ! [SY25: $i] :
( ( SY20 @ SY22 @ SY25 )
=> ( SY24 = SY25 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY21 )
& ( SY20 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY52: $i > $o] :
( ? [SY54: $i] :
( ( SY52 @ SY54 )
& ! [SY55: $i] :
( ( SY52 @ SY55 )
=> ( SY54 = SY55 ) ) )
=> ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY69: $i > $o] :
( ? [SY71: $i] :
( ( SY69 @ SY71 )
& ! [SY72: $i] :
( ( SY69 @ SY72 )
=> ( SY71 = SY72 ) ) )
=> ? [Xx: $i] :
( ( SY69 @ Xx )
& ! [Xy: $i] :
( ( SY69 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY81: $i > $o] :
( ? [SY83: $i] :
( ( SY81 @ SY83 )
& ! [SY84: $i] :
( ( SY81 @ SY84 )
=> ( SY83 = SY84 ) ) )
=> ? [Xx: $i] : ( SY81 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY98: $i] :
( ( SY98 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY98 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ( in @ SY102 @ SY100 )
=> ( ( SY101 @ SY102 )
=> ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY104: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY104 )
=> ( SY104 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY137: $i > $o] :
( ? [SY139: $i] :
( ( SY137 @ SY139 )
& ! [SY140: $i] :
( ( SY137 @ SY140 )
=> ( SY139 = SY140 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY137 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY143: $i] :
( ( SY143 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY143 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY192: $i > $o] :
( ? [Xx: $i] :
( ( SY192 @ Xx )
& ! [Xy: $i] :
( ( SY192 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY196: $i] :
( ( SY192 @ SY196 )
& ! [SY197: $i] :
( ( SY192 @ SY197 )
=> ( SY196 = SY197 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY198: $i > $o] :
( ? [Xx: $i] : ( SY198 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY198 @ Xx )
=> ( ( SY198 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY198 @ SY203 )
& ! [SY204: $i] :
( ( SY198 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY205: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY205 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY209: $i] :
( ( SY205 @ SY209 )
& ! [SY210: $i] :
( ( SY205 @ SY210 )
=> ( SY209 = SY210 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY219: $i > $o] :
( ? [SY221: $i] :
( ( SY219 @ SY221 )
& ! [SY222: $i] :
( ( SY219 @ SY222 )
=> ( SY221 = SY222 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY219 @ Xx )
=> ( ( SY219 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY225: $i > $o,SY226: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY225 @ Xx )
<=> ( SY226 @ Xy ) ) )
=> ( ? [SY230: $i] :
( ( SY225 @ SY230 )
& ! [SY231: $i] :
( ( SY225 @ SY231 )
=> ( SY230 = SY231 ) ) )
<=> ? [SY233: $i] :
( ( SY226 @ SY233 )
& ! [SY234: $i] :
( ( SY226 @ SY234 )
=> ( SY233 = SY234 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY243: $i > $o] :
( ? [SY245: $i] :
( ( SY243 @ SY245 )
& ! [SY246: $i] :
( ( SY243 @ SY246 )
=> ( SY245 = SY246 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY243 @ Xx )
=> ( ( SY243 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY249: $i > $o,SY250: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY249 @ Xx )
<=> ( SY250 @ Xy ) ) )
=> ( ? [SY254: $i] :
( ( SY249 @ SY254 )
& ! [SY255: $i] :
( ( SY249 @ SY255 )
=> ( SY254 = SY255 ) ) )
=> ( ? [SY257: $i] :
( ( SY250 @ SY257 )
& ! [SY258: $i] :
( ( SY250 @ SY258 )
=> ( SY257 = SY258 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [SY477: $i,SY478: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY477
@ ^ [SY482: $i] : ( SY478 @ SY482 ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY477 )
& ( SY478 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY484: $i,SY485: $i > $o,SY486: $i] :
( ( in @ SY486 @ SY484 )
=> ( ( SY485 @ SY486 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY484 )
=> ( ( SY485 @ Xy )
=> ( Xy = SY486 ) ) )
=> ( singleton
@ ( dsetconstr @ SY484
@ ^ [SY491: $i] : ( SY485 @ SY491 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY492: $i,SY493: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY492 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY492 )
=> ( ( SY493 @ Xx )
=> ( ( SY493 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY492 )
& ( SY493 @ Xx ) )
=> ( singleton
@ ( dsetconstr @ SY492
@ ^ [SY500: $i] : ( SY493 @ SY500 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(161,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(162,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(163,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(165,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(167,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(168,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(169,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(170,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(171,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(172,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(173,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(174,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(175,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(176,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(177,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(179,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(180,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(183,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(184,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(185,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(187,plain,
( ( ! [SY584: $i,SY585: $i,SY586: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY584 @ SY585
@ ^ [Xx: $i,Xy: $i] : ( SY586 @ Xx @ Xy ) )
@ ( cartprod @ SY584 @ SY585 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(188,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(189,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(190,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(191,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(192,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(197,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(199,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(200,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(201,plain,
( ( ! [SY660: $i,SY661: $i,SY662: $i] :
( ( subset @ SY662 @ ( cartprod @ SY660 @ SY661 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY660 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY661 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY662 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY662 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(202,plain,
( ( ! [SY670: $i,SY671: $i,SY672: $i] :
( ( subset @ SY672 @ ( cartprod @ SY670 @ SY671 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY670 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY671 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY672 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY672 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(203,plain,
( ( ! [SY680: $i,SY681: $i > $o] :
( ( singleton
@ ( dsetconstr @ SY680
@ ^ [SY685: $i] : ( SY681 @ SY685 ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY680 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY680 )
=> ( ( SY681 @ Xx )
=> ( ( SY681 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(204,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(205,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(206,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(207,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(209,plain,
( ( ! [SY713: $i,SY714: $i,SY715: $i] :
( ( subset @ SY715 @ ( cartprod @ SY713 @ SY714 ) )
=> ! [SY719: $i] :
( ( subset @ SY719 @ ( cartprod @ SY713 @ SY714 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY713 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY714 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY715 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY719 ) ) ) )
=> ( subset @ SY715 @ SY719 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(210,plain,
( ( ! [SY725: $i,SY726: $i,SY727: $i] :
( ( subset @ SY727 @ ( cartprod @ SY725 @ SY726 ) )
=> ! [SY731: $i] :
( ( subset @ SY731 @ ( cartprod @ SY725 @ SY726 ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY725 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY726 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY727 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY731 ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ SY725 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY726 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY731 )
=> ( in @ ( kpair @ Xx @ Xy ) @ SY727 ) ) ) )
=> ( SY727 = SY731 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(211,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(212,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(213,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(214,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(216,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(217,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(220,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(221,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(222,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(223,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(224,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(225,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(226,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(227,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(228,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(229,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(230,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(231,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(232,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(233,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(234,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[233]) ).
thf(235,plain,
( ( ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[234]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK4_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK4_Xx @ B @ A ) @ A )
| ( in @ ( sK4_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(237,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK5_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK5_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(239,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK6_B @ Xx @ A ) )
& ( in @ ( sK6_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(240,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(241,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK7_Xx @ A ) @ omega )
& ( in @ ( sK7_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK7_Xx @ A ) @ ( sK7_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(242,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ( ( in @ ( sK10_SY22 @ SY21 @ SY20 ) @ SY21 )
& ! [SY1631: $i] :
( ( ( SY20 @ ( sK10_SY22 @ SY21 @ SY20 ) @ ( sK11_SY1632 @ SY1631 @ SY21 @ SY20 ) )
& ( SY1631
!= ( sK11_SY1632 @ SY1631 @ SY21 @ SY20 ) ) )
| ~ ( SY20 @ ( sK10_SY22 @ SY21 @ SY20 ) @ SY1631 ) ) )
| ( ! [SY1627: $i] :
( ! [Xy: $i] :
( ~ ( SY20 @ Xy @ SY1627 )
| ~ ( in @ Xy @ SY21 ) )
| ( in @ SY1627 @ ( sK8_B @ SY21 @ SY20 ) ) )
& ! [SY1629: $i] :
( ~ ( in @ SY1629 @ ( sK8_B @ SY21 @ SY20 ) )
| ( ( SY20 @ ( sK9_Xy @ SY1629 @ SY21 @ SY20 ) @ SY1629 )
& ( in @ ( sK9_Xy @ SY1629 @ SY21 @ SY20 ) @ SY21 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(243,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK12_B @ A ) @ A )
& ! [SY1633: $i] :
( ~ ( in @ SY1633 @ ( sK12_B @ A ) )
| ~ ( in @ SY1633 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(244,plain,
( ( ! [A: $i] :
( ! [SY1634: $i] :
( ( ( in @ ( sK17_Xx @ SY1634 @ A ) @ SY1634 )
& ~ ( in @ ( sK17_Xx @ SY1634 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1634 )
| ( ! [SY1655: $i] :
( ~ ( in @ SY1655 @ ( sK13_B @ A ) )
| ! [SY1653: $i] :
( ~ ( in @ SY1653 @ SY1655 )
| ( in @ SY1653 @ ( sK15_SY1637 @ SY1634 @ A ) ) )
| ( in @ ( sK16_SY1651 @ SY1634 @ A ) @ SY1655 ) )
& ( in @ ( sK15_SY1637 @ SY1634 @ A ) @ ( sK13_B @ A ) )
& ( in @ ( sK16_SY1651 @ SY1634 @ A ) @ SY1634 )
& ! [SY1654: $i] :
( ~ ( in @ SY1654 @ ( sK15_SY1637 @ SY1634 @ A ) )
| ~ ( in @ SY1654 @ SY1634 ) ) ) )
& ! [SY1642: $i,SY1643: $i] :
( ~ ( in @ SY1642 @ ( sK13_B @ A ) )
| ~ ( in @ SY1643 @ ( sK13_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1642 )
| ( in @ Xx @ SY1643 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1643 )
| ( in @ Xx @ SY1642 ) ) )
& ! [SY1646: $i] :
( ~ ( in @ SY1646 @ ( sK13_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1646 )
| ( in @ Xx @ A ) ) )
& ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ SY1648 @ A )
| ~ ( in @ SY1649 @ A )
| ( ( in @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) @ ( sK13_B @ A ) )
& ( ~ ( in @ SY1648 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) )
| ~ ( in @ SY1649 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) ) )
& ( ( in @ SY1648 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) )
| ( in @ SY1649 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) ) ) )
| ( SY1648 = SY1649 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(245,plain,
( ( ! [SY52: $i > $o] :
( ! [SY54: $i] :
( ( ( SY52 @ ( sK18_SY55 @ SY54 @ SY52 ) )
& ( SY54
!= ( sK18_SY55 @ SY54 @ SY52 ) ) )
| ~ ( SY52 @ SY54 ) )
| ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(246,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(247,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(248,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(249,plain,
( ( ! [SY69: $i > $o] :
( ! [SY71: $i] :
( ( ( SY69 @ ( sK20_SY72 @ SY71 @ SY69 ) )
& ( SY71
!= ( sK20_SY72 @ SY71 @ SY69 ) ) )
| ~ ( SY69 @ SY71 ) )
| ( ! [SY1658: $i] :
( ~ ( SY69 @ SY1658 )
| ( ( sK19_Xx @ SY69 )
= SY1658 ) )
& ( SY69 @ ( sK19_Xx @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(250,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(251,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(252,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(253,plain,
( ( ! [SY81: $i > $o] :
( ! [SY83: $i] :
( ( ( SY81 @ ( sK22_SY84 @ SY83 @ SY81 ) )
& ( SY83
!= ( sK22_SY84 @ SY83 @ SY81 ) ) )
| ~ ( SY81 @ SY83 ) )
| ( SY81 @ ( sK21_Xx @ SY81 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK24_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK24_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK23_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK23_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( in @ ( sK25_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(256,plain,
( ( ! [A: $i] :
( ( in @ ( sK26_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(257,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(258,plain,
( ( ! [SY98: $i] :
( ( SY98 = emptyset )
| ( in @ ( sK27_Xx @ SY98 ) @ SY98 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(259,plain,
( ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ~ ( in @ SY102 @ SY100 )
| ~ ( SY101 @ SY102 )
| ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(260,plain,
( ( ! [SY104: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY104 )
| ( SY104 != emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(261,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(262,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(263,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK28_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK28_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(266,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(267,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK29_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK29_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(268,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(269,plain,
( ( ! [SY137: $i > $o] :
( ! [SY139: $i] :
( ( ( SY137 @ ( sK31_SY140 @ SY139 @ SY137 ) )
& ( SY139
!= ( sK31_SY140 @ SY139 @ SY137 ) ) )
| ~ ( SY137 @ SY139 ) )
| ( ! [SY1659: $i] :
( ( SY1659
!= ( sK30_Xx @ SY137 ) )
| ( SY137 @ SY1659 ) )
& ! [SY1660: $i] :
( ~ ( SY137 @ SY1660 )
| ( SY1660
= ( sK30_Xx @ SY137 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(270,plain,
( ( ! [SY143: $i] :
( ( SY143 = emptyset )
| ( in @ ( sK32_Xx @ SY143 ) @ SY143 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(271,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(272,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(273,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(274,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(275,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(276,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(277,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(278,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK33_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK33_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(279,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK34_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK34_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(280,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK35_Xx @ Xphi @ A ) )
& ( in @ ( sK35_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(281,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(282,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(283,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(284,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK37_Xx @ Xphi @ A ) )
& ( in @ ( sK37_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(285,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK38_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK38_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(286,plain,
( ( ! [SY192: $i > $o] :
( ! [Xx: $i] :
( ( ( SY192 @ ( sK40_Xy @ Xx @ SY192 ) )
& ( Xx
!= ( sK40_Xy @ Xx @ SY192 ) ) )
| ~ ( SY192 @ Xx ) )
| ( ! [SY1661: $i] :
( ~ ( SY192 @ SY1661 )
| ( ( sK39_SY196 @ SY192 )
= SY1661 ) )
& ( SY192 @ ( sK39_SY196 @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(287,plain,
( ( ! [SY198: $i > $o] :
( ! [Xx: $i] :
~ ( SY198 @ Xx )
| ( ( SY198 @ ( sK42_Xx @ SY198 ) )
& ( SY198 @ ( sK43_SY1663 @ SY198 ) )
& ( ( sK42_Xx @ SY198 )
!= ( sK43_SY1663 @ SY198 ) ) )
| ( ! [SY1662: $i] :
( ~ ( SY198 @ SY1662 )
| ( ( sK41_SY203 @ SY198 )
= SY1662 ) )
& ( SY198 @ ( sK41_SY203 @ SY198 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(288,plain,
( ( ! [SY205: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK45_Xy @ Xx @ SY205 )
!= Xx )
| ~ ( SY205 @ ( sK45_Xy @ Xx @ SY205 ) ) )
& ( ( ( sK45_Xy @ Xx @ SY205 )
= Xx )
| ( SY205 @ ( sK45_Xy @ Xx @ SY205 ) ) ) )
| ( ! [SY1664: $i] :
( ~ ( SY205 @ SY1664 )
| ( ( sK44_SY209 @ SY205 )
= SY1664 ) )
& ( SY205 @ ( sK44_SY209 @ SY205 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(291,plain,
( ( ! [SY219: $i > $o] :
( ! [SY221: $i] :
( ( ( SY219 @ ( sK46_SY222 @ SY221 @ SY219 ) )
& ( SY221
!= ( sK46_SY222 @ SY221 @ SY219 ) ) )
| ~ ( SY219 @ SY221 ) )
| ! [Xx: $i] :
( ~ ( SY219 @ Xx )
| ! [Xy: $i] :
( ~ ( SY219 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(292,plain,
( ( ! [SY225: $i > $o,SY226: $i > $o] :
( ( ( ( sK53_Xx @ SY226 @ SY225 )
= ( sK54_SY1668 @ SY226 @ SY225 ) )
& ( ~ ( SY225 @ ( sK53_Xx @ SY226 @ SY225 ) )
| ~ ( SY226 @ ( sK54_SY1668 @ SY226 @ SY225 ) ) )
& ( ( SY225 @ ( sK53_Xx @ SY226 @ SY225 ) )
| ( SY226 @ ( sK54_SY1668 @ SY226 @ SY225 ) ) ) )
| ! [SY230: $i] :
( ( ( SY225 @ ( sK52_SY231 @ SY230 @ SY226 @ SY225 ) )
& ( SY230
!= ( sK52_SY231 @ SY230 @ SY226 @ SY225 ) ) )
| ~ ( SY225 @ SY230 ) )
| ( ! [SY1667: $i] :
( ~ ( SY226 @ SY1667 )
| ( ( sK51_SY233 @ SY226 @ SY225 )
= SY1667 ) )
& ( SY226 @ ( sK51_SY233 @ SY226 @ SY225 ) ) ) )
& ! [SY225: $i > $o,SY226: $i > $o] :
( ( ( ( sK49_Xx @ SY226 @ SY225 )
= ( sK50_SY1666 @ SY226 @ SY225 ) )
& ( ~ ( SY225 @ ( sK49_Xx @ SY226 @ SY225 ) )
| ~ ( SY226 @ ( sK50_SY1666 @ SY226 @ SY225 ) ) )
& ( ( SY225 @ ( sK49_Xx @ SY226 @ SY225 ) )
| ( SY226 @ ( sK50_SY1666 @ SY226 @ SY225 ) ) ) )
| ! [SY233: $i] :
( ( ( SY226 @ ( sK48_SY234 @ SY233 @ SY226 @ SY225 ) )
& ( SY233
!= ( sK48_SY234 @ SY233 @ SY226 @ SY225 ) ) )
| ~ ( SY226 @ SY233 ) )
| ( ! [SY1665: $i] :
( ~ ( SY225 @ SY1665 )
| ( ( sK47_SY230 @ SY226 @ SY225 )
= SY1665 ) )
& ( SY225 @ ( sK47_SY230 @ SY226 @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(293,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[71]) ).
thf(294,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ! [Xz: $i,Xu: $i] :
( ( Xz != Xu )
| ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(297,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[75]) ).
thf(298,plain,
( ( ! [SY243: $i > $o] :
( ! [SY245: $i] :
( ( ( SY243 @ ( sK55_SY246 @ SY245 @ SY243 ) )
& ( SY245
!= ( sK55_SY246 @ SY245 @ SY243 ) ) )
| ~ ( SY243 @ SY245 ) )
| ! [Xx: $i] :
( ~ ( SY243 @ Xx )
| ! [Xy: $i] :
( ~ ( SY243 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(299,plain,
( ( ! [SY249: $i > $o,SY250: $i > $o] :
( ( ( ( sK58_Xx @ SY250 @ SY249 )
= ( sK59_SY1669 @ SY250 @ SY249 ) )
& ( ~ ( SY249 @ ( sK58_Xx @ SY250 @ SY249 ) )
| ~ ( SY250 @ ( sK59_SY1669 @ SY250 @ SY249 ) ) )
& ( ( SY249 @ ( sK58_Xx @ SY250 @ SY249 ) )
| ( SY250 @ ( sK59_SY1669 @ SY250 @ SY249 ) ) ) )
| ! [SY254: $i] :
( ( ( SY249 @ ( sK57_SY255 @ SY254 @ SY250 @ SY249 ) )
& ( SY254
!= ( sK57_SY255 @ SY254 @ SY250 @ SY249 ) ) )
| ~ ( SY249 @ SY254 ) )
| ! [SY257: $i] :
( ( ( SY250 @ ( sK56_SY258 @ SY257 @ SY250 @ SY249 ) )
& ( SY257
!= ( sK56_SY258 @ SY257 @ SY250 @ SY249 ) ) )
| ~ ( SY250 @ SY257 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK60_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK62_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK62_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK63_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK63_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(305,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(307,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(309,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(311,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(314,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(318,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(321,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(322,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(323,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(324,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(325,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(327,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(328,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(329,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(331,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(332,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(333,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(336,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(337,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(338,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(340,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(341,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(342,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(343,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(345,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(346,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(347,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(348,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(349,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(350,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(351,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(352,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(353,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(354,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(355,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK65_Xx @ Xu @ B @ A ) @ ( sK66_SY1671 @ Xu @ B @ A ) ) )
& ( in @ ( sK66_SY1671 @ Xu @ B @ A ) @ B )
& ( in @ ( sK65_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(356,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( iskpair @ Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(357,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK67_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK67_X @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(358,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK68_Xx @ Xphi @ A ) @ A )
& ( in @ ( sK69_SY1672 @ Xphi @ A ) @ A )
& ( Xphi @ ( sK68_Xx @ Xphi @ A ) )
& ( Xphi @ ( sK69_SY1672 @ Xphi @ A ) )
& ( ( sK68_Xx @ Xphi @ A )
!= ( sK69_SY1672 @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(359,plain,
( ( ! [SY477: $i,SY478: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SY477
@ ^ [SY482: $i] : ( SY478 @ SY482 ) ) )
| ( ( SY478 @ ( sK70_Xx @ SY478 @ SY477 ) )
& ( in @ ( sK70_Xx @ SY478 @ SY477 ) @ SY477 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(360,plain,
( ( ! [SY484: $i,SY485: $i > $o,SY486: $i] :
( ~ ( in @ SY486 @ SY484 )
| ~ ( SY485 @ SY486 )
| ( ( in @ ( sK71_Xy @ SY486 @ SY485 @ SY484 ) @ SY484 )
& ( SY485 @ ( sK71_Xy @ SY486 @ SY485 @ SY484 ) )
& ( ( sK71_Xy @ SY486 @ SY485 @ SY484 )
!= SY486 ) )
| ( singleton
@ ( dsetconstr @ SY484
@ ^ [SY491: $i] : ( SY485 @ SY491 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(361,plain,
( ( ! [SY492: $i,SY493: $i > $o] :
( ( ( in @ ( sK72_Xx @ SY493 @ SY492 ) @ SY492 )
& ( in @ ( sK73_SY1673 @ SY493 @ SY492 ) @ SY492 )
& ( SY493 @ ( sK72_Xx @ SY493 @ SY492 ) )
& ( SY493 @ ( sK73_SY1673 @ SY493 @ SY492 ) )
& ( ( sK72_Xx @ SY493 @ SY492 )
!= ( sK73_SY1673 @ SY493 @ SY492 ) ) )
| ! [Xx: $i] :
( ~ ( SY493 @ Xx )
| ~ ( in @ Xx @ SY492 ) )
| ( singleton
@ ( dsetconstr @ SY492
@ ^ [SY500: $i] : ( SY493 @ SY500 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(362,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(363,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(364,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(365,plain,
( ( ! [X: $i] :
( ~ ( singleton @ X )
| ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(366,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(367,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(368,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(369,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(370,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(371,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xz != Xu )
| ( Xy = Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(372,plain,
( ( ! [Xx: $i,Xy: $i] :
( ! [Xz: $i] :
( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
!= ( setadjoin @ Xz @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(373,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xy = Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(374,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xy = Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(375,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(376,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(377,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(378,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ! [Xy: $i] :
~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(379,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xy @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(380,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(381,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(382,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(383,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(384,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( Xphi @ Xx @ Xy )
| ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(385,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(386,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ! [Xy: $i] :
~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(387,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( in @ Xy @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(388,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( Xphi @ Xx @ Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(389,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(390,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(391,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(392,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ( func @ A @ B @ Xf ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(393,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(394,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(395,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK74_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK74_Xx @ Xf @ B @ A ) ) @ B ) )
| ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(396,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK75_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK75_Xx @ Xf @ B @ A ) ) @ B ) )
| ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(397,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK76_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK76_Xx @ Xf @ B @ A ) ) @ B ) )
| ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(398,plain,
( ( ! [SY660: $i,SY661: $i,SY662: $i] :
( ~ ( subset @ SY662 @ ( cartprod @ SY660 @ SY661 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ SY660 )
& ( in @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) @ SY661 )
& ( in @ ( kpair @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) ) @ SY662 )
& ~ ( Xphi @ ( kpair @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY662 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(399,plain,
( ( ! [SY670: $i,SY671: $i,SY672: $i] :
( ~ ( subset @ SY672 @ ( cartprod @ SY670 @ SY671 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ SY670 )
& ( in @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) @ SY671 )
& ( in @ ( kpair @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) ) @ SY672 )
& ~ ( Xphi @ ( kpair @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY672 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[202]) ).
thf(400,plain,
( ( ! [SY680: $i,SY681: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SY680
@ ^ [SY685: $i] : ( SY681 @ SY685 ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY680 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY680 )
| ~ ( SY681 @ Xx )
| ~ ( SY681 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(401,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[204]) ).
thf(402,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(403,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xf )
| ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(404,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xg: $i] :
( ~ ( func @ A @ B @ Xg )
| ( ( in @ ( sK81_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK81_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK81_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xg )
| ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[207]) ).
thf(405,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xf )
| ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(406,plain,
( ( ! [SY713: $i,SY714: $i,SY715: $i] :
( ~ ( subset @ SY715 @ ( cartprod @ SY713 @ SY714 ) )
| ! [SY719: $i] :
( ~ ( subset @ SY719 @ ( cartprod @ SY713 @ SY714 ) )
| ( ( in @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ SY713 )
& ( in @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) @ SY714 )
& ( in @ ( kpair @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) ) @ SY715 )
& ~ ( in @ ( kpair @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) ) @ SY719 ) )
| ( subset @ SY715 @ SY719 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[209]) ).
thf(407,plain,
( ( ! [SY725: $i,SY726: $i,SY727: $i] :
( ~ ( subset @ SY727 @ ( cartprod @ SY725 @ SY726 ) )
| ! [SY731: $i] :
( ~ ( subset @ SY731 @ ( cartprod @ SY725 @ SY726 ) )
| ( ( in @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY725 )
& ( in @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY726 )
& ( in @ ( kpair @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY727 )
& ~ ( in @ ( kpair @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY731 ) )
| ( ( in @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY725 )
& ( in @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY726 )
& ( in @ ( kpair @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY731 )
& ~ ( in @ ( kpair @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY727 ) )
| ( SY727 = SY731 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[210]) ).
thf(408,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xg: $i] :
( ~ ( func @ A @ B @ Xg )
| ( ( in @ ( sK88_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK88_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK88_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ( Xf = Xg ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(409,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xg: $i] :
( ~ ( in @ Xg @ ( funcSet @ A @ B ) )
| ( ( in @ ( sK89_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK89_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK89_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ( Xf = Xg ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(410,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i] :
~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
~ ( in @ Xx @ A )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(411,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i] :
~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
~ ( in @ Xx @ A )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[214]) ).
thf(412,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK90_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK90_Xx @ Xf @ B @ A ) ) @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[215]) ).
thf(413,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(414,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i > $i] :
( ( in @ ( sK91_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK91_Xx @ Xf @ B @ A ) ) @ B ) )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[217]) ).
thf(415,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK92_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK92_Xx @ Xf @ B @ A ) ) @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[218]) ).
thf(416,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[219]) ).
thf(417,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[220]) ).
thf(418,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[221]) ).
thf(419,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[222]) ).
thf(420,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[223]) ).
thf(421,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[224]) ).
thf(422,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(423,plain,
( ( ! [X: $i] :
( ~ ( singleton @ X )
| ! [Xx: $i] :
( ~ ( in @ Xx @ X )
| ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(424,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[227]) ).
thf(425,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(426,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[229]) ).
thf(427,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[230]) ).
thf(428,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[231]) ).
thf(429,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[232]) ).
thf(430,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(431,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(432,plain,
( ( ! [A: $i,X: $i] :
( ~ ( in @ X @ ( powerset @ A ) )
| ! [Y: $i] :
( ~ ( in @ Y @ ( powerset @ A ) )
| ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(433,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(434,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(435,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(436,plain,
( ( ! [X: $i] :
( ~ ( singleton @ X )
| ! [Xx: $i] :
( ~ ( in @ Xx @ X )
| ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(437,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(438,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(439,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(440,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| ~ Xphi
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(441,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(442,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ A )
| Xphi
| ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(444,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK92_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK92_Xx @ Xf @ B @ A ) ) @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(445,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i > $i] :
( ( in @ ( sK91_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK91_Xx @ Xf @ B @ A ) ) @ B ) )
| $true ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(446,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(447,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK90_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK90_Xx @ Xf @ B @ A ) ) @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(448,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i] :
~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
~ ( in @ Xx @ A )
| $true ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(449,plain,
( ( ! [A: $i] :
( ! [B: $i,Xf: $i] :
~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
~ ( in @ Xx @ A )
| $true ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(450,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xg: $i] :
( ~ ( in @ Xg @ ( funcSet @ A @ B ) )
| ( ( in @ ( sK89_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK89_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK89_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ( Xf = Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(451,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xg: $i] :
( ~ ( func @ A @ B @ Xg )
| ( ( in @ ( sK88_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK88_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK88_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ( Xf = Xg ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(452,plain,
( ( ! [SY725: $i,SY726: $i,SY727: $i] :
( ~ ( subset @ SY727 @ ( cartprod @ SY725 @ SY726 ) )
| ! [SY731: $i] :
( ~ ( subset @ SY731 @ ( cartprod @ SY725 @ SY726 ) )
| ( ( in @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY725 )
& ( in @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY726 )
& ( in @ ( kpair @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY727 )
& ~ ( in @ ( kpair @ ( sK86_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK87_SY1678 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY731 ) )
| ( ( in @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY725 )
& ( in @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) @ SY726 )
& ( in @ ( kpair @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY731 )
& ~ ( in @ ( kpair @ ( sK84_Xx @ SY731 @ SY727 @ SY726 @ SY725 ) @ ( sK85_SY1677 @ SY731 @ SY727 @ SY726 @ SY725 ) ) @ SY727 ) )
| ( SY727 = SY731 ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(453,plain,
( ( ! [SY713: $i,SY714: $i,SY715: $i] :
( ~ ( subset @ SY715 @ ( cartprod @ SY713 @ SY714 ) )
| ! [SY719: $i] :
( ~ ( subset @ SY719 @ ( cartprod @ SY713 @ SY714 ) )
| ( ( in @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ SY713 )
& ( in @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) @ SY714 )
& ( in @ ( kpair @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) ) @ SY715 )
& ~ ( in @ ( kpair @ ( sK82_Xx @ SY719 @ SY715 @ SY714 @ SY713 ) @ ( sK83_SY1676 @ SY719 @ SY715 @ SY714 @ SY713 ) ) @ SY719 ) )
| ( subset @ SY715 @ SY719 ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(454,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xf )
| ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(455,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xg: $i] :
( ~ ( func @ A @ B @ Xg )
| ( ( in @ ( sK81_Xx @ Xg @ Xf @ B @ A ) @ A )
& ( ( ap @ A @ B @ Xf @ ( sK81_Xx @ Xg @ Xf @ B @ A ) )
!= ( ap @ A @ B @ Xg @ ( sK81_Xx @ Xg @ Xf @ B @ A ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xg )
| ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(456,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy ) @ Xf )
| ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(457,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(459,plain,
( ( ! [SY680: $i,SY681: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SY680
@ ^ [SY685: $i] : ( SY681 @ SY685 ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY680 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY680 )
| ~ ( SY681 @ Xx )
| ~ ( SY681 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(460,plain,
( ( ! [SY670: $i,SY671: $i,SY672: $i] :
( ~ ( subset @ SY672 @ ( cartprod @ SY670 @ SY671 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ SY670 )
& ( in @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) @ SY671 )
& ( in @ ( kpair @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) ) @ SY672 )
& ~ ( Xphi @ ( kpair @ ( sK79_Xx @ Xphi @ SY672 @ SY671 @ SY670 ) @ ( sK80_SY1675 @ Xphi @ SY672 @ SY671 @ SY670 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY672 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(461,plain,
( ( ! [SY660: $i,SY661: $i,SY662: $i] :
( ~ ( subset @ SY662 @ ( cartprod @ SY660 @ SY661 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ SY660 )
& ( in @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) @ SY661 )
& ( in @ ( kpair @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) ) @ SY662 )
& ~ ( Xphi @ ( kpair @ ( sK77_Xx @ Xphi @ SY662 @ SY661 @ SY660 ) @ ( sK78_SY1674 @ Xphi @ SY662 @ SY661 @ SY660 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY662 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(462,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK76_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK76_Xx @ Xf @ B @ A ) ) @ B ) )
| ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(463,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK75_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK75_Xx @ Xf @ B @ A ) ) @ B ) )
| ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(464,plain,
( ( ! [A: $i,B: $i,Xf: $i > $i] :
( ( ( in @ ( sK74_Xx @ Xf @ B @ A ) @ A )
& ~ ( in @ ( Xf @ ( sK74_Xx @ Xf @ B @ A ) ) @ B ) )
| ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(465,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(466,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(467,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
| ( func @ A @ B @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(468,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(469,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(470,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ~ ( func @ A @ B @ Xf )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(471,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( Xphi @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(472,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(473,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ! [Xy: $i] :
~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(474,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
| ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(475,plain,
( ( ! [SY584: $i,SY585: $i,SY586: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY584 @ SY585
@ ^ [Xx: $i,Xy: $i] : ( SY586 @ Xx @ Xy ) )
@ ( cartprod @ SY584 @ SY585 ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(476,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(477,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ~ ( Xphi @ Xx @ Xy )
| ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(478,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(479,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(480,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(481,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(482,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(483,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ! [Xy: $i] :
~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(484,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(485,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(486,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(487,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(488,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(489,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(490,plain,
( ( ! [Xx: $i,Xy: $i] :
( ! [Xz: $i] :
( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
!= ( setadjoin @ Xz @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(491,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xz != Xu )
| ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(492,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(493,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(494,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(495,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(496,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(497,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(498,plain,
( ( ! [X: $i] :
( ~ ( singleton @ X )
| ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(499,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(500,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(501,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(502,plain,
( ( ! [SY492: $i,SY493: $i > $o] :
( ( ( in @ ( sK72_Xx @ SY493 @ SY492 ) @ SY492 )
& ( in @ ( sK73_SY1673 @ SY493 @ SY492 ) @ SY492 )
& ( SY493 @ ( sK72_Xx @ SY493 @ SY492 ) )
& ( SY493 @ ( sK73_SY1673 @ SY493 @ SY492 ) )
& ( ( sK72_Xx @ SY493 @ SY492 )
!= ( sK73_SY1673 @ SY493 @ SY492 ) ) )
| ! [Xx: $i] :
( ~ ( SY493 @ Xx )
| ~ ( in @ Xx @ SY492 ) )
| ( singleton
@ ( dsetconstr @ SY492
@ ^ [SY500: $i] : ( SY493 @ SY500 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(503,plain,
( ( ! [SY484: $i,SY485: $i > $o,SY486: $i] :
( ~ ( in @ SY486 @ SY484 )
| ~ ( SY485 @ SY486 )
| ( ( in @ ( sK71_Xy @ SY486 @ SY485 @ SY484 ) @ SY484 )
& ( SY485 @ ( sK71_Xy @ SY486 @ SY485 @ SY484 ) )
& ( ( sK71_Xy @ SY486 @ SY485 @ SY484 )
!= SY486 ) )
| ( singleton
@ ( dsetconstr @ SY484
@ ^ [SY491: $i] : ( SY485 @ SY491 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(504,plain,
( ( ! [SY477: $i,SY478: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SY477
@ ^ [SY482: $i] : ( SY478 @ SY482 ) ) )
| ( ( SY478 @ ( sK70_Xx @ SY478 @ SY477 ) )
& ( in @ ( sK70_Xx @ SY478 @ SY477 ) @ SY477 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(505,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK68_Xx @ Xphi @ A ) @ A )
& ( in @ ( sK69_SY1672 @ Xphi @ A ) @ A )
& ( Xphi @ ( sK68_Xx @ Xphi @ A ) )
& ( Xphi @ ( sK69_SY1672 @ Xphi @ A ) )
& ( ( sK68_Xx @ Xphi @ A )
!= ( sK69_SY1672 @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(506,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(507,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(508,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(509,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK67_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK67_X @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(510,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(511,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK65_Xx @ Xu @ B @ A ) @ ( sK66_SY1671 @ Xu @ B @ A ) ) )
& ( in @ ( sK66_SY1671 @ Xu @ B @ A ) @ B )
& ( in @ ( sK65_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(512,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(513,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(514,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(516,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(517,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(518,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(519,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(520,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(521,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(522,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(523,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(524,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(525,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(526,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(527,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(528,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(529,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(530,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(531,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(534,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(535,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(536,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(537,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(539,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(540,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[332]) ).
thf(541,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(542,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(543,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(547,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(551,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(552,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(553,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(556,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(558,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(559,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(560,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(561,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(562,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(563,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(564,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(566,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(567,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(570,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(571,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(573,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(574,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(575,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(576,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(579,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK63_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK63_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(581,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(583,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK62_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK62_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK60_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK60_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK61_SY1670 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(585,plain,
( ( ! [SY249: $i > $o,SY250: $i > $o] :
( ( ( ( sK58_Xx @ SY250 @ SY249 )
= ( sK59_SY1669 @ SY250 @ SY249 ) )
& ( ~ ( SY249 @ ( sK58_Xx @ SY250 @ SY249 ) )
| ~ ( SY250 @ ( sK59_SY1669 @ SY250 @ SY249 ) ) )
& ( ( SY249 @ ( sK58_Xx @ SY250 @ SY249 ) )
| ( SY250 @ ( sK59_SY1669 @ SY250 @ SY249 ) ) ) )
| ! [SY254: $i] :
( ( ( SY249 @ ( sK57_SY255 @ SY254 @ SY250 @ SY249 ) )
& ( SY254
!= ( sK57_SY255 @ SY254 @ SY250 @ SY249 ) ) )
| ~ ( SY249 @ SY254 ) )
| ! [SY257: $i] :
( ( ( SY250 @ ( sK56_SY258 @ SY257 @ SY250 @ SY249 ) )
& ( SY257
!= ( sK56_SY258 @ SY257 @ SY250 @ SY249 ) ) )
| ~ ( SY250 @ SY257 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(586,plain,
( ( ! [SY243: $i > $o] :
( ! [SY245: $i] :
( ( ( SY243 @ ( sK55_SY246 @ SY245 @ SY243 ) )
& ( SY245
!= ( sK55_SY246 @ SY245 @ SY243 ) ) )
| ~ ( SY243 @ SY245 ) )
| ! [Xx: $i] :
( ~ ( SY243 @ Xx )
| ! [Xy: $i] :
( ~ ( SY243 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(587,plain,
$true = $true,
inference(copy,[status(thm)],[297]) ).
thf(588,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(589,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(590,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ! [Xz: $i,Xu: $i] :
( ( Xz != Xu )
| ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(591,plain,
$true = $true,
inference(copy,[status(thm)],[293]) ).
thf(592,plain,
( ( ! [SY225: $i > $o,SY226: $i > $o] :
( ( ( ( sK53_Xx @ SY226 @ SY225 )
= ( sK54_SY1668 @ SY226 @ SY225 ) )
& ( ~ ( SY225 @ ( sK53_Xx @ SY226 @ SY225 ) )
| ~ ( SY226 @ ( sK54_SY1668 @ SY226 @ SY225 ) ) )
& ( ( SY225 @ ( sK53_Xx @ SY226 @ SY225 ) )
| ( SY226 @ ( sK54_SY1668 @ SY226 @ SY225 ) ) ) )
| ! [SY230: $i] :
( ( ( SY225 @ ( sK52_SY231 @ SY230 @ SY226 @ SY225 ) )
& ( SY230
!= ( sK52_SY231 @ SY230 @ SY226 @ SY225 ) ) )
| ~ ( SY225 @ SY230 ) )
| ( ! [SY1667: $i] :
( ~ ( SY226 @ SY1667 )
| ( ( sK51_SY233 @ SY226 @ SY225 )
= SY1667 ) )
& ( SY226 @ ( sK51_SY233 @ SY226 @ SY225 ) ) ) )
& ! [SY225: $i > $o,SY226: $i > $o] :
( ( ( ( sK49_Xx @ SY226 @ SY225 )
= ( sK50_SY1666 @ SY226 @ SY225 ) )
& ( ~ ( SY225 @ ( sK49_Xx @ SY226 @ SY225 ) )
| ~ ( SY226 @ ( sK50_SY1666 @ SY226 @ SY225 ) ) )
& ( ( SY225 @ ( sK49_Xx @ SY226 @ SY225 ) )
| ( SY226 @ ( sK50_SY1666 @ SY226 @ SY225 ) ) ) )
| ! [SY233: $i] :
( ( ( SY226 @ ( sK48_SY234 @ SY233 @ SY226 @ SY225 ) )
& ( SY233
!= ( sK48_SY234 @ SY233 @ SY226 @ SY225 ) ) )
| ~ ( SY226 @ SY233 ) )
| ( ! [SY1665: $i] :
( ~ ( SY225 @ SY1665 )
| ( ( sK47_SY230 @ SY226 @ SY225 )
= SY1665 ) )
& ( SY225 @ ( sK47_SY230 @ SY226 @ SY225 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(593,plain,
( ( ! [SY219: $i > $o] :
( ! [SY221: $i] :
( ( ( SY219 @ ( sK46_SY222 @ SY221 @ SY219 ) )
& ( SY221
!= ( sK46_SY222 @ SY221 @ SY219 ) ) )
| ~ ( SY219 @ SY221 ) )
| ! [Xx: $i] :
( ~ ( SY219 @ Xx )
| ! [Xy: $i] :
( ~ ( SY219 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(596,plain,
( ( ! [SY205: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK45_Xy @ Xx @ SY205 )
!= Xx )
| ~ ( SY205 @ ( sK45_Xy @ Xx @ SY205 ) ) )
& ( ( ( sK45_Xy @ Xx @ SY205 )
= Xx )
| ( SY205 @ ( sK45_Xy @ Xx @ SY205 ) ) ) )
| ( ! [SY1664: $i] :
( ~ ( SY205 @ SY1664 )
| ( ( sK44_SY209 @ SY205 )
= SY1664 ) )
& ( SY205 @ ( sK44_SY209 @ SY205 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(597,plain,
( ( ! [SY198: $i > $o] :
( ! [Xx: $i] :
~ ( SY198 @ Xx )
| ( ( SY198 @ ( sK42_Xx @ SY198 ) )
& ( SY198 @ ( sK43_SY1663 @ SY198 ) )
& ( ( sK42_Xx @ SY198 )
!= ( sK43_SY1663 @ SY198 ) ) )
| ( ! [SY1662: $i] :
( ~ ( SY198 @ SY1662 )
| ( ( sK41_SY203 @ SY198 )
= SY1662 ) )
& ( SY198 @ ( sK41_SY203 @ SY198 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(598,plain,
( ( ! [SY192: $i > $o] :
( ! [Xx: $i] :
( ( ( SY192 @ ( sK40_Xy @ Xx @ SY192 ) )
& ( Xx
!= ( sK40_Xy @ Xx @ SY192 ) ) )
| ~ ( SY192 @ Xx ) )
| ( ! [SY1661: $i] :
( ~ ( SY192 @ SY1661 )
| ( ( sK39_SY196 @ SY192 )
= SY1661 ) )
& ( SY192 @ ( sK39_SY196 @ SY192 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(599,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK38_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK38_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(600,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK37_Xx @ Xphi @ A ) )
& ( in @ ( sK37_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(601,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(602,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(603,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(604,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK35_Xx @ Xphi @ A ) )
& ( in @ ( sK35_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(605,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK34_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK34_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(606,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK33_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK33_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(607,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(608,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(609,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(610,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(611,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(612,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(613,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(614,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(615,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(616,plain,
( ( ! [SY143: $i] :
( ( SY143 = emptyset )
| ( in @ ( sK32_Xx @ SY143 ) @ SY143 ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(617,plain,
( ( ! [SY137: $i > $o] :
( ! [SY139: $i] :
( ( ( SY137 @ ( sK31_SY140 @ SY139 @ SY137 ) )
& ( SY139
!= ( sK31_SY140 @ SY139 @ SY137 ) ) )
| ~ ( SY137 @ SY139 ) )
| ( ! [SY1659: $i] :
( ( SY1659
!= ( sK30_Xx @ SY137 ) )
| ( SY137 @ SY1659 ) )
& ! [SY1660: $i] :
( ~ ( SY137 @ SY1660 )
| ( SY1660
= ( sK30_Xx @ SY137 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(618,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(619,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK29_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK29_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(620,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(621,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(622,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(623,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK28_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK28_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(625,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(626,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(627,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(628,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(629,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(630,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(631,plain,
( ( ! [SY104: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY104 )
| ( SY104 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(632,plain,
( ( ! [SY100: $i,SY101: $i > $o,SY102: $i] :
( ~ ( in @ SY102 @ SY100 )
| ~ ( SY101 @ SY102 )
| ( ( dsetconstr @ SY100
@ ^ [Xy: $i] : ( SY101 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(633,plain,
( ( ! [SY98: $i] :
( ( SY98 = emptyset )
| ( in @ ( sK27_Xx @ SY98 ) @ SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(634,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(635,plain,
( ( ! [A: $i] :
( ( in @ ( sK26_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(636,plain,
( ( ! [A: $i] :
( ( in @ ( sK25_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(637,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK24_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK24_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK23_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK23_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(638,plain,
( ( ! [SY81: $i > $o] :
( ! [SY83: $i] :
( ( ( SY81 @ ( sK22_SY84 @ SY83 @ SY81 ) )
& ( SY83
!= ( sK22_SY84 @ SY83 @ SY81 ) ) )
| ~ ( SY81 @ SY83 ) )
| ( SY81 @ ( sK21_Xx @ SY81 ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(639,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(640,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(641,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(642,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(643,plain,
( ( ! [SY69: $i > $o] :
( ! [SY71: $i] :
( ( ( SY69 @ ( sK20_SY72 @ SY71 @ SY69 ) )
& ( SY71
!= ( sK20_SY72 @ SY71 @ SY69 ) ) )
| ~ ( SY69 @ SY71 ) )
| ( ! [SY1658: $i] :
( ~ ( SY69 @ SY1658 )
| ( ( sK19_Xx @ SY69 )
= SY1658 ) )
& ( SY69 @ ( sK19_Xx @ SY69 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(644,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(645,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(646,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(647,plain,
( ( ! [SY52: $i > $o] :
( ! [SY54: $i] :
( ( ( SY52 @ ( sK18_SY55 @ SY54 @ SY52 ) )
& ( SY54
!= ( sK18_SY55 @ SY54 @ SY52 ) ) )
| ~ ( SY52 @ SY54 ) )
| ( SY52
@ ( descr
@ ^ [Xx: $i] : ( SY52 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(648,plain,
( ( ! [A: $i] :
( ! [SY1634: $i] :
( ( ( in @ ( sK17_Xx @ SY1634 @ A ) @ SY1634 )
& ~ ( in @ ( sK17_Xx @ SY1634 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1634 )
| ( ! [SY1655: $i] :
( ~ ( in @ SY1655 @ ( sK13_B @ A ) )
| ! [SY1653: $i] :
( ~ ( in @ SY1653 @ SY1655 )
| ( in @ SY1653 @ ( sK15_SY1637 @ SY1634 @ A ) ) )
| ( in @ ( sK16_SY1651 @ SY1634 @ A ) @ SY1655 ) )
& ( in @ ( sK15_SY1637 @ SY1634 @ A ) @ ( sK13_B @ A ) )
& ( in @ ( sK16_SY1651 @ SY1634 @ A ) @ SY1634 )
& ! [SY1654: $i] :
( ~ ( in @ SY1654 @ ( sK15_SY1637 @ SY1634 @ A ) )
| ~ ( in @ SY1654 @ SY1634 ) ) ) )
& ! [SY1642: $i,SY1643: $i] :
( ~ ( in @ SY1642 @ ( sK13_B @ A ) )
| ~ ( in @ SY1643 @ ( sK13_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1642 )
| ( in @ Xx @ SY1643 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1643 )
| ( in @ Xx @ SY1642 ) ) )
& ! [SY1646: $i] :
( ~ ( in @ SY1646 @ ( sK13_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1646 )
| ( in @ Xx @ A ) ) )
& ! [SY1648: $i,SY1649: $i] :
( ~ ( in @ SY1648 @ A )
| ~ ( in @ SY1649 @ A )
| ( ( in @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) @ ( sK13_B @ A ) )
& ( ~ ( in @ SY1648 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) )
| ~ ( in @ SY1649 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) ) )
& ( ( in @ SY1648 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) )
| ( in @ SY1649 @ ( sK14_SY1650 @ SY1649 @ SY1648 @ A ) ) ) )
| ( SY1648 = SY1649 ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(649,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK12_B @ A ) @ A )
& ! [SY1633: $i] :
( ~ ( in @ SY1633 @ ( sK12_B @ A ) )
| ~ ( in @ SY1633 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(650,plain,
( ( ! [SY20: $i > $i > $o,SY21: $i] :
( ( ( in @ ( sK10_SY22 @ SY21 @ SY20 ) @ SY21 )
& ! [SY1631: $i] :
( ( ( SY20 @ ( sK10_SY22 @ SY21 @ SY20 ) @ ( sK11_SY1632 @ SY1631 @ SY21 @ SY20 ) )
& ( SY1631
!= ( sK11_SY1632 @ SY1631 @ SY21 @ SY20 ) ) )
| ~ ( SY20 @ ( sK10_SY22 @ SY21 @ SY20 ) @ SY1631 ) ) )
| ( ! [SY1627: $i] :
( ! [Xy: $i] :
( ~ ( SY20 @ Xy @ SY1627 )
| ~ ( in @ Xy @ SY21 ) )
| ( in @ SY1627 @ ( sK8_B @ SY21 @ SY20 ) ) )
& ! [SY1629: $i] :
( ~ ( in @ SY1629 @ ( sK8_B @ SY21 @ SY20 ) )
| ( ( SY20 @ ( sK9_Xy @ SY1629 @ SY21 @ SY20 ) @ SY1629 )
& ( in @ ( sK9_Xy @ SY1629 @ SY21 @ SY20 ) @ SY21 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(651,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK7_Xx @ A ) @ omega )
& ( in @ ( sK7_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK7_Xx @ A ) @ ( sK7_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(652,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(653,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(654,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK6_B @ Xx @ A ) )
& ( in @ ( sK6_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(655,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK5_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK5_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(656,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(657,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK4_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK4_Xx @ B @ A ) @ A )
| ( in @ ( sK4_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(659,plain,
( ( ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(660,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK20_SY72 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK20_SY72 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK19_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK19_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ( ~ ( in @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX0 @ SX1 @ SX3 @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ! [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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(663,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK76_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK76_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in
@ ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) )
@ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,
( ( ~ ( ~ ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK40_Xy @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK40_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK39_SY196 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK39_SY196 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(667,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK17_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK17_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK13_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK15_SY1637 @ SX1 @ SX0 ) ) )
| ( in @ ( sK16_SY1651 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SX1 @ SX0 ) @ ( sK13_B @ SX0 ) )
| ~ ( in @ ( sK16_SY1651 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK15_SY1637 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK13_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK13_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK13_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SX2 @ SX1 @ SX0 ) @ ( sK13_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK14_SY1650 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK14_SY1650 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK14_SY1650 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK14_SY1650 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK89_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX0 @ SX1 @ SX3 @ ( sK89_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK33_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK33_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(671,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ~ ( ~ ( SX1 @ ( sK70_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK70_Xx @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK87_SY1678 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK87_SY1678 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK85_SY1677 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK85_SY1677 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $i] :
( ~ ( ~ ( in @ ( sK74_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK74_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) ) ) ) )
= $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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK90_Xx @ SX2 @ SX1 @ SX0 ) ) @ 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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ~ ( ~ ( in @ ( sK68_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK68_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK69_SY1672 @ SX1 @ SX0 ) )
| ~ ( ( ( sK68_Xx @ SX1 @ SX0 )
!= ( sK69_SY1672 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK38_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK38_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ ( sK67_X @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ SX1 @ ( sK67_X @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(679,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK24_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK24_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( in @ ( sK23_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK23_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK62_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK62_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(681,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK46_SY222 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK46_SY222 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ~ ( ~ ( SX1 @ ( sK37_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK37_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( kpair @ ( sK65_Xx @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY1671 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK65_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK10_SY22 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK10_SY22 @ SX1 @ SX0 ) @ ( sK11_SY1632 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK11_SY1632 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK10_SY22 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK8_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK8_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK9_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK9_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK35_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK35_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( ~ ( in @ ( sK28_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK28_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 ) )
| ~ ( ! [SX2: $i] :
~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ( ~ ( in @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= ( ap @ SX0 @ SX1 @ SX3 @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX2 = SX3 ) ) ) )
= $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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK36_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK36_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0 @ ( sK42_Xx @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK43_SY1663 @ SX0 ) )
| ~ ( ( ( sK42_Xx @ SX0 )
!= ( sK43_SY1663 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK41_SY203 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK41_SY203 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(691,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK55_SY246 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK55_SY246 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ( ( sK60_Xx @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK61_SY1670 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX2 @ ( sK60_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( SX3 @ ( sK61_SY1670 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2 @ ( sK60_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( SX3 @ ( sK61_SY1670 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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: $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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,SX2: $i > $i] :
~ ( ~ ( in @ ( sK91_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK91_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| $true ) )
= $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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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: $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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( ~ ( in @ ( sK71_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK71_Xy @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( ( sK71_Xy @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK75_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK75_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK22_SY84 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK22_SY84 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK21_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ~ ( ~ ( in @ ( sK72_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK72_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK73_SY1673 @ SX1 @ SX0 ) )
| ~ ( ( ( sK72_Xx @ SX1 @ SX0 )
!= ( sK73_SY1673 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) ) @ 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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK83_SY1676 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK83_SY1676 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK18_SY55 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK18_SY55 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK78_SY1674 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( SX3 @ ( kpair @ ( sK77_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK78_SY1674 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK12_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK12_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o,SX1: $i > $o] :
( ~ ( ( ( sK53_Xx @ SX1 @ SX0 )
!= ( sK54_SY1668 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK51_SY233 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK51_SY233 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK49_Xx @ SX1 @ SX0 )
!= ( sK50_SY1666 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK47_SY230 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK47_SY230 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ~ ( ~ ( in @ ( sK34_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( SX1 @ ( sK34_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SX0 ) @ ( sK7_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
~ ( ~ ( ( ( sK45_Xy @ SX1 @ SX0 )
!= SX1 )
| ~ ( SX0 @ ( sK45_Xy @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK45_Xy @ SX1 @ SX0 )
= SX1 )
| ( SX0 @ ( sK45_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK44_SY209 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK44_SY209 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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: $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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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 > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK31_SY140 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK31_SY140 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ( SX1
!= ( sK30_Xx @ SX0 ) )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( SX1
= ( sK30_Xx @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,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] :
( ~ ( ~ ( in @ ( sK63_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK63_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(715,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK80_SY1675 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( SX3 @ ( kpair @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK80_SY1675 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SX2 = SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(717,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ( ~ ( in @ SX1 @ ( sK29_B @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ SX2 ) )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(719,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK58_Xx @ SX1 @ SX0 )
!= ( sK59_SY1669 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK58_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK59_SY1669 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK58_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK59_SY1669 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK57_SY255 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK57_SY255 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK56_SY258 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK56_SY258 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(720,plain,
( ( ! [SX0: $i,SX1: $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)],[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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(721,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,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,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,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(722,plain,
! [SV1: $i] :
( ( ! [SY1679: $i] :
( ~ ( in @ SY1679 @ ( powerset @ SV1 ) )
| ( in @ ( powerset @ SY1679 ) @ ( powerset @ ( powerset @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(723,plain,
! [SV2: $i] :
( ( ! [SY1680: $i] :
( ~ ( in @ SY1680 @ ( powerset @ SV2 ) )
| ! [SY1681: $i] :
( ~ ( in @ SY1681 @ ( powerset @ SV2 ) )
| ( in @ ( binunion @ SY1680 @ SY1681 ) @ ( powerset @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(724,plain,
! [SV3: $i] :
( ( ! [SY1682: $i] :
( ~ ( in @ SY1682 @ ( powerset @ SV3 ) )
| ! [SY1683: $i] :
( ~ ( in @ SY1683 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SY1682 @ SY1683 ) @ ( powerset @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(725,plain,
! [SV4: $i] :
( ( ! [SY1684: $o,SY1685: $i] :
( ~ ( in @ SY1685 @ SV4 )
| ! [SY1686: $i] :
( ~ ( in @ SY1686 @ SV4 )
| ( in @ ( if @ SV4 @ SY1684 @ SY1685 @ SY1686 ) @ ( setadjoin @ SY1685 @ ( setadjoin @ SY1686 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(726,plain,
! [SV5: $i] :
( ( ! [SY1687: $o,SY1688: $i] :
( ~ ( in @ SY1688 @ SV5 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV5 )
| SY1687
| ( ( if @ SV5 @ SY1687 @ SY1688 @ SY1689 )
= SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(727,plain,
! [SV6: $i] :
( ( ! [SY1690: $o,SY1691: $i] :
( ~ ( in @ SY1691 @ SV6 )
| ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV6 )
| ~ SY1690
| ( ( if @ SV6 @ SY1690 @ SY1691 @ SY1692 )
= SY1691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(728,plain,
! [SV7: $i] :
( ( ~ ( singleton @ SV7 )
| ! [SY1693: $i] :
( ~ ( in @ SY1693 @ SV7 )
| ( ( setunion @ SV7 )
= SY1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(729,plain,
! [SV8: $i] :
( ( ! [SY1694: $o,SY1695: $i] :
( ~ ( in @ SY1695 @ SV8 )
| ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV8 )
| ( in @ ( if @ SV8 @ SY1694 @ SY1695 @ SY1696 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(730,plain,
! [SV9: $i] :
( ( ! [SY1697: $i,SY1698: $i] :
( ~ ( in @ SY1698 @ ( funcSet @ SV9 @ SY1697 ) )
| ( ( lam @ SV9 @ SY1697
@ ^ [SY1699: $i] : ( ap @ SV9 @ SY1697 @ SY1698 @ SY1699 ) )
= SY1698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(731,plain,
! [SV10: $i] :
( ( ! [SY1700: $i,SY1701: $i] :
( ~ ( func @ SV10 @ SY1700 @ SY1701 )
| ( ( lam @ SV10 @ SY1700
@ ^ [SY1702: $i] : ( ap @ SV10 @ SY1700 @ SY1701 @ SY1702 ) )
= SY1701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(732,plain,
! [SV11: $i] :
( ( ! [SY1703: $i,SY1704: $i] :
~ ( func @ SV11 @ SY1703 @ SY1704 )
| ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(733,plain,
! [SV12: $i] :
( ( ! [SY1706: $i,SY1707: $i] :
~ ( in @ SY1707 @ ( funcSet @ SV12 @ SY1706 ) )
| ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(734,plain,
! [SV13: $i] :
( ( ! [SY1709: $i,SY1710: $i] :
( ~ ( in @ SY1710 @ ( funcSet @ SV13 @ SY1709 ) )
| ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV13 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SY1709 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SY1710 )
| ( ( ap @ SV13 @ SY1709 @ SY1710 @ SY1711 )
= SY1712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(735,plain,
! [SV14: $i] :
( ( ! [SY1713: $i,SY1714: $i] :
( ~ ( func @ SV14 @ SY1713 @ SY1714 )
| ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV14 )
| ! [SY1716: $i] :
( ~ ( in @ SY1716 @ SY1713 )
| ~ ( in @ ( kpair @ SY1715 @ SY1716 ) @ SY1714 )
| ( ( ap @ SV14 @ SY1713 @ SY1714 @ SY1715 )
= SY1716 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(736,plain,
! [SV15: $i] :
( ( ! [SY1717: $i,SY1718: $i] :
( ~ ( in @ SY1718 @ ( funcSet @ SV15 @ SY1717 ) )
| ! [SY1719: $i] :
( ~ ( in @ SY1719 @ SV15 )
| ( in @ ( kpair @ SY1719 @ ( ap @ SV15 @ SY1717 @ SY1718 @ SY1719 ) ) @ SY1718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(737,plain,
! [SV16: $i] :
( ( ! [SY1720: $i,SY1721: $i] :
( ~ ( func @ SV16 @ SY1720 @ SY1721 )
| ! [SY1722: $i] :
( ~ ( in @ SY1722 @ SV16 )
| ( in @ ( kpair @ SY1722 @ ( ap @ SV16 @ SY1720 @ SY1721 @ SY1722 ) ) @ SY1721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(738,plain,
! [SV17: $i] :
( ( ! [SY1723: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY685: $i] : ( SY1723 @ SY685 ) ) )
| ! [SY1725: $i] :
( ~ ( in @ SY1725 @ SV17 )
| ! [SY1726: $i] :
( ~ ( in @ SY1726 @ SV17 )
| ~ ( SY1723 @ SY1725 )
| ~ ( SY1723 @ SY1726 )
| ( SY1725 = SY1726 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(739,plain,
! [SV18: $i] :
( ( ! [SY1727: $i,SY1728: $i] :
( ~ ( func @ SV18 @ SY1727 @ SY1728 )
| ( in @ SY1728 @ ( funcSet @ SV18 @ SY1727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(740,plain,
! [SV19: $i] :
( ( ! [SY1729: $i,SY1730: $i] :
( ~ ( in @ SY1730 @ ( funcSet @ SV19 @ SY1729 ) )
| ! [SY1731: $i] :
( ~ ( in @ SY1731 @ SV19 )
| ( in @ ( ap @ SV19 @ SY1729 @ SY1730 @ SY1731 ) @ SY1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(741,plain,
! [SV20: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ~ ( in @ SY1733 @ ( funcSet @ SV20 @ SY1732 ) )
| ( func @ SV20 @ SY1732 @ SY1733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(742,plain,
! [SV21: $i] :
( ( ! [SY1734: $i,SY1735: $i] :
( ~ ( func @ SV21 @ SY1734 @ SY1735 )
| ! [SY1736: $i] :
( ~ ( in @ SY1736 @ SV21 )
| ( in @ ( ap @ SV21 @ SY1734 @ SY1735 @ SY1736 ) @ SY1734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(743,plain,
! [SV22: $i] :
( ( ! [SY1737: $i,SY1738: $i] :
( ~ ( func @ SV22 @ SY1737 @ SY1738 )
| ! [SY1739: $i] :
( ~ ( in @ SY1739 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY1737
@ ^ [Xy: $i] : ( in @ ( kpair @ SY1739 @ Xy ) @ SY1738 ) ) )
@ SY1737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(744,plain,
! [SV23: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
( ~ ( func @ SV23 @ SY1741 @ SY1742 )
| ! [SY1743: $i] :
( ~ ( in @ SY1743 @ SV23 )
| ( singleton
@ ( dsetconstr @ SY1741
@ ^ [Xy: $i] : ( in @ ( kpair @ SY1743 @ Xy ) @ SY1742 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(745,plain,
! [SV24: $i] :
( ( ! [SY1745: $i,SY1746: $i > $i > $o,SY1747: $i,SY1748: $i] :
( ~ ( in @ ( kpair @ SY1747 @ SY1748 )
@ ( dpsetconstr @ SV24 @ SY1745
@ ^ [Xz: $i,Xu: $i] : ( SY1746 @ Xz @ Xu ) ) )
| ( SY1746 @ SY1747 @ SY1748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(746,plain,
! [SV25: $i] :
( ( ! [SY1751: $i,SY1752: $i > $i > $o,SY1753: $i,SY1754: $i] :
( ~ ( in @ ( kpair @ SY1753 @ SY1754 )
@ ( dpsetconstr @ SV25 @ SY1751
@ ^ [Xz: $i,Xu: $i] : ( SY1752 @ Xz @ Xu ) ) )
| ( in @ SY1754 @ SY1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(747,plain,
! [SV26: $i] :
( ( ! [SY1757: $i,SY1758: $i > $i > $o,SY1759: $i] :
( ! [SY1760: $i] :
~ ( in @ ( kpair @ SY1759 @ SY1760 )
@ ( dpsetconstr @ SV26 @ SY1757
@ ^ [Xz: $i,Xu: $i] : ( SY1758 @ Xz @ Xu ) ) )
| ( in @ SY1759 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(748,plain,
! [SV27: $i] :
( ( ! [SY1763: $i,SY1764: $i > $i > $o,SY1765: $i] :
( ~ ( in @ SY1765 @ SV27 )
| ! [SY1766: $i] :
( ~ ( in @ SY1766 @ SY1763 )
| ~ ( in @ ( kpair @ SY1765 @ SY1766 )
@ ( dpsetconstr @ SV27 @ SY1763
@ ^ [Xz: $i,Xu: $i] : ( SY1764 @ Xz @ Xu ) ) )
| ( SY1764 @ SY1765 @ SY1766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(749,plain,
! [SV28: $i] :
( ( ! [SY1769: $i,SY1770: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV28 @ SY1769
@ ^ [Xx: $i,Xy: $i] : ( SY1770 @ Xx @ Xy ) )
@ ( cartprod @ SV28 @ SY1769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(750,plain,
! [SV29: $i] :
( ( ! [SY1773: $i,SY1774: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV29 @ SY1773
@ ^ [Xx: $i,Xy: $i] : ( SY1774 @ Xx @ Xy ) )
@ ( cartprod @ SV29 @ SY1773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(751,plain,
! [SV30: $i] :
( ( ! [SY1777: $i,SY1778: $i > $i > $o,SY1779: $i] :
( ~ ( in @ SY1779 @ SV30 )
| ! [SY1780: $i] :
( ~ ( in @ SY1780 @ SY1777 )
| ~ ( SY1778 @ SY1779 @ SY1780 )
| ( in @ ( kpair @ SY1779 @ SY1780 )
@ ( dpsetconstr @ SV30 @ SY1777
@ ^ [Xz: $i,Xu: $i] : ( SY1778 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(752,plain,
! [SV31: $i] :
( ( ! [SY1783: $i,SY1784: $i] :
( ~ ( in @ SY1784 @ ( cartprod @ SV31 @ SY1783 ) )
| ( ( kpair @ ( kfst @ SY1784 ) @ ( ksnd @ SY1784 ) )
= SY1784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(753,plain,
! [SV32: $i] :
( ( ! [SY1785: $i,SY1786: $i] :
( ~ ( in @ SY1786 @ SV32 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY1785 )
| ( ( ksnd @ ( kpair @ SY1786 @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(754,plain,
! [SV33: $i] :
( ( ! [SY1788: $i,SY1789: $i] :
( ~ ( in @ SY1789 @ SV33 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY1788 )
| ( ( kfst @ ( kpair @ SY1789 @ Xy ) )
= SY1789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(755,plain,
! [SV34: $i] :
( ( ! [SY1791: $i] :
~ ( in @ SY1791 @ SV34 )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(756,plain,
! [SV35: $i] :
( ( ! [SY1794: $i,SY1795: $i,SY1796: $i] :
( ~ ( in @ ( kpair @ SY1795 @ SY1796 ) @ ( cartprod @ SV35 @ SY1794 ) )
| ( in @ SY1796 @ SY1794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(757,plain,
! [SV36: $i] :
( ( ! [SY1797: $i,SY1798: $i] :
( ! [SY1799: $i] :
~ ( in @ ( kpair @ SY1798 @ SY1799 ) @ ( cartprod @ SV36 @ SY1797 ) )
| ( in @ SY1798 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(758,plain,
! [SV37: $i] :
( ( ! [SY1800: $i,SY1801: $i] :
( ~ ( in @ SY1801 @ ( cartprod @ SV37 @ SY1800 ) )
| ( in @ ( ksnd @ SY1801 ) @ SY1800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(759,plain,
! [SV38: $i] :
( ( ~ ( iskpair @ SV38 )
| ( ( kpair @ ( kfst @ SV38 ) @ ( ksnd @ SV38 ) )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(760,plain,
! [SV39: $i] :
( ( ! [SY1802: $i] :
( ( ksnd @ ( kpair @ SV39 @ SY1802 ) )
= SY1802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(761,plain,
! [SV40: $i] :
( ( ~ ( iskpair @ SV40 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV40 )
@ ^ [SY1803: $i] :
( SV40
= ( kpair @ ( kfst @ SV40 ) @ SY1803 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(762,plain,
! [SV41: $i] :
( ( ! [SY1804: $i,SY1805: $i,SY1806: $i] :
( ( ( kpair @ SV41 @ SY1804 )
!= ( kpair @ SY1805 @ SY1806 ) )
| ( SY1804 = SY1806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(763,plain,
! [SV42: $i] :
( ( ! [SY1807: $i,SY1808: $i,SY1809: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SY1807 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1808 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1808 @ ( setadjoin @ SY1809 @ emptyset ) ) @ emptyset ) ) )
| ( SY1807 = SY1809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(764,plain,
! [SV43: $i] :
( ( ! [SY1810: $i] :
( ! [SY1811: $i] :
( ( setadjoin @ SV43 @ ( setadjoin @ SY1810 @ emptyset ) )
!= ( setadjoin @ SY1811 @ emptyset ) )
| ( SV43 = SY1810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(765,plain,
! [SV44: $i] :
( ( ! [SY1812: $i,SY1813: $i,SY1814: $i] :
( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SY1812 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1813 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1813 @ ( setadjoin @ SY1814 @ emptyset ) ) @ emptyset ) ) )
| ( SY1813 != SY1814 )
| ( SY1812 = SY1814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(766,plain,
! [SV45: $i] :
( ( ! [SY1815: $i] :
( ( SV45 != SY1815 )
| ( ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV45 @ ( setadjoin @ SY1815 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(767,plain,
! [SV46: $i] :
( ( ! [SY1816: $i] :
( ( SV46 != SY1816 )
| ( ( setadjoin @ SV46 @ ( setadjoin @ SY1816 @ emptyset ) )
= ( setadjoin @ SV46 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(768,plain,
! [SV47: $i] :
( ( ! [SY1817: $i,SY1818: $i] :
( ! [SY1819: $i] :
( ( kpair @ SV47 @ SY1817 )
!= ( kpair @ SY1818 @ SY1819 ) )
| ( SV47 = SY1818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(769,plain,
! [SV48: $i] :
( ( ! [SY1820: $i,SY1821: $i] :
( ! [SY1822: $i] :
( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SY1820 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1821 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1821 @ ( setadjoin @ SY1822 @ emptyset ) ) @ emptyset ) ) )
| ( SV48 = SY1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(770,plain,
! [SV49: $i] :
( ( ! [SY1823: $i,SY1824: $i] :
( ~ ( in @ SY1824 @ ( cartprod @ SV49 @ SY1823 ) )
| ( in @ ( kfst @ SY1824 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(771,plain,
! [SV50: $i] :
( ( ! [SY1825: $i] :
( ( kfst @ ( kpair @ SV50 @ SY1825 ) )
= SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(772,plain,
! [SV51: $i] :
( ( ~ ( singleton @ SV51 )
| ( in @ ( setunion @ SV51 ) @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(773,plain,
! [SV52: $i] :
( ( ~ ( iskpair @ SV52 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV52 )
@ ^ [SY1826: $i] : ( in @ ( setadjoin @ SY1826 @ emptyset ) @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(774,plain,
! [SV53: $i] :
( ( ! [SY1827: $i,SY1828: $i] :
( ~ ( in @ ( setadjoin @ SY1828 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SY1827 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SY1828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(775,plain,
! [SV54: $i] :
( ( ! [SY1829: $i] :
( ( ( setadjoin @ SV54 @ emptyset )
!= ( setadjoin @ SY1829 @ emptyset ) )
| ( SV54 = SY1829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(776,plain,
! [SV55: $i] :
( ( ( setunion @ ( setadjoin @ SV55 @ emptyset ) )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(777,plain,
! [SV56: $i] :
( ( subset @ SV56 @ ( setunion @ ( setadjoin @ SV56 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(778,plain,
! [SV57: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV57 @ emptyset ) ) @ SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(779,plain,
! [SV58: $i] :
( ( ! [SY1830: $i,SY1831: $i] :
( ~ ( in @ SY1831 @ ( cartprod @ SV58 @ SY1830 ) )
| ( iskpair @ SY1831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(780,plain,
! [SV59: $i] :
( ( ! [SY1832: $i,SY1833: $i] :
( ~ ( in @ SY1833 @ SV59 )
| ! [SY1834: $i] :
( ~ ( in @ SY1834 @ SY1832 )
| ( in @ ( kpair @ SY1833 @ SY1834 ) @ ( cartprod @ SV59 @ SY1832 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(781,plain,
! [SV60: $i] :
( ( ! [SY1835: $i,SY1836: $i] :
( ~ ( in @ SY1836 @ SV60 )
| ! [SY1837: $i] :
( ~ ( in @ SY1837 @ SY1835 )
| ( in @ ( kpair @ SY1836 @ SY1837 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SY1835 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(782,plain,
! [SV61: $i] :
( ( ! [SY1838: $i,SY1839: $i] :
( ~ ( in @ SY1839 @ SV61 )
| ! [SY1840: $i] :
( ~ ( in @ SY1840 @ SY1838 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1839 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1839 @ ( setadjoin @ SY1840 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SY1838 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(783,plain,
! [SV62: $i] :
( ( ! [SY1841: $i,SY1842: $i] :
( ~ ( in @ SY1842 @ SV62 )
| ! [SY1843: $i] :
( ~ ( in @ SY1843 @ SY1841 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1842 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1842 @ ( setadjoin @ SY1843 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SY1841 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(784,plain,
! [SV63: $i] :
( ( ! [SY1844: $i,SY1845: $i] :
( ~ ( in @ SY1845 @ SV63 )
| ! [SY1846: $i] :
( ~ ( in @ SY1846 @ SY1844 )
| ( in @ ( setadjoin @ SY1845 @ ( setadjoin @ SY1846 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SY1844 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(785,plain,
! [SV64: $i] :
( ( ! [SY1847: $i,SY1848: $i] :
( ~ ( in @ SY1848 @ SV64 )
| ! [SY1849: $i] :
( ~ ( in @ SY1849 @ SY1847 )
| ( subset @ ( setadjoin @ SY1848 @ ( setadjoin @ SY1849 @ emptyset ) ) @ ( binunion @ SV64 @ SY1847 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(786,plain,
! [SV65: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( in @ SY1851 @ ( setadjoin @ SV65 @ ( setadjoin @ SY1850 @ emptyset ) ) )
| ( SY1851 = SV65 )
| ( SY1851 = SY1850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(787,plain,
! [SV66: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( in @ SY1853 @ SV66 )
| ( in @ ( setadjoin @ SY1853 @ emptyset ) @ ( powerset @ ( binunion @ SV66 @ SY1852 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(788,plain,
! [SV67: $i] :
( ( ! [SY1854: $i] :
( ~ ( in @ SY1854 @ SV67 )
| ( in @ ( setadjoin @ SY1854 @ emptyset ) @ ( powerset @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(789,plain,
! [SV68: $i] :
( ( ! [SY1855: $i] :
( ~ ( in @ SY1855 @ SV68 )
| ( subset @ ( setadjoin @ SY1855 @ emptyset ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(790,plain,
! [SV69: $i] :
( ( ! [SY1856: $i] : ( iskpair @ ( kpair @ SV69 @ SY1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(791,plain,
! [SV70: $i] :
( ( ! [SY1857: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SY1857 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(792,plain,
! [SV71: $i] :
( ( ! [SY1858: $i] : ( in @ SY1858 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV71 @ ( setadjoin @ SY1858 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(793,plain,
! [SV72: $i] :
( ( ! [SY1859: $i] : ( in @ SV72 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV72 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV72 @ ( setadjoin @ SY1859 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(794,plain,
! [SV73: $i] :
( ( ! [SY1860: $i] : ( in @ SY1860 @ ( setadjoin @ SV73 @ ( setadjoin @ SY1860 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(795,plain,
! [SV74: $i] :
( ( ! [SY1861: $i,SY1862: $i] :
( ( in @ SY1862 @ SV74 )
| ( in @ SY1862 @ SY1861 )
| ~ ( in @ SY1862 @ ( symdiff @ SV74 @ SY1861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(796,plain,
! [SV75: $i] :
( ( ! [SY1863: $i,SY1864: $i] :
( ~ ( in @ SY1864 @ SV75 )
| ~ ( in @ SY1864 @ SY1863 )
| ~ ( in @ SY1864 @ ( symdiff @ SV75 @ SY1863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(797,plain,
! [SV76: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ( in @ SY1866 @ SV76 )
| ~ ( in @ SY1866 @ SY1865 )
| ( in @ SY1866 @ ( symdiff @ SV76 @ SY1865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(798,plain,
! [SV77: $i] :
( ( ! [SY1867: $i,SY1868: $i] :
( ~ ( in @ SY1868 @ SV77 )
| ( in @ SY1868 @ SY1867 )
| ( in @ SY1868 @ ( symdiff @ SV77 @ SY1867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(799,plain,
! [SV78: $i] :
( ( ! [SY1869: $i] :
( ( ( setminus @ SV78 @ SY1869 )
!= emptyset )
| ( subset @ SV78 @ SY1869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(800,plain,
! [SV79: $i] :
( ( ! [SY1870: $i] : ( subset @ ( setminus @ SV79 @ SY1870 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(801,plain,
! [SV80: $i] :
( ( ! [SY1871: $i,SY1872: $i] :
( ~ ( in @ SY1872 @ SY1871 )
| ~ ( in @ SY1872 @ ( setminus @ SV80 @ SY1871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(802,plain,
! [SV81: $i] :
( ( ! [SY1873: $i,SY1874: $i] :
( ( in @ SY1874 @ SV81 )
| ~ ( in @ SY1874 @ ( setminus @ SV81 @ SY1873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(803,plain,
! [SV82: $i] :
( ( ! [SY1875: $i,SY1876: $i] :
( ( in @ SY1876 @ ( setminus @ SV82 @ SY1875 ) )
| ( in @ SY1876 @ SY1875 )
| ~ ( in @ SY1876 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(804,plain,
! [SV83: $i] :
( ( ! [SY1877: $i,SY1878: $i] :
( ( in @ SY1878 @ ( setminus @ SV83 @ SY1877 ) )
| ~ ( in @ SY1878 @ SV83 )
| ( in @ SY1878 @ SY1877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(805,plain,
! [SV84: $i] :
( ( ! [SY1879: $i] :
( ~ ( subset @ SV84 @ SY1879 )
| ( ( setminus @ SV84 @ SY1879 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(806,plain,
! [SV85: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
( ~ ( in @ SY1881 @ ( setminus @ SV85 @ SY1880 ) )
| ~ ( in @ SY1881 @ SY1880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(807,plain,
! [SV86: $i] :
( ( ! [SY1882: $i,SY1883: $i] :
( ~ ( in @ SY1883 @ ( setminus @ SV86 @ SY1882 ) )
| ( in @ SY1883 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(808,plain,
! [SV87: $i] :
( ( ! [SY1884: $i,SY1885: $i] :
( ~ ( in @ SY1885 @ SV87 )
| ( in @ SY1885 @ SY1884 )
| ( in @ SY1885 @ ( setminus @ SV87 @ SY1884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(809,plain,
! [SV88: $i] :
( ( ! [SY1886: $i,SY1887: $i] :
( ( binintersect @ SV88 @ ( binunion @ SY1886 @ SY1887 ) )
= ( binunion @ ( binintersect @ SV88 @ SY1886 ) @ ( binintersect @ SV88 @ SY1887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(810,plain,
! [SV89: $i] :
( ( ! [SY1888: $i] :
( ( ( binintersect @ SV89 @ SY1888 )
!= SV89 )
| ( subset @ SV89 @ SY1888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(811,plain,
! [SV90: $i] :
( ( ! [SY1889: $i] :
( ~ ( subset @ SY1889 @ SV90 )
| ( ( binintersect @ SV90 @ SY1889 )
= SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(812,plain,
! [SV91: $i] :
( ( ! [SY1890: $i] : ( subset @ ( binintersect @ SV91 @ SY1890 ) @ SY1890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(813,plain,
! [SV92: $i] :
( ( ! [SY1891: $i,SY1892: $i] :
( ~ ( in @ SY1892 @ ( binintersect @ SV92 @ SY1891 ) )
| ( in @ SY1892 @ SY1891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(814,plain,
! [SV93: $i] :
( ( ! [SY1893: $i] :
( ( ( binintersect @ SV93 @ SY1893 )
!= SY1893 )
| ( subset @ SY1893 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(815,plain,
! [SV94: $i] :
( ( ! [SY1894: $i] :
( ~ ( subset @ SV94 @ SY1894 )
| ( ( binintersect @ SV94 @ SY1894 )
= SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(816,plain,
! [SV95: $i] :
( ( ! [SY1895: $i] : ( subset @ ( binintersect @ SV95 @ SY1895 ) @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(817,plain,
! [SV96: $i] :
( ( ! [SY1896: $i,SY1897: $i] :
( ~ ( in @ SY1897 @ ( binintersect @ SV96 @ SY1896 ) )
| ( in @ SY1897 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(818,plain,
! [SV97: $i] :
( ( ! [SY1898: $i,SY1899: $i] :
( ~ ( subset @ SY1899 @ SV97 )
| ~ ( subset @ SY1899 @ SY1898 )
| ( subset @ SY1899 @ ( binintersect @ SV97 @ SY1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(819,plain,
! [SV98: $i] :
( ( ! [SY1900: $i,SY1901: $i] :
( ~ ( in @ SY1901 @ SV98 )
| ~ ( in @ SY1901 @ SY1900 )
| ( in @ SY1901 @ ( binintersect @ SV98 @ SY1900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(820,plain,
! [SV99: $i] :
( ( ! [SY1902: $i] : ( subset @ SY1902 @ ( binunion @ SV99 @ SY1902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(821,plain,
! [SV100: $i] :
( ( ! [SY1903: $i] : ( subset @ SV100 @ ( binunion @ SV100 @ SY1903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(822,plain,
! [SV101: $i] :
( ( ! [SY1904: $i,SY1905: $i] :
( ~ ( in @ SY1905 @ ( binunion @ SV101 @ SY1904 ) )
| ( in @ SY1905 @ SV101 )
| ( in @ SY1905 @ SY1904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(823,plain,
! [SV102: $i] :
( ( ! [SY1906: $i,SY1907: $i] :
( ~ ( in @ SY1907 @ SY1906 )
| ( in @ SY1907 @ ( binunion @ SV102 @ SY1906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(824,plain,
! [SV103: $i] :
( ( ! [SY1908: $i] : ( in @ SY1908 @ ( setadjoin @ SV103 @ ( setadjoin @ SY1908 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(825,plain,
! [SV104: $i] :
( ( ! [SY1909: $i,SY1910: $i] :
( ~ ( in @ SY1910 @ SV104 )
| ( in @ SY1910 @ ( binunion @ SV104 @ SY1909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(826,plain,
! [SV105: $i] :
( ( ! [SY1911: $i > $o] :
( subset
@ ( dsetconstr @ SV105
@ ^ [Xx: $i] : ( SY1911 @ Xx ) )
@ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(827,plain,
! [SV106: $i] :
( ( ! [SY1913: $i > $o] :
( in
@ ( dsetconstr @ SV106
@ ^ [Xx: $i] : ( SY1913 @ Xx ) )
@ ( powerset @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(828,plain,
! [SV107: $i] :
( ( ! [SY1915: $i] :
( ~ ( subset @ SV107 @ SY1915 )
| ( subset @ ( powerset @ SV107 ) @ ( powerset @ SY1915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(829,plain,
! [SV108: $i] :
( ( in @ SV108 @ ( powerset @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(830,plain,
! [SV109: $i] :
( ( ! [SY1916: $i] :
( ~ ( in @ SY1916 @ ( powerset @ SV109 ) )
| ( subset @ SY1916 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(831,plain,
! [SV110: $i] :
( ( ! [SY1917: $i] :
( ~ ( subset @ SY1917 @ SV110 )
| ( in @ SY1917 @ ( powerset @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(832,plain,
! [SV111: $i] :
( ( ~ ( subset @ SV111 @ emptyset )
| ( SV111 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(833,plain,
! [SV112: $i] :
( ( ! [SY1918: $i] :
( ~ ( subset @ SV112 @ SY1918 )
| ~ ( subset @ SY1918 @ SV112 )
| ( SV112 = SY1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(834,plain,
! [SV113: $i] :
( ( ! [SY1919: $i] :
( ~ ( subset @ SV113 @ SY1919 )
| ( in @ SV113 @ ( powerset @ SY1919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(835,plain,
! [SV114: $i] :
( ( ! [SY1920: $i,SY1921: $i] :
( ~ ( subset @ SV114 @ SY1921 )
| ( subset @ SV114 @ ( setadjoin @ SY1920 @ SY1921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(836,plain,
! [SV115: $i] :
( ( ! [SY1922: $i] : ( subset @ SY1922 @ ( setadjoin @ SV115 @ SY1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(837,plain,
! [SV116: $i] :
( ( ! [SY1923: $i] :
( ~ ( subset @ SV116 @ SY1923 )
| ! [SY1924: $i] :
( ~ ( subset @ SY1923 @ SY1924 )
| ( subset @ SV116 @ SY1924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(838,plain,
! [SV117: $i] :
( ( subset @ SV117 @ SV117 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(839,plain,
! [SV118: $i] :
( ( ! [SY1925: $i,SY1926: $i] :
( ~ ( in @ SY1926 @ SV118 )
| ( in @ SY1926 @ SY1925 )
| ( SV118 != SY1925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(840,plain,
! [SV119: $i] :
( ( ! [SY1927: $i] :
( ( subset @ SV119 @ SY1927 )
| ( SV119 != SY1927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(841,plain,
! [SV120: $i] :
( ( ! [SY1928: $i,SY1929: $i] :
( ~ ( in @ SY1929 @ SV120 )
| ( in @ SY1929 @ SY1928 )
| ~ ( subset @ SV120 @ SY1928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(842,plain,
! [SV121: $i] :
( ( ! [SY1930: $i] :
( ~ ( subset @ SV121 @ SY1930 )
| ! [SY1931: $i] :
( ( in @ SY1931 @ SY1930 )
| ~ ( in @ SY1931 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(843,plain,
! [SV122: $i] :
( ( ! [SY1932: $i] :
( ~ ( subset @ SV122 @ SY1932 )
| ! [SY1933: $i] :
( ~ ( in @ SY1933 @ SV122 )
| ( in @ SY1933 @ SY1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(844,plain,
! [SV123: $i] :
( ( subset @ emptyset @ SV123 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(845,plain,
! [SV124: $i] :
( ( ! [SY1934: $i] :
( ( SV124 != SY1934 )
| ( subset @ SV124 @ SY1934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(846,plain,
! [SV125: $i] :
( ( ! [SY1935: $i] :
( ( SV125 != SY1935 )
| ( subset @ SY1935 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(847,plain,
! [SV126: $i] :
( ( ! [SY1936: $i] :
( ( SV126 != SY1936 )
| ( ( setunion @ SV126 )
= ( setunion @ SY1936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(848,plain,
! [SV127: $i] :
( ( ! [SY1937: $i] :
( ( SV127 != SY1937 )
| ( ( powerset @ SV127 )
= ( powerset @ SY1937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(849,plain,
! [SV128: $i] :
( ( ! [SY1938: $i] :
( ( SV128 != SY1938 )
| ! [SY1939: $i,SY1940: $i] :
( ( SY1939 != SY1940 )
| ( ( setadjoin @ SV128 @ SY1939 )
= ( setadjoin @ SY1938 @ SY1940 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(850,plain,
! [SV129: $i] :
( ( ! [SY1941: $i] :
( ( SV129 != SY1941 )
| ! [SY1942: $i,SY1943: $i] :
( ( SY1942 != SY1943 )
| ~ ( in @ SY1942 @ SV129 )
| ( in @ SY1943 @ SY1941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(851,plain,
! [SV130: $o] :
( ( ~ SV130
| ( set2prop @ ( prop2set @ SV130 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(852,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(853,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(854,plain,
! [SV131: $o] :
( ( ~ SV131
| ( in @ emptyset @ ( prop2set @ SV131 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[602]) ).
thf(855,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[602]) ).
thf(856,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[602]) ).
thf(857,plain,
! [SV132: $i > $o] :
( ( ! [SY1944: $i] :
( ~ ( in @ SY1944 @ emptyset )
| ( SV132 @ SY1944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(858,plain,
! [SV133: $i] :
( ( ! [SY1945: $i > $o] :
( ! [SY1946: $i] :
( ~ ( SY1945 @ SY1946 )
| ~ ( in @ SY1946 @ SV133 ) )
| ( ( dsetconstr @ SV133
@ ^ [Xx: $i] : ( SY1945 @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(859,plain,
! [SV134: $i] :
( ( ! [SY1948: $i] : ( in @ SY1948 @ ( setadjoin @ SV134 @ ( setadjoin @ SY1948 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(860,plain,
! [SV135: $i] :
( ( ! [SY1949: $i] : ( in @ SV135 @ ( setadjoin @ SV135 @ ( setadjoin @ SY1949 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(861,plain,
! [SV136: $i] :
( ( ! [SY1950: $i,SY1951: $i] :
( ~ ( in @ SY1951 @ ( setadjoin @ SV136 @ ( setadjoin @ SY1950 @ emptyset ) ) )
| ( SY1951 = SV136 )
| ( SY1951 = SY1950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(862,plain,
! [SV137: $i] :
( ( ! [SY1952: $i] :
( ~ ( in @ SV137 @ ( setadjoin @ SY1952 @ emptyset ) )
| ( in @ SY1952 @ ( setadjoin @ SV137 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(863,plain,
! [SV138: $i] :
( ( ! [SY1953: $i] :
( ( SV138 != SY1953 )
| ( in @ SV138 @ ( setadjoin @ SY1953 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(864,plain,
! [SV139: $i] :
( ( ! [SY1954: $i] :
( ( SV139 = SY1954 )
| ~ ( in @ SY1954 @ ( setadjoin @ SV139 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(865,plain,
! [SV140: $i] :
( ( ! [SY1955: $i] :
( ~ ( in @ SV140 @ ( setadjoin @ SY1955 @ emptyset ) )
| ( SV140 = SY1955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(866,plain,
! [SV141: $i] :
( ( ( SV141 = emptyset )
| ( in @ ( sK32_Xx @ SV141 ) @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(867,plain,
! [SV142: $i] :
( ( ! [SY1956: $i] :
( ~ ( in @ SY1956 @ SV142 )
| ( in @ SY1956 @ ( powerset @ ( setunion @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(868,plain,
! [SV143: $i] :
( ( ! [SY1957: $i,SY1958: $i] :
( ~ ( in @ SY1957 @ SY1958 )
| ~ ( in @ SY1958 @ SV143 )
| ( in @ SY1957 @ ( setunion @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(869,plain,
! [SV144: $i] :
( ( ! [SY1959: $i] :
( ~ ( in @ SY1959 @ ( powerset @ SV144 ) )
| ! [SY1960: $i] :
( ~ ( in @ SY1960 @ SY1959 )
| ( in @ SY1960 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(870,plain,
! [SV145: $i] :
( ( in @ emptyset @ ( powerset @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(871,plain,
! [SV146: $i] :
( ( in @ emptyset @ ( powerset @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(872,plain,
! [SV147: $i] :
( ( ( dsetconstr @ SV147
@ ^ [Xx: $i] : $true )
= SV147 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(873,plain,
! [SV148: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ~ ( in @ SY1963 @ ( setadjoin @ SV148 @ SY1962 ) )
| ( SY1963 = SV148 )
| ( in @ SY1963 @ SY1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(874,plain,
! [SV149: $i] :
( ( ! [SY1964: $i,SY1965: $i] :
( ~ ( in @ SY1965 @ SY1964 )
| ( in @ SY1965 @ ( setadjoin @ SV149 @ SY1964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(875,plain,
! [SV150: $i] :
( ( ! [SY1966: $i] : ( in @ SV150 @ ( setadjoin @ SV150 @ SY1966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(876,plain,
! [SV151: $i] :
( ( ! [SY1967: $i] :
~ ( in @ SY1967 @ SV151 )
| ( SV151 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(877,plain,
! [SV152: $i] :
( ( ! [SY1968: $i > $o,SY1969: $i] :
( ~ ( in @ SY1969 @ SV152 )
| ~ ( SY1968 @ SY1969 )
| ( ( dsetconstr @ SV152
@ ^ [Xy: $i] : ( SY1968 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(878,plain,
! [SV153: $i] :
( ( ( SV153 = emptyset )
| ( in @ ( sK27_Xx @ SV153 ) @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(879,plain,
! [SV154: $i] :
( ( ( in @ ( sK26_Xx @ SV154 ) @ SV154 )
| ( SV154 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(880,plain,
! [SV155: $i] :
( ( ( in @ ( sK25_Xx @ SV155 ) @ SV155 )
| ( SV155 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(881,plain,
! [SV156: $i] :
( ( ~ ( in @ SV156 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(882,plain,
! [SV157: $i] :
( ( ~ ( in @ SV157 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(883,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(884,plain,
! [SV158: $o] :
( ( ! [SY1971: $i] :
~ ( in @ SY1971 @ ( prop2set @ SV158 ) )
| SV158 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[642]) ).
thf(885,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[642]) ).
thf(886,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[642]) ).
thf(887,plain,
! [SV159: $i] :
( ( ! [SY1972: $i > $o,SY1973: $i] :
( ~ ( in @ SY1973
@ ( dsetconstr @ SV159
@ ^ [Xy: $i] : ( SY1972 @ Xy ) ) )
| ( SY1972 @ SY1973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(888,plain,
! [SV160: $i] :
( ( ! [SY1975: $i > $o,SY1976: $i] :
( ~ ( in @ SY1976
@ ( dsetconstr @ SV160
@ ^ [Xy: $i] : ( SY1975 @ Xy ) ) )
| ( in @ SY1976 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(889,plain,
! [SV161: $i] :
( ( ! [SY1978: $i > $o,SY1979: $i] :
( ~ ( in @ SY1979 @ SV161 )
| ~ ( SY1978 @ SY1979 )
| ( in @ SY1979
@ ( dsetconstr @ SV161
@ ^ [Xy: $i] : ( SY1978 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(890,plain,
! [SV162: $i] :
( ( ~ ( in @ SV162 @ omega )
| ( in @ ( setadjoin @ SV162 @ SV162 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(891,plain,
! [SV163: $i] :
( ( ~ ( in @ SV163 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(892,plain,
! [SV164: $i > $o] :
( ( ! [SY1981: $i] :
( ~ ( ~ ( SV164 @ ( sK20_SY72 @ SY1981 @ SV164 ) )
| ~ ( ( SY1981
!= ( sK20_SY72 @ SY1981 @ SV164 ) ) ) )
| ~ ( SV164 @ SY1981 ) )
| ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(893,plain,
! [SV165: $i] :
( ( ! [SY1983: $i] :
( ( SV165 != SY1983 )
| ~ ( ~ ! [SY1984: $i,SY1985: $i] :
( ( SY1984 != SY1985 )
| ~ ( in @ SY1984 @ SV165 )
| ( in @ SY1985 @ SY1983 ) )
| ~ ! [SY1986: $i,SY1987: $i] :
( ( SY1986 != SY1987 )
| ~ ( in @ SY1987 @ SY1983 )
| ( in @ SY1986 @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(894,plain,
! [SV166: $i] :
( ( ! [SY1988: $i,SY1989: $i] :
( ~ ( func @ SV166 @ SY1988 @ SY1989 )
| ! [SY1990: $i] :
( ~ ( func @ SV166 @ SY1988 @ SY1990 )
| ~ ( ~ ( in @ ( sK81_Xx @ SY1990 @ SY1989 @ SY1988 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SY1988 @ SY1989 @ ( sK81_Xx @ SY1990 @ SY1989 @ SY1988 @ SV166 ) )
!= ( ap @ SV166 @ SY1988 @ SY1990 @ ( sK81_Xx @ SY1990 @ SY1989 @ SY1988 @ SV166 ) ) ) ) )
| ! [SY1991: $i] :
( ~ ( in @ SY1991 @ SV166 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1988 )
| ~ ( in @ ( kpair @ SY1991 @ SX5 ) @ SY1990 )
| ( in @ ( kpair @ SY1991 @ SX5 ) @ SY1989 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(895,plain,
! [SV167: $i] :
( ( ! [SY1993: $i,SY1994: $i > $i] :
( ~ ( ~ ( in @ ( sK76_Xx @ SY1994 @ SY1993 @ SV167 ) @ SV167 )
| ~ ~ ( in @ ( SY1994 @ ( sK76_Xx @ SY1994 @ SY1993 @ SV167 ) ) @ SY1993 ) )
| ( in
@ ( lam @ SV167 @ SY1993
@ ^ [SX3: $i] : ( SY1994 @ SX3 ) )
@ ( funcSet @ SV167 @ SY1993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(896,plain,
! [SV168: $i] :
( ( ! [SY1996: $i,SY1997: $i] :
( ~ ( in @ SY1997 @ ( symdiff @ SV168 @ SY1996 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY1997 @ SV168 )
| ~ ( in @ SY1997 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY1997 @ SV168 )
| ( in @ SY1997 @ SY1996 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY1997 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY1997 @ SY1996 )
| ~ ( in @ SY1997 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY1997 @ SY1996 )
| ( in @ SY1997 @ SY1996 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY1997 @ SY1996 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2004: $o] :
( ~ SY2004
| ~ ( in @ SY1997 @ SV168 )
| SY2004 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY1997 @ SY1996 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(897,plain,
( ( ~ ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(898,plain,
! [SV169: $i > $o] :
( ( ! [SY2007: $i] :
( ~ ( ~ ( SV169 @ ( sK40_Xy @ SY2007 @ SV169 ) )
| ~ ( ( SY2007
!= ( sK40_Xy @ SY2007 @ SV169 ) ) ) )
| ~ ( SV169 @ SY2007 ) )
| ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(899,plain,
! [SV170: $i] :
( ( ~ ( ~ ! [SY2009: $i] :
( ~ ( ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SY2009 )
| ~ ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SV170 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2009 )
| ~ ( ~ ! [SY2011: $i] :
( ~ ( in @ SY2011 @ ( sK13_B @ SV170 ) )
| ! [SY2012: $i] :
( ~ ( in @ SY2012 @ SY2011 )
| ( in @ SY2012 @ ( sK15_SY1637 @ SY2009 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2011 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SY2009 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2009 ) )
| ~ ! [SY2013: $i] :
( ~ ( in @ SY2013 @ ( sK15_SY1637 @ SY2009 @ SV170 ) )
| ~ ( in @ SY2013 @ SY2009 ) ) ) ) )
| ~ ~ ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) )
| ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(900,plain,
! [SV171: $i] :
( ( ! [SY2022: $i,SY2023: $i] :
( ~ ( in @ SY2023 @ ( funcSet @ SV171 @ SY2022 ) )
| ! [SY2024: $i] :
( ~ ( in @ SY2024 @ ( funcSet @ SV171 @ SY2022 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SY2024 @ SY2023 @ SY2022 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SY2022 @ SY2023 @ ( sK89_Xx @ SY2024 @ SY2023 @ SY2022 @ SV171 ) )
!= ( ap @ SV171 @ SY2022 @ SY2024 @ ( sK89_Xx @ SY2024 @ SY2023 @ SY2022 @ SV171 ) ) ) ) )
| ( SY2023 = SY2024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(901,plain,
! [SV172: $i] :
( ( ! [SY2025: $i] :
( ~ ( ~ ( in @ ( sK64_Xx @ SY2025 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK64_Xx @ SY2025 @ SV172 ) @ SY2025 ) )
| ( ( binintersect @ SV172 @ SY2025 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(902,plain,
! [SV173: $i] :
( ( ! [SY2026: $i > $o] :
( ! [SY2027: $i] :
( ~ ( in @ SY2027 @ SV173 )
| ( SY2026 @ SY2027 ) )
| ~ ( ~ ( in @ ( sK33_Xx @ SY2026 @ SV173 ) @ SV173 )
| ~ ~ ( SY2026 @ ( sK33_Xx @ SY2026 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(903,plain,
! [SV174: $i] :
( ( ~ ( ~ ! [SY2028: $i,SY2029: $i] :
( ~ ( in @ SY2029 @ ( setadjoin @ SV174 @ SY2028 ) )
| ( SY2029 = SV174 )
| ( in @ SY2029 @ SY2028 ) )
| ~ ~ ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) )
| ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(904,plain,
! [SV175: $i] :
( ( ! [SY2034: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV175
@ ^ [SX2: $i] : ( SY2034 @ SX2 ) ) )
| ~ ( ~ ( SY2034 @ ( sK70_Xx @ SY2034 @ SV175 ) )
| ~ ( in @ ( sK70_Xx @ SY2034 @ SV175 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(905,plain,
! [SV176: $i] :
( ( ! [SY2036: $i,SY2037: $i] :
( ~ ( subset @ SY2037 @ ( cartprod @ SV176 @ SY2036 ) )
| ! [SY2038: $i] :
( ~ ( subset @ SY2038 @ ( cartprod @ SV176 @ SY2036 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ SY2036 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ ( sK87_SY1678 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) ) @ SY2037 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ ( sK87_SY1678 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) ) @ SY2038 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ SY2036 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ ( sK85_SY1677 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) ) @ SY2038 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2038 @ SY2037 @ SY2036 @ SV176 ) @ ( sK85_SY1677 @ SY2038 @ SY2037 @ SY2036 @ SV176 ) ) @ SY2037 ) ) ) )
| ( SY2037 = SY2038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(906,plain,
! [SV177: $i] :
( ( ! [SY2039: $i,SY2040: $i > $i] :
( ~ ( ~ ( in @ ( sK74_Xx @ SY2040 @ SY2039 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( SY2040 @ ( sK74_Xx @ SY2040 @ SY2039 @ SV177 ) ) @ SY2039 ) )
| ( func @ SV177 @ SY2039
@ ( dpsetconstr @ SV177 @ SY2039
@ ^ [SX3: $i,SX4: $i] :
( ( SY2040 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(907,plain,
! [SV178: $i] :
( ( ! [SY2043: $i,SY2044: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2044 @ SY2043 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( SY2044 @ ( sK90_Xx @ SY2044 @ SY2043 @ SV178 ) ) @ SY2043 ) )
| ! [SY2045: $i] :
( ~ ( in @ SY2045 @ SV178 )
| ( ( ap @ SV178 @ SY2043
@ ( lam @ SV178 @ SY2043
@ ^ [SX4: $i] : ( SY2044 @ SX4 ) )
@ SY2045 )
= ( SY2044 @ SY2045 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(908,plain,
! [SV179: $i] :
( ( ! [SY2047: $i > $o] :
( ~ ( ~ ( in @ ( sK68_Xx @ SY2047 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SY2047 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SY2047 @ ( sK68_Xx @ SY2047 @ SV179 ) )
| ~ ~ ( ~ ( SY2047 @ ( sK69_SY1672 @ SY2047 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SY2047 @ SV179 )
!= ( sK69_SY1672 @ SY2047 @ SV179 ) ) ) ) ) ) )
| ! [SY2048: $i] :
( ~ ( SY2047 @ SY2048 )
| ~ ( in @ SY2048 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SX2: $i] : ( SY2047 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(909,plain,
! [SV180: $i] :
( ( ! [SY2050: $i > $o] :
( ! [SY2051: $i] :
( ~ ( in @ SY2051 @ SV180 )
| ( SY2050 @ SY2051 ) )
| ~ ( ~ ( in @ ( sK38_Xx @ SY2050 @ SV180 ) @ SV180 )
| ~ ~ ( SY2050 @ ( sK38_Xx @ SY2050 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(910,plain,
! [SV181: $i] :
( ( ! [SY2052: $i] :
( ~ ( in @ SY2052 @ ( setunion @ SV181 ) )
| ~ ( ~ ( in @ ( sK67_X @ SY2052 @ SV181 ) @ SV181 )
| ~ ( in @ SY2052 @ ( sK67_X @ SY2052 @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(911,plain,
! [SV182: $i] :
( ( ! [SY2053: $i] :
( ~ ( ~ ( in @ ( sK24_Xx @ SY2053 @ SV182 ) @ SV182 )
| ~ ~ ( in @ ( sK24_Xx @ SY2053 @ SV182 ) @ SY2053 ) )
| ~ ( ~ ( in @ ( sK23_Xx @ SY2053 @ SV182 ) @ SY2053 )
| ~ ~ ( in @ ( sK23_Xx @ SY2053 @ SV182 ) @ SV182 ) )
| ( SV182 = SY2053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(912,plain,
! [SV183: $i] :
( ( ! [SY2054: $i] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY2054 @ SV183 ) @ SV183 )
| ~ ~ ( in @ ( sK62_Xx @ SY2054 @ SV183 ) @ SY2054 ) )
| ( subset @ SV183 @ SY2054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(913,plain,
! [SV184: $i > $o] :
( ( ! [SY2055: $i] :
( ~ ( ~ ( SV184 @ ( sK46_SY222 @ SY2055 @ SV184 ) )
| ~ ( ( SY2055
!= ( sK46_SY222 @ SY2055 @ SV184 ) ) ) )
| ~ ( SV184 @ SY2055 ) )
| ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(914,plain,
! [SV185: $i] :
( ( ! [SY2058: $i > $o] :
( ~ ( ~ ( SY2058 @ ( sK37_Xx @ SY2058 @ SV185 ) )
| ~ ( in @ ( sK37_Xx @ SY2058 @ SV185 ) @ SV185 ) )
| ! [SY2059: $i] :
( ~ ( in @ SY2059 @ SV185 )
| ~ ( SY2058 @ SY2059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(915,plain,
! [SV186: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ~ ( in @ SY2061 @ ( cartprod @ SV186 @ SY2060 ) )
| ~ ( ~ ~ ( ( SY2061
!= ( kpair @ ( sK65_Xx @ SY2061 @ SY2060 @ SV186 ) @ ( sK66_SY1671 @ SY2061 @ SY2060 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SY2061 @ SY2060 @ SV186 ) @ SY2060 ) )
| ~ ( in @ ( sK65_Xx @ SY2061 @ SY2060 @ SV186 ) @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(916,plain,
! [SV187: $i > $i > $o] :
( ( ! [SY2062: $i] :
( ~ ( ~ ( in @ ( sK10_SY22 @ SY2062 @ SV187 ) @ SY2062 )
| ~ ! [SY2063: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SY2062 @ SV187 ) @ ( sK11_SY1632 @ SY2063 @ SY2062 @ SV187 ) )
| ~ ( ( SY2063
!= ( sK11_SY1632 @ SY2063 @ SY2062 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SY2062 @ SV187 ) @ SY2063 ) ) )
| ~ ( ~ ! [SY2064: $i] :
( ! [SY2065: $i] :
( ~ ( SV187 @ SY2065 @ SY2064 )
| ~ ( in @ SY2065 @ SY2062 ) )
| ( in @ SY2064 @ ( sK8_B @ SY2062 @ SV187 ) ) )
| ~ ! [SY2066: $i] :
( ~ ( in @ SY2066 @ ( sK8_B @ SY2062 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2066 @ SY2062 @ SV187 ) @ SY2066 )
| ~ ( in @ ( sK9_Xy @ SY2066 @ SY2062 @ SV187 ) @ SY2062 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(917,plain,
! [SV188: $i] :
( ( ! [SY2067: $i > $o] :
( ~ ( ~ ( SY2067 @ ( sK35_Xx @ SY2067 @ SV188 ) )
| ~ ( in @ ( sK35_Xx @ SY2067 @ SV188 ) @ SV188 ) )
| ! [SY2068: $i] :
( ~ ( in @ SY2068 @ SV188 )
| ~ ( SY2067 @ SY2068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(918,plain,
! [SV189: $i] :
( ( ! [SY2069: $i] :
( ~ ( ~ ( in @ ( sK28_Xx @ SY2069 @ SV189 ) @ SY2069 )
| ~ ~ ( in @ ( sK28_Xx @ SY2069 @ SV189 ) @ SV189 ) )
| ( in @ SY2069 @ ( powerset @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(919,plain,
! [SV190: $i] :
( ( ! [SY2070: $i] :
~ ( ~ ~ ( ~ ! [SY2071: $i] :
( ~ ( in @ SY2071 @ ( binunion @ SV190 @ SY2070 ) )
| ( in @ SY2071 @ SV190 )
| ( in @ SY2071 @ SY2070 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2073: $i] :
( ~ ( in @ SY2073 @ ( binunion @ SV190 @ SY2070 ) )
| ( in @ SY2073 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2075: $i] :
( ~ ( in @ SY2075 @ ( binunion @ SV190 @ SY2070 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SY2075 @ SY2070 )
| SX3 ) )
| ~ ( ! [SY2077: $i] :
~ ( in @ SY2077 @ ( binunion @ SV190 @ SY2070 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(920,plain,
! [SV191: $i] :
( ( ! [SY2079: $i,SY2080: $i] :
( ~ ( func @ SV191 @ SY2079 @ SY2080 )
| ! [SY2081: $i] :
( ~ ( func @ SV191 @ SY2079 @ SY2081 )
| ~ ( ~ ( in @ ( sK88_Xx @ SY2081 @ SY2080 @ SY2079 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SY2079 @ SY2080 @ ( sK88_Xx @ SY2081 @ SY2080 @ SY2079 @ SV191 ) )
!= ( ap @ SV191 @ SY2079 @ SY2081 @ ( sK88_Xx @ SY2081 @ SY2080 @ SY2079 @ SV191 ) ) ) ) )
| ( SY2080 = SY2081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(921,plain,
! [SV192: $i] :
( ( ! [SY2082: $i > $o] :
( ! [SY2083: $i] :
( ~ ( in @ SY2083 @ SV192 )
| ( SY2082 @ SY2083 ) )
| ~ ( ~ ( in @ ( sK36_Xx @ SY2082 @ SV192 ) @ SV192 )
| ~ ~ ( SY2082 @ ( sK36_Xx @ SY2082 @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(922,plain,
! [SV193: $i > $o] :
( ( ! [SY2084: $i] :
~ ( SV193 @ SY2084 )
| ~ ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
| ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(923,plain,
! [SV194: $i > $o] :
( ( ! [SY2086: $i] :
( ~ ( ~ ( SV194 @ ( sK55_SY246 @ SY2086 @ SV194 ) )
| ~ ( ( SY2086
!= ( sK55_SY246 @ SY2086 @ SV194 ) ) ) )
| ~ ( SV194 @ SY2086 ) )
| ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(924,plain,
! [SV195: $i] :
( ( ! [SY2089: $o,SY2090: $i] :
( ~ ( in @ SY2090 @ SV195 )
| ! [SY2091: $i] :
( ~ ( in @ SY2091 @ SV195 )
| SY2089
| ( in @ SY2091
@ ( dsetconstr @ SV195
@ ^ [SX4: $i] :
( ~ ( ~ SY2089
| ( SX4 != SY2090 ) )
| ~ ( ~ ~ SY2089
| ( SX4 != SY2091 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(925,plain,
! [SV196: $i] :
( ( ! [SY2093: $i] :
( ( SV196 != SY2093 )
| ! [SY2094: $i > $o,SY2095: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SY2095 @ SY2094 @ SY2093 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SY2095 @ SY2094 @ SY2093 @ SV196 ) @ SY2093 )
| ~ ~ ( ( ( sK60_Xx @ SY2095 @ SY2094 @ SY2093 @ SV196 )
!= ( sK61_SY1670 @ SY2095 @ SY2094 @ SY2093 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SY2094 @ ( sK60_Xx @ SY2095 @ SY2094 @ SY2093 @ SV196 ) )
| ~ ( SY2095 @ ( sK61_SY1670 @ SY2095 @ SY2094 @ SY2093 @ SV196 ) ) )
| ~ ( ( SY2094 @ ( sK60_Xx @ SY2095 @ SY2094 @ SY2093 @ SV196 ) )
| ( SY2095 @ ( sK61_SY1670 @ SY2095 @ SY2094 @ SY2093 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SX4: $i] : ( SY2094 @ SX4 ) )
= ( dsetconstr @ SY2093
@ ^ [SX4: $i] : ( SY2095 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(926,plain,
! [SV197: $i] :
( ( ! [SY2098: $o,SY2099: $i] :
( ~ ( in @ SY2099 @ SV197 )
| ! [SY2100: $i] :
( ~ ( in @ SY2100 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SX4: $i] :
( ~ ( ~ SY2098
| ( SX4 != SY2099 ) )
| ~ ( ~ ~ SY2098
| ( SX4 != SY2100 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(927,plain,
! [SV198: $i] :
( ( ! [SY2102: $i,SY2103: $i > $i] :
~ ( ~ ( in @ ( sK91_Xx @ SY2103 @ SY2102 @ SV198 ) @ SV198 )
| ~ ~ ( in @ ( SY2103 @ ( sK91_Xx @ SY2103 @ SY2102 @ SV198 ) ) @ SY2102 ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(928,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(929,plain,
! [SV199: $i] :
( ( ! [SY2104: $o,SY2105: $i] :
( ~ ( in @ SY2105 @ SV199 )
| ! [SY2106: $i] :
( ~ ( in @ SY2106 @ SV199 )
| ~ SY2104
| ( in @ SY2105
@ ( dsetconstr @ SV199
@ ^ [SX4: $i] :
( ~ ( ~ SY2104
| ( SX4 != SY2105 ) )
| ~ ( ~ ~ SY2104
| ( SX4 != SY2106 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(930,plain,
! [SV200: $i] :
( ( ! [SY2108: $i > $o,SY2109: $i] :
( ~ ( in @ SY2109 @ SV200 )
| ~ ( SY2108 @ SY2109 )
| ~ ( ~ ( in @ ( sK71_Xy @ SY2109 @ SY2108 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SY2108 @ ( sK71_Xy @ SY2109 @ SY2108 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SY2109 @ SY2108 @ SV200 )
!= SY2109 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SX3: $i] : ( SY2108 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(931,plain,
! [SV201: $i] :
( ( ! [SY2111: $i,SY2112: $i > $i] :
( ~ ( ~ ( in @ ( sK75_Xx @ SY2112 @ SY2111 @ SV201 ) @ SV201 )
| ~ ~ ( in @ ( SY2112 @ ( sK75_Xx @ SY2112 @ SY2111 @ SV201 ) ) @ SY2111 ) )
| ( func @ SV201 @ SY2111
@ ( lam @ SV201 @ SY2111
@ ^ [SX3: $i] : ( SY2112 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(932,plain,
! [SV202: $i] :
( ( ! [SY2114: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_Xx @ SY2114 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SY2114 @ SV202 ) @ SY2114 ) )
| ~ ( ( in @ ( sK4_Xx @ SY2114 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SY2114 @ SV202 ) @ SY2114 ) ) )
| ( SV202 = SY2114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(933,plain,
! [SV203: $i > $o] :
( ( ! [SY2115: $i] :
( ~ ( ~ ( SV203 @ ( sK22_SY84 @ SY2115 @ SV203 ) )
| ~ ( ( SY2115
!= ( sK22_SY84 @ SY2115 @ SV203 ) ) ) )
| ~ ( SV203 @ SY2115 ) )
| ( SV203 @ ( sK21_Xx @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(934,plain,
! [SV204: $i] :
( ( ! [SY2116: $i > $o] :
( ~ ( ~ ( in @ ( sK72_Xx @ SY2116 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SY2116 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SY2116 @ ( sK72_Xx @ SY2116 @ SV204 ) )
| ~ ~ ( ~ ( SY2116 @ ( sK73_SY1673 @ SY2116 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SY2116 @ SV204 )
!= ( sK73_SY1673 @ SY2116 @ SV204 ) ) ) ) ) ) )
| ! [SY2117: $i] :
( ~ ( SY2116 @ SY2117 )
| ~ ( in @ SY2117 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SX2: $i] : ( SY2116 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(935,plain,
! [SV205: $i] :
( ( ! [SY2119: $i,SY2120: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2120 @ SY2119 @ SV205 ) @ SV205 )
| ~ ~ ( in @ ( SY2120 @ ( sK92_Xx @ SY2120 @ SY2119 @ SV205 ) ) @ SY2119 ) )
| ! [SY2121: $i] :
( ~ ( in @ SY2121 @ SV205 )
| ( ( ap @ SV205 @ SY2119
@ ( lam @ SV205 @ SY2119
@ ^ [SX4: $i] : ( SY2120 @ SX4 ) )
@ SY2121 )
= ( SY2120 @ SY2121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(936,plain,
! [SV206: $i] :
( ( ! [SY2123: $i,SY2124: $i] :
( ~ ( subset @ SY2124 @ ( cartprod @ SV206 @ SY2123 ) )
| ! [SY2125: $i] :
( ~ ( subset @ SY2125 @ ( cartprod @ SV206 @ SY2123 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SY2125 @ SY2124 @ SY2123 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SY2125 @ SY2124 @ SY2123 @ SV206 ) @ SY2123 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SY2125 @ SY2124 @ SY2123 @ SV206 ) @ ( sK83_SY1676 @ SY2125 @ SY2124 @ SY2123 @ SV206 ) ) @ SY2124 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SY2125 @ SY2124 @ SY2123 @ SV206 ) @ ( sK83_SY1676 @ SY2125 @ SY2124 @ SY2123 @ SV206 ) ) @ SY2125 ) ) ) )
| ( subset @ SY2124 @ SY2125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(937,plain,
! [SV207: $i > $o] :
( ( ! [SY2126: $i] :
( ~ ( ~ ( SV207 @ ( sK18_SY55 @ SY2126 @ SV207 ) )
| ~ ( ( SY2126
!= ( sK18_SY55 @ SY2126 @ SV207 ) ) ) )
| ~ ( SV207 @ SY2126 ) )
| ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(938,plain,
! [SV208: $i] :
( ( ! [SY2128: $i,SY2129: $i] :
( ~ ( subset @ SY2129 @ ( cartprod @ SV208 @ SY2128 ) )
| ! [SY2130: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2130 @ SY2129 @ SY2128 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SY2130 @ SY2129 @ SY2128 @ SV208 ) @ SY2128 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SY2130 @ SY2129 @ SY2128 @ SV208 ) @ ( sK78_SY1674 @ SY2130 @ SY2129 @ SY2128 @ SV208 ) ) @ SY2129 )
| ~ ~ ( SY2130 @ ( kpair @ ( sK77_Xx @ SY2130 @ SY2129 @ SY2128 @ SV208 ) @ ( sK78_SY1674 @ SY2130 @ SY2129 @ SY2128 @ SV208 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2129 )
| ( SY2130 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(939,plain,
! [SV209: $i] :
( ( ! [SY2132: $i] :
~ ( in @ SY2132 @ SV209 )
| ~ ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 )
| ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(940,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK53_Xx @ SX1 @ SX0 )
!= ( sK54_SY1668 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK51_SY233 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK51_SY233 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK49_Xx @ SX1 @ SX0 )
!= ( sK50_SY1666 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK47_SY230 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK47_SY230 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(941,plain,
! [SV210: $i] :
( ( ! [SY2134: $i > $o] :
( ~ ( ~ ( in @ ( sK34_Xx @ SY2134 @ SV210 ) @ SV210 )
| ~ ( SY2134 @ ( sK34_Xx @ SY2134 @ SV210 ) ) )
| ! [SY2135: $i] :
( ~ ( SY2134 @ SY2135 )
| ~ ( in @ SY2135 @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(942,plain,
! [SV211: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) )
| ~ ( in @ emptyset @ SV211 )
| ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(943,plain,
! [SV212: $i > $o] :
( ( ! [SY2137: $i] :
~ ( ~ ( ( ( sK45_Xy @ SY2137 @ SV212 )
!= SY2137 )
| ~ ( SV212 @ ( sK45_Xy @ SY2137 @ SV212 ) ) )
| ~ ( ( ( sK45_Xy @ SY2137 @ SV212 )
= SY2137 )
| ( SV212 @ ( sK45_Xy @ SY2137 @ SV212 ) ) ) )
| ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(944,plain,
! [SV213: $i] :
( ( ! [SY2139: $o,SY2140: $i] :
( ~ ( in @ SY2140 @ SV213 )
| ! [SY2141: $i] :
( ~ ( in @ SY2141 @ SV213 )
| SY2139
| ( ( dsetconstr @ SV213
@ ^ [SX4: $i] :
( ~ ( ~ SY2139
| ( SX4 != SY2140 ) )
| ~ ( ~ ~ SY2139
| ( SX4 != SY2141 ) ) ) )
= ( setadjoin @ SY2141 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(945,plain,
! [SV214: $i > $o] :
( ( ! [SY2143: $i] :
( ~ ( ~ ( SV214 @ ( sK31_SY140 @ SY2143 @ SV214 ) )
| ~ ( ( SY2143
!= ( sK31_SY140 @ SY2143 @ SV214 ) ) ) )
| ~ ( SV214 @ SY2143 ) )
| ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(946,plain,
! [SV215: $i] :
( ( ! [SY2146: $i] :
( ~ ( ~ ( in @ ( sK63_Xx @ SY2146 @ SV215 ) @ SV215 )
| ~ ~ ( in @ ( sK63_Xx @ SY2146 @ SV215 ) @ SY2146 ) )
| ( subset @ SV215 @ SY2146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(947,plain,
! [SV216: $i] :
( ( ! [SY2147: $i,SY2148: $i] :
( ~ ( subset @ SY2148 @ ( cartprod @ SV216 @ SY2147 ) )
| ! [SY2149: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SY2149 @ SY2148 @ SY2147 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SY2149 @ SY2148 @ SY2147 @ SV216 ) @ SY2147 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2149 @ SY2148 @ SY2147 @ SV216 ) @ ( sK80_SY1675 @ SY2149 @ SY2148 @ SY2147 @ SV216 ) ) @ SY2148 )
| ~ ~ ( SY2149 @ ( kpair @ ( sK79_Xx @ SY2149 @ SY2148 @ SY2147 @ SV216 ) @ ( sK80_SY1675 @ SY2149 @ SY2148 @ SY2147 @ SV216 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2148 )
| ( SY2149 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(948,plain,
! [SV217: $i] :
( ( ! [SY2151: $i,SY2152: $i] :
( ~ ( in @ SY2152 @ ( setadjoin @ SV217 @ SY2151 ) )
| ~ ( ~ ~ ( ~ ( ( SY2152 = SV217 )
| ( in @ SY2152 @ SY2151 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY2152 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY2152 @ SY2151 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(949,plain,
! [SV218: $i] :
( ( ~ ( ~ ! [SY2157: $i > $o,SY2158: $i] :
( ~ ( in @ SY2158 @ SV218 )
| ~ ( SY2157 @ SY2158 )
| ( in @ SY2158
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2157 @ SX3 ) ) ) )
| ~ ! [SY2160: $i > $o,SY2161: $i] :
( ~ ( in @ SY2161 @ SV218 )
| ~ ( in @ SY2161
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2160 @ SX3 ) ) )
| ( SY2160 @ SY2161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(950,plain,
! [SV219: $i] :
( ( ! [SY2163: $i] :
( ~ ( in @ SY2163 @ ( setunion @ SV219 ) )
| ! [SY2164: $o] :
( ~ ( ~ ( in @ SY2163 @ ( sK29_B @ SY2164 @ SY2163 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SY2164 @ SY2163 @ SV219 ) @ SV219 )
| ~ ~ SY2164 ) )
| SY2164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(951,plain,
! [SV220: $i > $o] :
( ( ! [SY2165: $i > $o] :
( ~ ( ( ( sK58_Xx @ SY2165 @ SV220 )
!= ( sK59_SY1669 @ SY2165 @ SV220 ) )
| ~ ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SY2165 @ SV220 ) )
| ~ ( SY2165 @ ( sK59_SY1669 @ SY2165 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SY2165 @ SV220 ) )
| ( SY2165 @ ( sK59_SY1669 @ SY2165 @ SV220 ) ) ) ) )
| ! [SY2166: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2166 @ SY2165 @ SV220 ) )
| ~ ( ( SY2166
!= ( sK57_SY255 @ SY2166 @ SY2165 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2166 ) )
| ! [SY2167: $i] :
( ~ ( ~ ( SY2165 @ ( sK56_SY258 @ SY2167 @ SY2165 @ SV220 ) )
| ~ ( ( SY2167
!= ( sK56_SY258 @ SY2167 @ SY2165 @ SV220 ) ) ) )
| ~ ( SY2165 @ SY2167 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SX2: $i] : ( SY2165 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(952,plain,
! [SV221: $i] :
( ( ! [SY2170: $o,SY2171: $i] :
( ~ ( in @ SY2171 @ SV221 )
| ! [SY2172: $i] :
( ~ ( in @ SY2172 @ SV221 )
| ~ SY2170
| ( ( dsetconstr @ SV221
@ ^ [SX4: $i] :
( ~ ( ~ SY2170
| ( SX4 != SY2171 ) )
| ~ ( ~ ~ SY2170
| ( SX4 != SY2172 ) ) ) )
= ( setadjoin @ SY2171 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(953,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(954,plain,
! [SV1: $i,SV222: $i] :
( ( ~ ( in @ SV222 @ ( powerset @ SV1 ) )
| ( in @ ( powerset @ SV222 ) @ ( powerset @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(955,plain,
! [SV2: $i,SV223: $i] :
( ( ~ ( in @ SV223 @ ( powerset @ SV2 ) )
| ! [SY2174: $i] :
( ~ ( in @ SY2174 @ ( powerset @ SV2 ) )
| ( in @ ( binunion @ SV223 @ SY2174 ) @ ( powerset @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(956,plain,
! [SV3: $i,SV224: $i] :
( ( ~ ( in @ SV224 @ ( powerset @ SV3 ) )
| ! [SY2175: $i] :
( ~ ( in @ SY2175 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV224 @ SY2175 ) @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(957,plain,
! [SV225: $o,SV4: $i] :
( ( ! [SY2176: $i] :
( ~ ( in @ SY2176 @ SV4 )
| ! [SY2177: $i] :
( ~ ( in @ SY2177 @ SV4 )
| ( in @ ( if @ SV4 @ SV225 @ SY2176 @ SY2177 ) @ ( setadjoin @ SY2176 @ ( setadjoin @ SY2177 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[725]) ).
thf(958,plain,
! [SV4: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV4 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV4 )
| ( in @ ( if @ SV4 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[725]) ).
thf(959,plain,
! [SV4: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV4 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV4 )
| ( in @ ( if @ SV4 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[725]) ).
thf(960,plain,
! [SV226: $o,SV5: $i] :
( ( ! [SY2178: $i] :
( ~ ( in @ SY2178 @ SV5 )
| ! [SY2179: $i] :
( ~ ( in @ SY2179 @ SV5 )
| SV226
| ( ( if @ SV5 @ SV226 @ SY2178 @ SY2179 )
= SY2179 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[726]) ).
thf(961,plain,
! [SV5: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV5 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV5 )
| $true
| ( ( if @ SV5 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[726]) ).
thf(962,plain,
! [SV5: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV5 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV5 )
| $false
| ( ( if @ SV5 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[726]) ).
thf(963,plain,
! [SV227: $o,SV6: $i] :
( ( ! [SY2180: $i] :
( ~ ( in @ SY2180 @ SV6 )
| ! [SY2181: $i] :
( ~ ( in @ SY2181 @ SV6 )
| ~ SV227
| ( ( if @ SV6 @ SV227 @ SY2180 @ SY2181 )
= SY2180 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[727]) ).
thf(964,plain,
! [SV6: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV6 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV6 )
| ~ $true
| ( ( if @ SV6 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[727]) ).
thf(965,plain,
! [SV6: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV6 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV6 )
| ~ $false
| ( ( if @ SV6 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[727]) ).
thf(966,plain,
! [SV7: $i] :
( ( ( ~ ( singleton @ SV7 ) )
= $true )
| ( ( ! [SY1693: $i] :
( ~ ( in @ SY1693 @ SV7 )
| ( ( setunion @ SV7 )
= SY1693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(967,plain,
! [SV228: $o,SV8: $i] :
( ( ! [SY2182: $i] :
( ~ ( in @ SY2182 @ SV8 )
| ! [SY2183: $i] :
( ~ ( in @ SY2183 @ SV8 )
| ( in @ ( if @ SV8 @ SV228 @ SY2182 @ SY2183 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(968,plain,
! [SV8: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV8 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV8 )
| ( in @ ( if @ SV8 @ $true @ SX0 @ SX1 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(969,plain,
! [SV8: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV8 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV8 )
| ( in @ ( if @ SV8 @ $false @ SX0 @ SX1 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[729]) ).
thf(970,plain,
! [SV229: $i,SV9: $i] :
( ( ! [SY2184: $i] :
( ~ ( in @ SY2184 @ ( funcSet @ SV9 @ SV229 ) )
| ( ( lam @ SV9 @ SV229
@ ^ [SY2185: $i] : ( ap @ SV9 @ SV229 @ SY2184 @ SY2185 ) )
= SY2184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(971,plain,
! [SV230: $i,SV10: $i] :
( ( ! [SY2186: $i] :
( ~ ( func @ SV10 @ SV230 @ SY2186 )
| ( ( lam @ SV10 @ SV230
@ ^ [SY2187: $i] : ( ap @ SV10 @ SV230 @ SY2186 @ SY2187 ) )
= SY2186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(972,plain,
! [SV11: $i] :
( ( ( ! [SY1703: $i,SY1704: $i] :
~ ( func @ SV11 @ SY1703 @ SY1704 ) )
= $true )
| ( ( ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(973,plain,
! [SV12: $i] :
( ( ( ! [SY1706: $i,SY1707: $i] :
~ ( in @ SY1707 @ ( funcSet @ SV12 @ SY1706 ) ) )
= $true )
| ( ( ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(974,plain,
! [SV231: $i,SV13: $i] :
( ( ! [SY2188: $i] :
( ~ ( in @ SY2188 @ ( funcSet @ SV13 @ SV231 ) )
| ! [SY2189: $i] :
( ~ ( in @ SY2189 @ SV13 )
| ! [SY2190: $i] :
( ~ ( in @ SY2190 @ SV231 )
| ~ ( in @ ( kpair @ SY2189 @ SY2190 ) @ SY2188 )
| ( ( ap @ SV13 @ SV231 @ SY2188 @ SY2189 )
= SY2190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(975,plain,
! [SV232: $i,SV14: $i] :
( ( ! [SY2191: $i] :
( ~ ( func @ SV14 @ SV232 @ SY2191 )
| ! [SY2192: $i] :
( ~ ( in @ SY2192 @ SV14 )
| ! [SY2193: $i] :
( ~ ( in @ SY2193 @ SV232 )
| ~ ( in @ ( kpair @ SY2192 @ SY2193 ) @ SY2191 )
| ( ( ap @ SV14 @ SV232 @ SY2191 @ SY2192 )
= SY2193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(976,plain,
! [SV233: $i,SV15: $i] :
( ( ! [SY2194: $i] :
( ~ ( in @ SY2194 @ ( funcSet @ SV15 @ SV233 ) )
| ! [SY2195: $i] :
( ~ ( in @ SY2195 @ SV15 )
| ( in @ ( kpair @ SY2195 @ ( ap @ SV15 @ SV233 @ SY2194 @ SY2195 ) ) @ SY2194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(977,plain,
! [SV234: $i,SV16: $i] :
( ( ! [SY2196: $i] :
( ~ ( func @ SV16 @ SV234 @ SY2196 )
| ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SV16 )
| ( in @ ( kpair @ SY2197 @ ( ap @ SV16 @ SV234 @ SY2196 @ SY2197 ) ) @ SY2196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(978,plain,
! [SV235: $i > $o,SV17: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
| ! [SY2199: $i] :
( ~ ( in @ SY2199 @ SV17 )
| ! [SY2200: $i] :
( ~ ( in @ SY2200 @ SV17 )
| ~ ( SV235 @ SY2199 )
| ~ ( SV235 @ SY2200 )
| ( SY2199 = SY2200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(979,plain,
! [SV236: $i,SV18: $i] :
( ( ! [SY2201: $i] :
( ~ ( func @ SV18 @ SV236 @ SY2201 )
| ( in @ SY2201 @ ( funcSet @ SV18 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(980,plain,
! [SV237: $i,SV19: $i] :
( ( ! [SY2202: $i] :
( ~ ( in @ SY2202 @ ( funcSet @ SV19 @ SV237 ) )
| ! [SY2203: $i] :
( ~ ( in @ SY2203 @ SV19 )
| ( in @ ( ap @ SV19 @ SV237 @ SY2202 @ SY2203 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(981,plain,
! [SV238: $i,SV20: $i] :
( ( ! [SY2204: $i] :
( ~ ( in @ SY2204 @ ( funcSet @ SV20 @ SV238 ) )
| ( func @ SV20 @ SV238 @ SY2204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(982,plain,
! [SV239: $i,SV21: $i] :
( ( ! [SY2205: $i] :
( ~ ( func @ SV21 @ SV239 @ SY2205 )
| ! [SY2206: $i] :
( ~ ( in @ SY2206 @ SV21 )
| ( in @ ( ap @ SV21 @ SV239 @ SY2205 @ SY2206 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(983,plain,
! [SV240: $i,SV22: $i] :
( ( ! [SY2207: $i] :
( ~ ( func @ SV22 @ SV240 @ SY2207 )
| ! [SY2208: $i] :
( ~ ( in @ SY2208 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [Xy: $i] : ( in @ ( kpair @ SY2208 @ Xy ) @ SY2207 ) ) )
@ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(984,plain,
! [SV241: $i,SV23: $i] :
( ( ! [SY2210: $i] :
( ~ ( func @ SV23 @ SV241 @ SY2210 )
| ! [SY2211: $i] :
( ~ ( in @ SY2211 @ SV23 )
| ( singleton
@ ( dsetconstr @ SV241
@ ^ [Xy: $i] : ( in @ ( kpair @ SY2211 @ Xy ) @ SY2210 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(985,plain,
! [SV242: $i,SV24: $i] :
( ( ! [SY2213: $i > $i > $o,SY2214: $i,SY2215: $i] :
( ~ ( in @ ( kpair @ SY2214 @ SY2215 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [Xz: $i,Xu: $i] : ( SY2213 @ Xz @ Xu ) ) )
| ( SY2213 @ SY2214 @ SY2215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(986,plain,
! [SV243: $i,SV25: $i] :
( ( ! [SY2218: $i > $i > $o,SY2219: $i,SY2220: $i] :
( ~ ( in @ ( kpair @ SY2219 @ SY2220 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [Xz: $i,Xu: $i] : ( SY2218 @ Xz @ Xu ) ) )
| ( in @ SY2220 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(987,plain,
! [SV244: $i,SV26: $i] :
( ( ! [SY2223: $i > $i > $o,SY2224: $i] :
( ! [SY2225: $i] :
~ ( in @ ( kpair @ SY2224 @ SY2225 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [Xz: $i,Xu: $i] : ( SY2223 @ Xz @ Xu ) ) )
| ( in @ SY2224 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(988,plain,
! [SV245: $i,SV27: $i] :
( ( ! [SY2228: $i > $i > $o,SY2229: $i] :
( ~ ( in @ SY2229 @ SV27 )
| ! [SY2230: $i] :
( ~ ( in @ SY2230 @ SV245 )
| ~ ( in @ ( kpair @ SY2229 @ SY2230 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [Xz: $i,Xu: $i] : ( SY2228 @ Xz @ Xu ) ) )
| ( SY2228 @ SY2229 @ SY2230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(989,plain,
! [SV246: $i,SV28: $i] :
( ( ! [SY2233: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV28 @ SV246
@ ^ [Xx: $i,Xy: $i] : ( SY2233 @ Xx @ Xy ) )
@ ( cartprod @ SV28 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(990,plain,
! [SV247: $i,SV29: $i] :
( ( ! [SY2236: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV29 @ SV247
@ ^ [Xx: $i,Xy: $i] : ( SY2236 @ Xx @ Xy ) )
@ ( cartprod @ SV29 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(991,plain,
! [SV248: $i,SV30: $i] :
( ( ! [SY2239: $i > $i > $o,SY2240: $i] :
( ~ ( in @ SY2240 @ SV30 )
| ! [SY2241: $i] :
( ~ ( in @ SY2241 @ SV248 )
| ~ ( SY2239 @ SY2240 @ SY2241 )
| ( in @ ( kpair @ SY2240 @ SY2241 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [Xz: $i,Xu: $i] : ( SY2239 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(992,plain,
! [SV249: $i,SV31: $i] :
( ( ! [SY2244: $i] :
( ~ ( in @ SY2244 @ ( cartprod @ SV31 @ SV249 ) )
| ( ( kpair @ ( kfst @ SY2244 ) @ ( ksnd @ SY2244 ) )
= SY2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(993,plain,
! [SV250: $i,SV32: $i] :
( ( ! [SY2245: $i] :
( ~ ( in @ SY2245 @ SV32 )
| ! [SY2246: $i] :
( ~ ( in @ SY2246 @ SV250 )
| ( ( ksnd @ ( kpair @ SY2245 @ SY2246 ) )
= SY2246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(994,plain,
! [SV251: $i,SV33: $i] :
( ( ! [SY2247: $i] :
( ~ ( in @ SY2247 @ SV33 )
| ! [SY2248: $i] :
( ~ ( in @ SY2248 @ SV251 )
| ( ( kfst @ ( kpair @ SY2247 @ SY2248 ) )
= SY2247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(995,plain,
! [SV34: $i] :
( ( ( ! [SY1791: $i] :
~ ( in @ SY1791 @ SV34 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(996,plain,
! [SV252: $i,SV35: $i] :
( ( ! [SY2249: $i,SY2250: $i] :
( ~ ( in @ ( kpair @ SY2249 @ SY2250 ) @ ( cartprod @ SV35 @ SV252 ) )
| ( in @ SY2250 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(997,plain,
! [SV253: $i,SV36: $i] :
( ( ! [SY2251: $i] :
( ! [SY2252: $i] :
~ ( in @ ( kpair @ SY2251 @ SY2252 ) @ ( cartprod @ SV36 @ SV253 ) )
| ( in @ SY2251 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(998,plain,
! [SV254: $i,SV37: $i] :
( ( ! [SY2253: $i] :
( ~ ( in @ SY2253 @ ( cartprod @ SV37 @ SV254 ) )
| ( in @ ( ksnd @ SY2253 ) @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(999,plain,
! [SV38: $i] :
( ( ( ~ ( iskpair @ SV38 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV38 ) @ ( ksnd @ SV38 ) )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(1000,plain,
! [SV255: $i,SV39: $i] :
( ( ( ksnd @ ( kpair @ SV39 @ SV255 ) )
= SV255 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1001,plain,
! [SV40: $i] :
( ( ( ~ ( iskpair @ SV40 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV40 )
@ ^ [SY1803: $i] :
( SV40
= ( kpair @ ( kfst @ SV40 ) @ SY1803 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(1002,plain,
! [SV256: $i,SV41: $i] :
( ( ! [SY2254: $i,SY2255: $i] :
( ( ( kpair @ SV41 @ SV256 )
!= ( kpair @ SY2254 @ SY2255 ) )
| ( SV256 = SY2255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1003,plain,
! [SV257: $i,SV42: $i] :
( ( ! [SY2256: $i,SY2257: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV257 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2256 @ ( setadjoin @ SY2257 @ emptyset ) ) @ emptyset ) ) )
| ( SV257 = SY2257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1004,plain,
! [SV258: $i,SV43: $i] :
( ( ! [SY2258: $i] :
( ( setadjoin @ SV43 @ ( setadjoin @ SV258 @ emptyset ) )
!= ( setadjoin @ SY2258 @ emptyset ) )
| ( SV43 = SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1005,plain,
! [SV259: $i,SV44: $i] :
( ( ! [SY2259: $i,SY2260: $i] :
( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2259 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2259 @ ( setadjoin @ SY2260 @ emptyset ) ) @ emptyset ) ) )
| ( SY2259 != SY2260 )
| ( SV259 = SY2260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1006,plain,
! [SV260: $i,SV45: $i] :
( ( ( SV45 != SV260 )
| ( ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV45 @ ( setadjoin @ SV260 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1007,plain,
! [SV261: $i,SV46: $i] :
( ( ( SV46 != SV261 )
| ( ( setadjoin @ SV46 @ ( setadjoin @ SV261 @ emptyset ) )
= ( setadjoin @ SV46 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1008,plain,
! [SV262: $i,SV47: $i] :
( ( ! [SY2261: $i] :
( ! [SY2262: $i] :
( ( kpair @ SV47 @ SV262 )
!= ( kpair @ SY2261 @ SY2262 ) )
| ( SV47 = SY2261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1009,plain,
! [SV263: $i,SV48: $i] :
( ( ! [SY2263: $i] :
( ! [SY2264: $i] :
( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2263 @ ( setadjoin @ SY2264 @ emptyset ) ) @ emptyset ) ) )
| ( SV48 = SY2263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1010,plain,
! [SV264: $i,SV49: $i] :
( ( ! [SY2265: $i] :
( ~ ( in @ SY2265 @ ( cartprod @ SV49 @ SV264 ) )
| ( in @ ( kfst @ SY2265 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1011,plain,
! [SV265: $i,SV50: $i] :
( ( ( kfst @ ( kpair @ SV50 @ SV265 ) )
= SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1012,plain,
! [SV51: $i] :
( ( ( ~ ( singleton @ SV51 ) )
= $true )
| ( ( in @ ( setunion @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(1013,plain,
! [SV52: $i] :
( ( ( ~ ( iskpair @ SV52 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV52 )
@ ^ [SY1826: $i] : ( in @ ( setadjoin @ SY1826 @ emptyset ) @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(1014,plain,
! [SV266: $i,SV53: $i] :
( ( ! [SY2266: $i] :
( ~ ( in @ ( setadjoin @ SY2266 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV266 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SY2266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1015,plain,
! [SV267: $i,SV54: $i] :
( ( ( ( setadjoin @ SV54 @ emptyset )
!= ( setadjoin @ SV267 @ emptyset ) )
| ( SV54 = SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1016,plain,
! [SV268: $i,SV58: $i] :
( ( ! [SY2267: $i] :
( ~ ( in @ SY2267 @ ( cartprod @ SV58 @ SV268 ) )
| ( iskpair @ SY2267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1017,plain,
! [SV269: $i,SV59: $i] :
( ( ! [SY2268: $i] :
( ~ ( in @ SY2268 @ SV59 )
| ! [SY2269: $i] :
( ~ ( in @ SY2269 @ SV269 )
| ( in @ ( kpair @ SY2268 @ SY2269 ) @ ( cartprod @ SV59 @ SV269 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1018,plain,
! [SV270: $i,SV60: $i] :
( ( ! [SY2270: $i] :
( ~ ( in @ SY2270 @ SV60 )
| ! [SY2271: $i] :
( ~ ( in @ SY2271 @ SV270 )
| ( in @ ( kpair @ SY2270 @ SY2271 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1019,plain,
! [SV271: $i,SV61: $i] :
( ( ! [SY2272: $i] :
( ~ ( in @ SY2272 @ SV61 )
| ! [SY2273: $i] :
( ~ ( in @ SY2273 @ SV271 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2272 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2272 @ ( setadjoin @ SY2273 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1020,plain,
! [SV272: $i,SV62: $i] :
( ( ! [SY2274: $i] :
( ~ ( in @ SY2274 @ SV62 )
| ! [SY2275: $i] :
( ~ ( in @ SY2275 @ SV272 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2274 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2274 @ ( setadjoin @ SY2275 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1021,plain,
! [SV273: $i,SV63: $i] :
( ( ! [SY2276: $i] :
( ~ ( in @ SY2276 @ SV63 )
| ! [SY2277: $i] :
( ~ ( in @ SY2277 @ SV273 )
| ( in @ ( setadjoin @ SY2276 @ ( setadjoin @ SY2277 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1022,plain,
! [SV274: $i,SV64: $i] :
( ( ! [SY2278: $i] :
( ~ ( in @ SY2278 @ SV64 )
| ! [SY2279: $i] :
( ~ ( in @ SY2279 @ SV274 )
| ( subset @ ( setadjoin @ SY2278 @ ( setadjoin @ SY2279 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1023,plain,
! [SV275: $i,SV65: $i] :
( ( ! [SY2280: $i] :
( ~ ( in @ SY2280 @ ( setadjoin @ SV65 @ ( setadjoin @ SV275 @ emptyset ) ) )
| ( SY2280 = SV65 )
| ( SY2280 = SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1024,plain,
! [SV276: $i,SV66: $i] :
( ( ! [SY2281: $i] :
( ~ ( in @ SY2281 @ SV66 )
| ( in @ ( setadjoin @ SY2281 @ emptyset ) @ ( powerset @ ( binunion @ SV66 @ SV276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1025,plain,
! [SV67: $i,SV277: $i] :
( ( ~ ( in @ SV277 @ SV67 )
| ( in @ ( setadjoin @ SV277 @ emptyset ) @ ( powerset @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1026,plain,
! [SV68: $i,SV278: $i] :
( ( ~ ( in @ SV278 @ SV68 )
| ( subset @ ( setadjoin @ SV278 @ emptyset ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1027,plain,
! [SV279: $i,SV69: $i] :
( ( iskpair @ ( kpair @ SV69 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1028,plain,
! [SV280: $i,SV70: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SV280 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1029,plain,
! [SV71: $i,SV281: $i] :
( ( in @ SV281 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV71 @ ( setadjoin @ SV281 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1030,plain,
! [SV282: $i,SV72: $i] :
( ( in @ SV72 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV72 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV72 @ ( setadjoin @ SV282 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1031,plain,
! [SV73: $i,SV283: $i] :
( ( in @ SV283 @ ( setadjoin @ SV73 @ ( setadjoin @ SV283 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1032,plain,
! [SV284: $i,SV74: $i] :
( ( ! [SY2282: $i] :
( ( in @ SY2282 @ SV74 )
| ( in @ SY2282 @ SV284 )
| ~ ( in @ SY2282 @ ( symdiff @ SV74 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1033,plain,
! [SV285: $i,SV75: $i] :
( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV75 )
| ~ ( in @ SY2283 @ SV285 )
| ~ ( in @ SY2283 @ ( symdiff @ SV75 @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1034,plain,
! [SV286: $i,SV76: $i] :
( ( ! [SY2284: $i] :
( ( in @ SY2284 @ SV76 )
| ~ ( in @ SY2284 @ SV286 )
| ( in @ SY2284 @ ( symdiff @ SV76 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1035,plain,
! [SV287: $i,SV77: $i] :
( ( ! [SY2285: $i] :
( ~ ( in @ SY2285 @ SV77 )
| ( in @ SY2285 @ SV287 )
| ( in @ SY2285 @ ( symdiff @ SV77 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1036,plain,
! [SV288: $i,SV78: $i] :
( ( ( ( setminus @ SV78 @ SV288 )
!= emptyset )
| ( subset @ SV78 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1037,plain,
! [SV289: $i,SV79: $i] :
( ( subset @ ( setminus @ SV79 @ SV289 ) @ SV79 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1038,plain,
! [SV80: $i,SV290: $i] :
( ( ! [SY2286: $i] :
( ~ ( in @ SY2286 @ SV290 )
| ~ ( in @ SY2286 @ ( setminus @ SV80 @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1039,plain,
! [SV291: $i,SV81: $i] :
( ( ! [SY2287: $i] :
( ( in @ SY2287 @ SV81 )
| ~ ( in @ SY2287 @ ( setminus @ SV81 @ SV291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1040,plain,
! [SV292: $i,SV82: $i] :
( ( ! [SY2288: $i] :
( ( in @ SY2288 @ ( setminus @ SV82 @ SV292 ) )
| ( in @ SY2288 @ SV292 )
| ~ ( in @ SY2288 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1041,plain,
! [SV293: $i,SV83: $i] :
( ( ! [SY2289: $i] :
( ( in @ SY2289 @ ( setminus @ SV83 @ SV293 ) )
| ~ ( in @ SY2289 @ SV83 )
| ( in @ SY2289 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1042,plain,
! [SV294: $i,SV84: $i] :
( ( ~ ( subset @ SV84 @ SV294 )
| ( ( setminus @ SV84 @ SV294 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1043,plain,
! [SV295: $i,SV85: $i] :
( ( ! [SY2290: $i] :
( ~ ( in @ SY2290 @ ( setminus @ SV85 @ SV295 ) )
| ~ ( in @ SY2290 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1044,plain,
! [SV296: $i,SV86: $i] :
( ( ! [SY2291: $i] :
( ~ ( in @ SY2291 @ ( setminus @ SV86 @ SV296 ) )
| ( in @ SY2291 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1045,plain,
! [SV297: $i,SV87: $i] :
( ( ! [SY2292: $i] :
( ~ ( in @ SY2292 @ SV87 )
| ( in @ SY2292 @ SV297 )
| ( in @ SY2292 @ ( setminus @ SV87 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1046,plain,
! [SV298: $i,SV88: $i] :
( ( ! [SY2293: $i] :
( ( binintersect @ SV88 @ ( binunion @ SV298 @ SY2293 ) )
= ( binunion @ ( binintersect @ SV88 @ SV298 ) @ ( binintersect @ SV88 @ SY2293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1047,plain,
! [SV299: $i,SV89: $i] :
( ( ( ( binintersect @ SV89 @ SV299 )
!= SV89 )
| ( subset @ SV89 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1048,plain,
! [SV90: $i,SV300: $i] :
( ( ~ ( subset @ SV300 @ SV90 )
| ( ( binintersect @ SV90 @ SV300 )
= SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1049,plain,
! [SV301: $i,SV91: $i] :
( ( subset @ ( binintersect @ SV91 @ SV301 ) @ SV301 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1050,plain,
! [SV302: $i,SV92: $i] :
( ( ! [SY2294: $i] :
( ~ ( in @ SY2294 @ ( binintersect @ SV92 @ SV302 ) )
| ( in @ SY2294 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1051,plain,
! [SV303: $i,SV93: $i] :
( ( ( ( binintersect @ SV93 @ SV303 )
!= SV303 )
| ( subset @ SV303 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1052,plain,
! [SV304: $i,SV94: $i] :
( ( ~ ( subset @ SV94 @ SV304 )
| ( ( binintersect @ SV94 @ SV304 )
= SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1053,plain,
! [SV305: $i,SV95: $i] :
( ( subset @ ( binintersect @ SV95 @ SV305 ) @ SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1054,plain,
! [SV306: $i,SV96: $i] :
( ( ! [SY2295: $i] :
( ~ ( in @ SY2295 @ ( binintersect @ SV96 @ SV306 ) )
| ( in @ SY2295 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1055,plain,
! [SV307: $i,SV97: $i] :
( ( ! [SY2296: $i] :
( ~ ( subset @ SY2296 @ SV97 )
| ~ ( subset @ SY2296 @ SV307 )
| ( subset @ SY2296 @ ( binintersect @ SV97 @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1056,plain,
! [SV308: $i,SV98: $i] :
( ( ! [SY2297: $i] :
( ~ ( in @ SY2297 @ SV98 )
| ~ ( in @ SY2297 @ SV308 )
| ( in @ SY2297 @ ( binintersect @ SV98 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1057,plain,
! [SV99: $i,SV309: $i] :
( ( subset @ SV309 @ ( binunion @ SV99 @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1058,plain,
! [SV310: $i,SV100: $i] :
( ( subset @ SV100 @ ( binunion @ SV100 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1059,plain,
! [SV311: $i,SV101: $i] :
( ( ! [SY2298: $i] :
( ~ ( in @ SY2298 @ ( binunion @ SV101 @ SV311 ) )
| ( in @ SY2298 @ SV101 )
| ( in @ SY2298 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1060,plain,
! [SV102: $i,SV312: $i] :
( ( ! [SY2299: $i] :
( ~ ( in @ SY2299 @ SV312 )
| ( in @ SY2299 @ ( binunion @ SV102 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1061,plain,
! [SV103: $i,SV313: $i] :
( ( in @ SV313 @ ( setadjoin @ SV103 @ ( setadjoin @ SV313 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1062,plain,
! [SV314: $i,SV104: $i] :
( ( ! [SY2300: $i] :
( ~ ( in @ SY2300 @ SV104 )
| ( in @ SY2300 @ ( binunion @ SV104 @ SV314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1063,plain,
! [SV315: $i > $o,SV105: $i] :
( ( subset
@ ( dsetconstr @ SV105
@ ^ [SY2301: $i] : ( SV315 @ SY2301 ) )
@ SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1064,plain,
! [SV316: $i > $o,SV106: $i] :
( ( in
@ ( dsetconstr @ SV106
@ ^ [SY2302: $i] : ( SV316 @ SY2302 ) )
@ ( powerset @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1065,plain,
! [SV317: $i,SV107: $i] :
( ( ~ ( subset @ SV107 @ SV317 )
| ( subset @ ( powerset @ SV107 ) @ ( powerset @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1066,plain,
! [SV109: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ ( powerset @ SV109 ) )
| ( subset @ SV318 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1067,plain,
! [SV110: $i,SV319: $i] :
( ( ~ ( subset @ SV319 @ SV110 )
| ( in @ SV319 @ ( powerset @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1068,plain,
! [SV111: $i] :
( ( ( ~ ( subset @ SV111 @ emptyset ) )
= $true )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(1069,plain,
! [SV320: $i,SV112: $i] :
( ( ~ ( subset @ SV112 @ SV320 )
| ~ ( subset @ SV320 @ SV112 )
| ( SV112 = SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1070,plain,
! [SV321: $i,SV113: $i] :
( ( ~ ( subset @ SV113 @ SV321 )
| ( in @ SV113 @ ( powerset @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1071,plain,
! [SV322: $i,SV114: $i] :
( ( ! [SY2303: $i] :
( ~ ( subset @ SV114 @ SY2303 )
| ( subset @ SV114 @ ( setadjoin @ SV322 @ SY2303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1072,plain,
! [SV115: $i,SV323: $i] :
( ( subset @ SV323 @ ( setadjoin @ SV115 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1073,plain,
! [SV324: $i,SV116: $i] :
( ( ~ ( subset @ SV116 @ SV324 )
| ! [SY2304: $i] :
( ~ ( subset @ SV324 @ SY2304 )
| ( subset @ SV116 @ SY2304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1074,plain,
! [SV325: $i,SV118: $i] :
( ( ! [SY2305: $i] :
( ~ ( in @ SY2305 @ SV118 )
| ( in @ SY2305 @ SV325 )
| ( SV118 != SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1075,plain,
! [SV326: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV326 )
| ( SV119 != SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1076,plain,
! [SV327: $i,SV120: $i] :
( ( ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV120 )
| ( in @ SY2306 @ SV327 )
| ~ ( subset @ SV120 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1077,plain,
! [SV328: $i,SV121: $i] :
( ( ~ ( subset @ SV121 @ SV328 )
| ! [SY2307: $i] :
( ( in @ SY2307 @ SV328 )
| ~ ( in @ SY2307 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1078,plain,
! [SV329: $i,SV122: $i] :
( ( ~ ( subset @ SV122 @ SV329 )
| ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV122 )
| ( in @ SY2308 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1079,plain,
! [SV330: $i,SV124: $i] :
( ( ( SV124 != SV330 )
| ( subset @ SV124 @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1080,plain,
! [SV331: $i,SV125: $i] :
( ( ( SV125 != SV331 )
| ( subset @ SV331 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1081,plain,
! [SV332: $i,SV126: $i] :
( ( ( SV126 != SV332 )
| ( ( setunion @ SV126 )
= ( setunion @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1082,plain,
! [SV333: $i,SV127: $i] :
( ( ( SV127 != SV333 )
| ( ( powerset @ SV127 )
= ( powerset @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1083,plain,
! [SV334: $i,SV128: $i] :
( ( ( SV128 != SV334 )
| ! [SY2309: $i,SY2310: $i] :
( ( SY2309 != SY2310 )
| ( ( setadjoin @ SV128 @ SY2309 )
= ( setadjoin @ SV334 @ SY2310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1084,plain,
! [SV335: $i,SV129: $i] :
( ( ( SV129 != SV335 )
| ! [SY2311: $i,SY2312: $i] :
( ( SY2311 != SY2312 )
| ~ ( in @ SY2311 @ SV129 )
| ( in @ SY2312 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1085,plain,
! [SV130: $o] :
( ( ( ~ SV130 ) = $true )
| ( ( set2prop @ ( prop2set @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(1086,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(1087,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(1088,plain,
! [SV131: $o] :
( ( ( ~ SV131 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(1089,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(1090,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(1091,plain,
! [SV132: $i > $o,SV336: $i] :
( ( ~ ( in @ SV336 @ emptyset )
| ( SV132 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1092,plain,
! [SV133: $i,SV337: $i > $o] :
( ( ! [SY2313: $i] :
( ~ ( SV337 @ SY2313 )
| ~ ( in @ SY2313 @ SV133 ) )
| ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1093,plain,
! [SV134: $i,SV338: $i] :
( ( in @ SV338 @ ( setadjoin @ SV134 @ ( setadjoin @ SV338 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1094,plain,
! [SV339: $i,SV135: $i] :
( ( in @ SV135 @ ( setadjoin @ SV135 @ ( setadjoin @ SV339 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1095,plain,
! [SV340: $i,SV136: $i] :
( ( ! [SY2315: $i] :
( ~ ( in @ SY2315 @ ( setadjoin @ SV136 @ ( setadjoin @ SV340 @ emptyset ) ) )
| ( SY2315 = SV136 )
| ( SY2315 = SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1096,plain,
! [SV341: $i,SV137: $i] :
( ( ~ ( in @ SV137 @ ( setadjoin @ SV341 @ emptyset ) )
| ( in @ SV341 @ ( setadjoin @ SV137 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1097,plain,
! [SV342: $i,SV138: $i] :
( ( ( SV138 != SV342 )
| ( in @ SV138 @ ( setadjoin @ SV342 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1098,plain,
! [SV343: $i,SV139: $i] :
( ( ( SV139 = SV343 )
| ~ ( in @ SV343 @ ( setadjoin @ SV139 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1099,plain,
! [SV344: $i,SV140: $i] :
( ( ~ ( in @ SV140 @ ( setadjoin @ SV344 @ emptyset ) )
| ( SV140 = SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1100,plain,
! [SV141: $i] :
( ( ( SV141 = emptyset )
= $true )
| ( ( in @ ( sK32_Xx @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1101,plain,
! [SV142: $i,SV345: $i] :
( ( ~ ( in @ SV345 @ SV142 )
| ( in @ SV345 @ ( powerset @ ( setunion @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1102,plain,
! [SV143: $i,SV346: $i] :
( ( ! [SY2316: $i] :
( ~ ( in @ SV346 @ SY2316 )
| ~ ( in @ SY2316 @ SV143 )
| ( in @ SV346 @ ( setunion @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1103,plain,
! [SV144: $i,SV347: $i] :
( ( ~ ( in @ SV347 @ ( powerset @ SV144 ) )
| ! [SY2317: $i] :
( ~ ( in @ SY2317 @ SV347 )
| ( in @ SY2317 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1104,plain,
! [SV348: $i,SV148: $i] :
( ( ! [SY2318: $i] :
( ~ ( in @ SY2318 @ ( setadjoin @ SV148 @ SV348 ) )
| ( SY2318 = SV148 )
| ( in @ SY2318 @ SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1105,plain,
! [SV149: $i,SV349: $i] :
( ( ! [SY2319: $i] :
( ~ ( in @ SY2319 @ SV349 )
| ( in @ SY2319 @ ( setadjoin @ SV149 @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1106,plain,
! [SV350: $i,SV150: $i] :
( ( in @ SV150 @ ( setadjoin @ SV150 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1107,plain,
! [SV151: $i] :
( ( ( ! [SY1967: $i] :
~ ( in @ SY1967 @ SV151 ) )
= $true )
| ( ( SV151 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1108,plain,
! [SV351: $i > $o,SV152: $i] :
( ( ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV152 )
| ~ ( SV351 @ SY2320 )
| ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1109,plain,
! [SV153: $i] :
( ( ( SV153 = emptyset )
= $true )
| ( ( in @ ( sK27_Xx @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1110,plain,
! [SV154: $i] :
( ( ( in @ ( sK26_Xx @ SV154 ) @ SV154 )
= $true )
| ( ( SV154 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1111,plain,
! [SV155: $i] :
( ( ( in @ ( sK25_Xx @ SV155 ) @ SV155 )
= $true )
| ( ( SV155 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1112,plain,
! [SV156: $i] :
( ( in @ SV156 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(1113,plain,
! [SV157: $i] :
( ( in @ SV157 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1114,plain,
! [SV352: $i] :
( ( ( ~ ( in @ SV352 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1115,plain,
! [SV158: $o] :
( ( ( ! [SY1971: $i] :
~ ( in @ SY1971 @ ( prop2set @ SV158 ) ) )
= $true )
| ( SV158 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1116,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(1117,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(1118,plain,
! [SV353: $i > $o,SV159: $i] :
( ( ! [SY2322: $i] :
( ~ ( in @ SY2322
@ ( dsetconstr @ SV159
@ ^ [SY2323: $i] : ( SV353 @ SY2323 ) ) )
| ( SV353 @ SY2322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1119,plain,
! [SV354: $i > $o,SV160: $i] :
( ( ! [SY2324: $i] :
( ~ ( in @ SY2324
@ ( dsetconstr @ SV160
@ ^ [SY2325: $i] : ( SV354 @ SY2325 ) ) )
| ( in @ SY2324 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1120,plain,
! [SV355: $i > $o,SV161: $i] :
( ( ! [SY2326: $i] :
( ~ ( in @ SY2326 @ SV161 )
| ~ ( SV355 @ SY2326 )
| ( in @ SY2326
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1121,plain,
! [SV162: $i] :
( ( ( ~ ( in @ SV162 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV162 @ SV162 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(1122,plain,
! [SV163: $i] :
( ( in @ SV163 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(1123,plain,
! [SV164: $i > $o] :
( ( ( ! [SY1981: $i] :
( ~ ( ~ ( SV164 @ ( sK20_SY72 @ SY1981 @ SV164 ) )
| ~ ( ( SY1981
!= ( sK20_SY72 @ SY1981 @ SV164 ) ) ) )
| ~ ( SV164 @ SY1981 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1124,plain,
! [SV356: $i,SV165: $i] :
( ( ( SV165 != SV356 )
| ~ ( ~ ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) )
| ~ ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1125,plain,
! [SV357: $i,SV166: $i] :
( ( ! [SY2332: $i] :
( ~ ( func @ SV166 @ SV357 @ SY2332 )
| ! [SY2333: $i] :
( ~ ( func @ SV166 @ SV357 @ SY2333 )
| ~ ( ~ ( in @ ( sK81_Xx @ SY2333 @ SY2332 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SY2332 @ ( sK81_Xx @ SY2333 @ SY2332 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SY2333 @ ( sK81_Xx @ SY2333 @ SY2332 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2334: $i] :
( ~ ( in @ SY2334 @ SV166 )
| ! [SY2335: $i] :
( ~ ( in @ SY2335 @ SV357 )
| ~ ( in @ ( kpair @ SY2334 @ SY2335 ) @ SY2333 )
| ( in @ ( kpair @ SY2334 @ SY2335 ) @ SY2332 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1126,plain,
! [SV167: $i,SV358: $i] :
( ( ! [SY2336: $i > $i] :
( ~ ( ~ ( in @ ( sK76_Xx @ SY2336 @ SV358 @ SV167 ) @ SV167 )
| ~ ~ ( in @ ( SY2336 @ ( sK76_Xx @ SY2336 @ SV358 @ SV167 ) ) @ SV358 ) )
| ( in
@ ( lam @ SV167 @ SV358
@ ^ [SX3: $i] : ( SY2336 @ SX3 ) )
@ ( funcSet @ SV167 @ SV358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1127,plain,
! [SV359: $i,SV168: $i] :
( ( ! [SY2338: $i] :
( ~ ( in @ SY2338 @ ( symdiff @ SV168 @ SV359 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY2338 @ SV168 )
| ~ ( in @ SY2338 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY2338 @ SV168 )
| ( in @ SY2338 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY2338 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY2338 @ SV359 )
| ~ ( in @ SY2338 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY2338 @ SV359 )
| ( in @ SY2338 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY2338 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2004: $o] :
( ~ SY2004
| ~ ( in @ SY2338 @ SV168 )
| SY2004 )
| ~ ~ ( ~ ! [SY2346: $o] :
( ~ SY2346
| ( in @ SY2338 @ SV359 )
| SY2346 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1128,plain,
( ( ~ ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1129,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(1130,plain,
! [SV169: $i > $o] :
( ( ( ! [SY2007: $i] :
( ~ ( ~ ( SV169 @ ( sK40_Xy @ SY2007 @ SV169 ) )
| ~ ( ( SY2007
!= ( sK40_Xy @ SY2007 @ SV169 ) ) ) )
| ~ ( SV169 @ SY2007 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1131,plain,
! [SV170: $i] :
( ( ~ ! [SY2009: $i] :
( ~ ( ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SY2009 )
| ~ ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SV170 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2009 )
| ~ ( ~ ! [SY2011: $i] :
( ~ ( in @ SY2011 @ ( sK13_B @ SV170 ) )
| ! [SY2012: $i] :
( ~ ( in @ SY2012 @ SY2011 )
| ( in @ SY2012 @ ( sK15_SY1637 @ SY2009 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2011 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SY2009 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2009 ) )
| ~ ! [SY2013: $i] :
( ~ ( in @ SY2013 @ ( sK15_SY1637 @ SY2009 @ SV170 ) )
| ~ ( in @ SY2013 @ SY2009 ) ) ) ) )
| ~ ~ ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) )
| ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1132,plain,
! [SV360: $i,SV171: $i] :
( ( ! [SY2348: $i] :
( ~ ( in @ SY2348 @ ( funcSet @ SV171 @ SV360 ) )
| ! [SY2349: $i] :
( ~ ( in @ SY2349 @ ( funcSet @ SV171 @ SV360 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SY2349 @ SY2348 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SY2348 @ ( sK89_Xx @ SY2349 @ SY2348 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SY2349 @ ( sK89_Xx @ SY2349 @ SY2348 @ SV360 @ SV171 ) ) ) ) )
| ( SY2348 = SY2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1133,plain,
! [SV172: $i,SV361: $i] :
( ( ~ ( ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV361 ) )
| ( ( binintersect @ SV172 @ SV361 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1134,plain,
! [SV362: $i > $o,SV173: $i] :
( ( ! [SY2350: $i] :
( ~ ( in @ SY2350 @ SV173 )
| ( SV362 @ SY2350 ) )
| ~ ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1135,plain,
! [SV174: $i] :
( ( ~ ! [SY2028: $i,SY2029: $i] :
( ~ ( in @ SY2029 @ ( setadjoin @ SV174 @ SY2028 ) )
| ( SY2029 = SV174 )
| ( in @ SY2029 @ SY2028 ) )
| ~ ~ ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) )
| ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1136,plain,
! [SV363: $i > $o,SV175: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
| ~ ( ~ ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) )
| ~ ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1137,plain,
! [SV364: $i,SV176: $i] :
( ( ! [SY2352: $i] :
( ~ ( subset @ SY2352 @ ( cartprod @ SV176 @ SV364 ) )
| ! [SY2353: $i] :
( ~ ( subset @ SY2353 @ ( cartprod @ SV176 @ SV364 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2353 @ SY2352 @ SV364 @ SV176 ) ) @ SY2352 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2353 @ SY2352 @ SV364 @ SV176 ) ) @ SY2353 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2353 @ SY2352 @ SV364 @ SV176 ) ) @ SY2353 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2353 @ SY2352 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2353 @ SY2352 @ SV364 @ SV176 ) ) @ SY2352 ) ) ) )
| ( SY2352 = SY2353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1138,plain,
! [SV177: $i,SV365: $i] :
( ( ! [SY2354: $i > $i] :
( ~ ( ~ ( in @ ( sK74_Xx @ SY2354 @ SV365 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( SY2354 @ ( sK74_Xx @ SY2354 @ SV365 @ SV177 ) ) @ SV365 ) )
| ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SX3: $i,SX4: $i] :
( ( SY2354 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1139,plain,
! [SV178: $i,SV366: $i] :
( ( ! [SY2357: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2357 @ SV366 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( SY2357 @ ( sK90_Xx @ SY2357 @ SV366 @ SV178 ) ) @ SV366 ) )
| ! [SY2358: $i] :
( ~ ( in @ SY2358 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SX4: $i] : ( SY2357 @ SX4 ) )
@ SY2358 )
= ( SY2357 @ SY2358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1140,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ~ ( ~ ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) ) )
| ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1141,plain,
! [SV368: $i > $o,SV180: $i] :
( ( ! [SY2362: $i] :
( ~ ( in @ SY2362 @ SV180 )
| ( SV368 @ SY2362 ) )
| ~ ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1142,plain,
! [SV181: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( setunion @ SV181 ) )
| ~ ( ~ ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 )
| ~ ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1143,plain,
! [SV182: $i,SV370: $i] :
( ( ~ ( ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
| ~ ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 ) )
| ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1144,plain,
! [SV183: $i,SV371: $i] :
( ( ~ ( ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV183 )
| ~ ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 ) )
| ( subset @ SV183 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1145,plain,
! [SV184: $i > $o] :
( ( ( ! [SY2055: $i] :
( ~ ( ~ ( SV184 @ ( sK46_SY222 @ SY2055 @ SV184 ) )
| ~ ( ( SY2055
!= ( sK46_SY222 @ SY2055 @ SV184 ) ) ) )
| ~ ( SV184 @ SY2055 ) ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1146,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ~ ( ~ ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
| ~ ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 ) )
| ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1147,plain,
! [SV373: $i,SV186: $i] :
( ( ! [SY2364: $i] :
( ~ ( in @ SY2364 @ ( cartprod @ SV186 @ SV373 ) )
| ~ ( ~ ~ ( ( SY2364
!= ( kpair @ ( sK65_Xx @ SY2364 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SY2364 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SY2364 @ SV373 @ SV186 ) @ SV373 ) )
| ~ ( in @ ( sK65_Xx @ SY2364 @ SV373 @ SV186 ) @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1148,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ~ ( ~ ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
| ~ ! [SY2365: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) )
| ~ ( ( SY2365
!= ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SY2365 ) ) )
| ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1149,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ~ ( ~ ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
| ~ ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 ) )
| ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1150,plain,
! [SV189: $i,SV376: $i] :
( ( ~ ( ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV376 )
| ~ ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 ) )
| ( in @ SV376 @ ( powerset @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1151,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) )
| ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1152,plain,
! [SV378: $i,SV191: $i] :
( ( ! [SY2378: $i] :
( ~ ( func @ SV191 @ SV378 @ SY2378 )
| ! [SY2379: $i] :
( ~ ( func @ SV191 @ SV378 @ SY2379 )
| ~ ( ~ ( in @ ( sK88_Xx @ SY2379 @ SY2378 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SY2378 @ ( sK88_Xx @ SY2379 @ SY2378 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SY2379 @ ( sK88_Xx @ SY2379 @ SY2378 @ SV378 @ SV191 ) ) ) ) )
| ( SY2378 = SY2379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1153,plain,
! [SV379: $i > $o,SV192: $i] :
( ( ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV192 )
| ( SV379 @ SY2380 ) )
| ~ ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1154,plain,
! [SV193: $i > $o] :
( ( ( ! [SY2084: $i] :
~ ( SV193 @ SY2084 ) )
= $true )
| ( ( ~ ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
| ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1155,plain,
! [SV194: $i > $o] :
( ( ( ! [SY2086: $i] :
( ~ ( ~ ( SV194 @ ( sK55_SY246 @ SY2086 @ SV194 ) )
| ~ ( ( SY2086
!= ( sK55_SY246 @ SY2086 @ SV194 ) ) ) )
| ~ ( SV194 @ SY2086 ) ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1156,plain,
! [SV380: $o,SV195: $i] :
( ( ! [SY2381: $i] :
( ~ ( in @ SY2381 @ SV195 )
| ! [SY2382: $i] :
( ~ ( in @ SY2382 @ SV195 )
| SV380
| ( in @ SY2382
@ ( dsetconstr @ SV195
@ ^ [SY2383: $i] :
( ~ ( ~ SV380
| ( SY2383 != SY2381 ) )
| ~ ( ~ ~ SV380
| ( SY2383 != SY2382 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1157,plain,
! [SV195: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV195 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV195 )
| $true
| ( in @ SX1
@ ( dsetconstr @ SV195
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1158,plain,
! [SV195: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV195 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV195 )
| $false
| ( in @ SX1
@ ( dsetconstr @ SV195
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1159,plain,
! [SV381: $i,SV196: $i] :
( ( ( SV196 != SV381 )
| ! [SY2384: $i > $o,SY2385: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) )
| ~ ( ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SX4: $i] : ( SY2384 @ SX4 ) )
= ( dsetconstr @ SV381
@ ^ [SX4: $i] : ( SY2385 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1160,plain,
! [SV382: $o,SV197: $i] :
( ( ! [SY2388: $i] :
( ~ ( in @ SY2388 @ SV197 )
| ! [SY2389: $i] :
( ~ ( in @ SY2389 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2390: $i] :
( ~ ( ~ SV382
| ( SY2390 != SY2388 ) )
| ~ ( ~ ~ SV382
| ( SY2390 != SY2389 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[926]) ).
thf(1161,plain,
! [SV197: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV197 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[926]) ).
thf(1162,plain,
! [SV197: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV197 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[926]) ).
thf(1163,plain,
! [SV198: $i] :
( ( ( ! [SY2102: $i,SY2103: $i > $i] :
~ ( ~ ( in @ ( sK91_Xx @ SY2103 @ SY2102 @ SV198 ) @ SV198 )
| ~ ~ ( in @ ( SY2103 @ ( sK91_Xx @ SY2103 @ SY2102 @ SV198 ) ) @ SY2102 ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1164,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1166,plain,
! [SV383: $o,SV199: $i] :
( ( ! [SY2391: $i] :
( ~ ( in @ SY2391 @ SV199 )
| ! [SY2392: $i] :
( ~ ( in @ SY2392 @ SV199 )
| ~ SV383
| ( in @ SY2391
@ ( dsetconstr @ SV199
@ ^ [SY2393: $i] :
( ~ ( ~ SV383
| ( SY2393 != SY2391 ) )
| ~ ( ~ ~ SV383
| ( SY2393 != SY2392 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[929]) ).
thf(1167,plain,
! [SV199: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV199 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV199 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV199
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[929]) ).
thf(1168,plain,
! [SV199: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV199 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV199 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV199
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[929]) ).
thf(1169,plain,
! [SV384: $i > $o,SV200: $i] :
( ( ! [SY2394: $i] :
( ~ ( in @ SY2394 @ SV200 )
| ~ ( SV384 @ SY2394 )
| ~ ( ~ ( in @ ( sK71_Xy @ SY2394 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SY2394 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SY2394 @ SV384 @ SV200 )
!= SY2394 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1170,plain,
! [SV201: $i,SV385: $i] :
( ( ! [SY2396: $i > $i] :
( ~ ( ~ ( in @ ( sK75_Xx @ SY2396 @ SV385 @ SV201 ) @ SV201 )
| ~ ~ ( in @ ( SY2396 @ ( sK75_Xx @ SY2396 @ SV385 @ SV201 ) ) @ SV385 ) )
| ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SX3: $i] : ( SY2396 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1171,plain,
! [SV202: $i,SV386: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
| ~ ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) ) )
| ( SV202 = SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1172,plain,
! [SV203: $i > $o] :
( ( ( ! [SY2115: $i] :
( ~ ( ~ ( SV203 @ ( sK22_SY84 @ SY2115 @ SV203 ) )
| ~ ( ( SY2115
!= ( sK22_SY84 @ SY2115 @ SV203 ) ) ) )
| ~ ( SV203 @ SY2115 ) ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1173,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ~ ( ~ ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) ) )
| ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1174,plain,
! [SV205: $i,SV388: $i] :
( ( ! [SY2400: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2400 @ SV388 @ SV205 ) @ SV205 )
| ~ ~ ( in @ ( SY2400 @ ( sK92_Xx @ SY2400 @ SV388 @ SV205 ) ) @ SV388 ) )
| ! [SY2401: $i] :
( ~ ( in @ SY2401 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SX4: $i] : ( SY2400 @ SX4 ) )
@ SY2401 )
= ( SY2400 @ SY2401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1175,plain,
! [SV389: $i,SV206: $i] :
( ( ! [SY2403: $i] :
( ~ ( subset @ SY2403 @ ( cartprod @ SV206 @ SV389 ) )
| ! [SY2404: $i] :
( ~ ( subset @ SY2404 @ ( cartprod @ SV206 @ SV389 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SY2404 @ SY2403 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SY2404 @ SY2403 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SY2404 @ SY2403 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2404 @ SY2403 @ SV389 @ SV206 ) ) @ SY2403 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SY2404 @ SY2403 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2404 @ SY2403 @ SV389 @ SV206 ) ) @ SY2404 ) ) ) )
| ( subset @ SY2403 @ SY2404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1176,plain,
! [SV207: $i > $o] :
( ( ( ! [SY2126: $i] :
( ~ ( ~ ( SV207 @ ( sK18_SY55 @ SY2126 @ SV207 ) )
| ~ ( ( SY2126
!= ( sK18_SY55 @ SY2126 @ SV207 ) ) ) )
| ~ ( SV207 @ SY2126 ) ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1177,plain,
! [SV390: $i,SV208: $i] :
( ( ! [SY2405: $i] :
( ~ ( subset @ SY2405 @ ( cartprod @ SV208 @ SV390 ) )
| ! [SY2406: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2406 @ SY2405 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SY2406 @ SY2405 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SY2406 @ SY2405 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2406 @ SY2405 @ SV390 @ SV208 ) ) @ SY2405 )
| ~ ~ ( SY2406 @ ( kpair @ ( sK77_Xx @ SY2406 @ SY2405 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2406 @ SY2405 @ SV390 @ SV208 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2405 )
| ( SY2406 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1178,plain,
! [SV209: $i] :
( ( ( ! [SY2132: $i] :
~ ( in @ SY2132 @ SV209 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 )
| ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1179,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK53_Xx @ SX1 @ SX0 )
!= ( sK54_SY1668 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK51_SY233 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK51_SY233 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1180,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK49_Xx @ SX1 @ SX0 )
!= ( sK50_SY1666 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK47_SY230 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK47_SY230 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(1181,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ~ ( ~ ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
| ~ ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) ) )
| ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1182,plain,
! [SV211: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) )
| ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1183,plain,
! [SV212: $i > $o] :
( ( ( ! [SY2137: $i] :
~ ( ~ ( ( ( sK45_Xy @ SY2137 @ SV212 )
!= SY2137 )
| ~ ( SV212 @ ( sK45_Xy @ SY2137 @ SV212 ) ) )
| ~ ( ( ( sK45_Xy @ SY2137 @ SV212 )
= SY2137 )
| ( SV212 @ ( sK45_Xy @ SY2137 @ SV212 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1184,plain,
! [SV392: $o,SV213: $i] :
( ( ! [SY2409: $i] :
( ~ ( in @ SY2409 @ SV213 )
| ! [SY2410: $i] :
( ~ ( in @ SY2410 @ SV213 )
| SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2411: $i] :
( ~ ( ~ SV392
| ( SY2411 != SY2409 ) )
| ~ ( ~ ~ SV392
| ( SY2411 != SY2410 ) ) ) )
= ( setadjoin @ SY2410 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[944]) ).
thf(1185,plain,
! [SV213: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV213 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV213 )
| $true
| ( ( dsetconstr @ SV213
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[944]) ).
thf(1186,plain,
! [SV213: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV213 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV213 )
| $false
| ( ( dsetconstr @ SV213
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[944]) ).
thf(1187,plain,
! [SV214: $i > $o] :
( ( ( ! [SY2143: $i] :
( ~ ( ~ ( SV214 @ ( sK31_SY140 @ SY2143 @ SV214 ) )
| ~ ( ( SY2143
!= ( sK31_SY140 @ SY2143 @ SV214 ) ) ) )
| ~ ( SV214 @ SY2143 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1188,plain,
! [SV215: $i,SV393: $i] :
( ( ~ ( ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV215 )
| ~ ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 ) )
| ( subset @ SV215 @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1189,plain,
! [SV394: $i,SV216: $i] :
( ( ! [SY2412: $i] :
( ~ ( subset @ SY2412 @ ( cartprod @ SV216 @ SV394 ) )
| ! [SY2413: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SY2413 @ SY2412 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SY2413 @ SY2412 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2413 @ SY2412 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2413 @ SY2412 @ SV394 @ SV216 ) ) @ SY2412 )
| ~ ~ ( SY2413 @ ( kpair @ ( sK79_Xx @ SY2413 @ SY2412 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2413 @ SY2412 @ SV394 @ SV216 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2412 )
| ( SY2413 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1190,plain,
! [SV395: $i,SV217: $i] :
( ( ! [SY2415: $i] :
( ~ ( in @ SY2415 @ ( setadjoin @ SV217 @ SV395 ) )
| ~ ( ~ ~ ( ~ ( ( SY2415 = SV217 )
| ( in @ SY2415 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY2415 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2418: $o] :
( ~ SY2418
| ( in @ SY2415 @ SV395 )
| SY2418 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1191,plain,
! [SV218: $i] :
( ( ~ ! [SY2157: $i > $o,SY2158: $i] :
( ~ ( in @ SY2158 @ SV218 )
| ~ ( SY2157 @ SY2158 )
| ( in @ SY2158
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2157 @ SX3 ) ) ) )
| ~ ! [SY2160: $i > $o,SY2161: $i] :
( ~ ( in @ SY2161 @ SV218 )
| ~ ( in @ SY2161
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2160 @ SX3 ) ) )
| ( SY2160 @ SY2161 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1192,plain,
! [SV219: $i,SV396: $i] :
( ( ~ ( in @ SV396 @ ( setunion @ SV219 ) )
| ! [SY2420: $o] :
( ~ ( ~ ( in @ SV396 @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SY2420 ) )
| SY2420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1193,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ~ ( ( ( sK58_Xx @ SV397 @ SV220 )
!= ( sK59_SY1669 @ SV397 @ SV220 ) )
| ~ ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) ) )
| ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1194,plain,
! [SV398: $o,SV221: $i] :
( ( ! [SY2425: $i] :
( ~ ( in @ SY2425 @ SV221 )
| ! [SY2426: $i] :
( ~ ( in @ SY2426 @ SV221 )
| ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2427: $i] :
( ~ ( ~ SV398
| ( SY2427 != SY2425 ) )
| ~ ( ~ ~ SV398
| ( SY2427 != SY2426 ) ) ) )
= ( setadjoin @ SY2425 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1195,plain,
! [SV221: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV221 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV221 )
| ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1196,plain,
! [SV221: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV221 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV221 )
| ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[952]) ).
thf(1197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1199,plain,
! [SV1: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( in @ ( powerset @ SV222 ) @ ( powerset @ ( powerset @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1200,plain,
! [SV2: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY2174: $i] :
( ~ ( in @ SY2174 @ ( powerset @ SV2 ) )
| ( in @ ( binunion @ SV223 @ SY2174 ) @ ( powerset @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1201,plain,
! [SV3: $i,SV224: $i] :
( ( ( ~ ( in @ SV224 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( ! [SY2175: $i] :
( ~ ( in @ SY2175 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV224 @ SY2175 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1202,plain,
! [SV225: $o,SV4: $i,SV399: $i] :
( ( ~ ( in @ SV399 @ SV4 )
| ! [SY2428: $i] :
( ~ ( in @ SY2428 @ SV4 )
| ( in @ ( if @ SV4 @ SV225 @ SV399 @ SY2428 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SY2428 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1203,plain,
! [SV4: $i,SV400: $i] :
( ( ~ ( in @ SV400 @ SV4 )
| ! [SY2429: $i] :
( ~ ( in @ SY2429 @ SV4 )
| ( in @ ( if @ SV4 @ $true @ SV400 @ SY2429 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SY2429 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1204,plain,
! [SV4: $i,SV401: $i] :
( ( ~ ( in @ SV401 @ SV4 )
| ! [SY2430: $i] :
( ~ ( in @ SY2430 @ SV4 )
| ( in @ ( if @ SV4 @ $false @ SV401 @ SY2430 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SY2430 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1205,plain,
! [SV226: $o,SV5: $i,SV402: $i] :
( ( ~ ( in @ SV402 @ SV5 )
| ! [SY2431: $i] :
( ~ ( in @ SY2431 @ SV5 )
| SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SY2431 )
= SY2431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1206,plain,
! [SV5: $i,SV403: $i] :
( ( ~ ( in @ SV403 @ SV5 )
| ! [SY2432: $i] :
( ~ ( in @ SY2432 @ SV5 )
| $true
| ( ( if @ SV5 @ $true @ SV403 @ SY2432 )
= SY2432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1207,plain,
! [SV5: $i,SV404: $i] :
( ( ~ ( in @ SV404 @ SV5 )
| ! [SY2433: $i] :
( ~ ( in @ SY2433 @ SV5 )
| $false
| ( ( if @ SV5 @ $false @ SV404 @ SY2433 )
= SY2433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1208,plain,
! [SV227: $o,SV6: $i,SV405: $i] :
( ( ~ ( in @ SV405 @ SV6 )
| ! [SY2434: $i] :
( ~ ( in @ SY2434 @ SV6 )
| ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SY2434 )
= SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1209,plain,
! [SV6: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ SV6 )
| ! [SY2435: $i] :
( ~ ( in @ SY2435 @ SV6 )
| ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SY2435 )
= SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1210,plain,
! [SV6: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ SV6 )
| ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV6 )
| ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SY2436 )
= SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1211,plain,
! [SV7: $i] :
( ( ( singleton @ SV7 )
= $false )
| ( ( ! [SY1693: $i] :
( ~ ( in @ SY1693 @ SV7 )
| ( ( setunion @ SV7 )
= SY1693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1212,plain,
! [SV228: $o,SV8: $i,SV408: $i] :
( ( ~ ( in @ SV408 @ SV8 )
| ! [SY2437: $i] :
( ~ ( in @ SY2437 @ SV8 )
| ( in @ ( if @ SV8 @ SV228 @ SV408 @ SY2437 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1213,plain,
! [SV8: $i,SV409: $i] :
( ( ~ ( in @ SV409 @ SV8 )
| ! [SY2438: $i] :
( ~ ( in @ SY2438 @ SV8 )
| ( in @ ( if @ SV8 @ $true @ SV409 @ SY2438 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1214,plain,
! [SV8: $i,SV410: $i] :
( ( ~ ( in @ SV410 @ SV8 )
| ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV8 )
| ( in @ ( if @ SV8 @ $false @ SV410 @ SY2439 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1215,plain,
! [SV229: $i,SV9: $i,SV411: $i] :
( ( ~ ( in @ SV411 @ ( funcSet @ SV9 @ SV229 ) )
| ( ( lam @ SV9 @ SV229
@ ^ [SY2440: $i] : ( ap @ SV9 @ SV229 @ SV411 @ SY2440 ) )
= SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1216,plain,
! [SV412: $i,SV230: $i,SV10: $i] :
( ( ~ ( func @ SV10 @ SV230 @ SV412 )
| ( ( lam @ SV10 @ SV230
@ ^ [SY2441: $i] : ( ap @ SV10 @ SV230 @ SV412 @ SY2441 ) )
= SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1217,plain,
! [SV413: $i,SV11: $i] :
( ( ( ! [SY2442: $i] :
~ ( func @ SV11 @ SV413 @ SY2442 ) )
= $true )
| ( ( ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1218,plain,
! [SV414: $i,SV12: $i] :
( ( ( ! [SY2443: $i] :
~ ( in @ SY2443 @ ( funcSet @ SV12 @ SV414 ) ) )
= $true )
| ( ( ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1219,plain,
! [SV231: $i,SV13: $i,SV415: $i] :
( ( ~ ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
| ! [SY2444: $i] :
( ~ ( in @ SY2444 @ SV13 )
| ! [SY2445: $i] :
( ~ ( in @ SY2445 @ SV231 )
| ~ ( in @ ( kpair @ SY2444 @ SY2445 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SY2444 )
= SY2445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1220,plain,
! [SV416: $i,SV232: $i,SV14: $i] :
( ( ~ ( func @ SV14 @ SV232 @ SV416 )
| ! [SY2446: $i] :
( ~ ( in @ SY2446 @ SV14 )
| ! [SY2447: $i] :
( ~ ( in @ SY2447 @ SV232 )
| ~ ( in @ ( kpair @ SY2446 @ SY2447 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SY2446 )
= SY2447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1221,plain,
! [SV233: $i,SV15: $i,SV417: $i] :
( ( ~ ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) )
| ! [SY2448: $i] :
( ~ ( in @ SY2448 @ SV15 )
| ( in @ ( kpair @ SY2448 @ ( ap @ SV15 @ SV233 @ SV417 @ SY2448 ) ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1222,plain,
! [SV418: $i,SV234: $i,SV16: $i] :
( ( ~ ( func @ SV16 @ SV234 @ SV418 )
| ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SV16 )
| ( in @ ( kpair @ SY2449 @ ( ap @ SV16 @ SV234 @ SV418 @ SY2449 ) ) @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1223,plain,
! [SV235: $i > $o,SV17: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) ) )
= $true )
| ( ( ! [SY2199: $i] :
( ~ ( in @ SY2199 @ SV17 )
| ! [SY2200: $i] :
( ~ ( in @ SY2200 @ SV17 )
| ~ ( SV235 @ SY2199 )
| ~ ( SV235 @ SY2200 )
| ( SY2199 = SY2200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1224,plain,
! [SV419: $i,SV236: $i,SV18: $i] :
( ( ~ ( func @ SV18 @ SV236 @ SV419 )
| ( in @ SV419 @ ( funcSet @ SV18 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1225,plain,
! [SV237: $i,SV19: $i,SV420: $i] :
( ( ~ ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) )
| ! [SY2450: $i] :
( ~ ( in @ SY2450 @ SV19 )
| ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SY2450 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1226,plain,
! [SV238: $i,SV20: $i,SV421: $i] :
( ( ~ ( in @ SV421 @ ( funcSet @ SV20 @ SV238 ) )
| ( func @ SV20 @ SV238 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1227,plain,
! [SV422: $i,SV239: $i,SV21: $i] :
( ( ~ ( func @ SV21 @ SV239 @ SV422 )
| ! [SY2451: $i] :
( ~ ( in @ SY2451 @ SV21 )
| ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SY2451 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1228,plain,
! [SV423: $i,SV240: $i,SV22: $i] :
( ( ~ ( func @ SV22 @ SV240 @ SV423 )
| ! [SY2452: $i] :
( ~ ( in @ SY2452 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2453: $i] : ( in @ ( kpair @ SY2452 @ SY2453 ) @ SV423 ) ) )
@ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1229,plain,
! [SV424: $i,SV241: $i,SV23: $i] :
( ( ~ ( func @ SV23 @ SV241 @ SV424 )
| ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SV23 )
| ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2455: $i] : ( in @ ( kpair @ SY2454 @ SY2455 ) @ SV424 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1230,plain,
! [SV425: $i > $i > $o,SV242: $i,SV24: $i] :
( ( ! [SY2456: $i,SY2457: $i] :
( ~ ( in @ ( kpair @ SY2456 @ SY2457 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [SY2458: $i,SY2459: $i] : ( SV425 @ SY2458 @ SY2459 ) ) )
| ( SV425 @ SY2456 @ SY2457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1231,plain,
! [SV426: $i > $i > $o,SV243: $i,SV25: $i] :
( ( ! [SY2460: $i,SY2461: $i] :
( ~ ( in @ ( kpair @ SY2460 @ SY2461 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [SY2462: $i,SY2463: $i] : ( SV426 @ SY2462 @ SY2463 ) ) )
| ( in @ SY2461 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1232,plain,
! [SV427: $i > $i > $o,SV244: $i,SV26: $i] :
( ( ! [SY2464: $i] :
( ! [SY2465: $i] :
~ ( in @ ( kpair @ SY2464 @ SY2465 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [SY2466: $i,SY2467: $i] : ( SV427 @ SY2466 @ SY2467 ) ) )
| ( in @ SY2464 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1233,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i] :
( ( ! [SY2468: $i] :
( ~ ( in @ SY2468 @ SV27 )
| ! [SY2469: $i] :
( ~ ( in @ SY2469 @ SV245 )
| ~ ( in @ ( kpair @ SY2468 @ SY2469 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SY2468 @ SY2469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1234,plain,
! [SV429: $i > $i > $o,SV246: $i,SV28: $i] :
( ( subset
@ ( dpsetconstr @ SV28 @ SV246
@ ^ [SY2472: $i,SY2473: $i] : ( SV429 @ SY2472 @ SY2473 ) )
@ ( cartprod @ SV28 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1235,plain,
! [SV430: $i > $i > $o,SV247: $i,SV29: $i] :
( ( subset
@ ( dpsetconstr @ SV29 @ SV247
@ ^ [SY2474: $i,SY2475: $i] : ( SV430 @ SY2474 @ SY2475 ) )
@ ( cartprod @ SV29 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1236,plain,
! [SV431: $i > $i > $o,SV248: $i,SV30: $i] :
( ( ! [SY2476: $i] :
( ~ ( in @ SY2476 @ SV30 )
| ! [SY2477: $i] :
( ~ ( in @ SY2477 @ SV248 )
| ~ ( SV431 @ SY2476 @ SY2477 )
| ( in @ ( kpair @ SY2476 @ SY2477 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1237,plain,
! [SV249: $i,SV31: $i,SV432: $i] :
( ( ~ ( in @ SV432 @ ( cartprod @ SV31 @ SV249 ) )
| ( ( kpair @ ( kfst @ SV432 ) @ ( ksnd @ SV432 ) )
= SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1238,plain,
! [SV250: $i,SV32: $i,SV433: $i] :
( ( ~ ( in @ SV433 @ SV32 )
| ! [SY2480: $i] :
( ~ ( in @ SY2480 @ SV250 )
| ( ( ksnd @ ( kpair @ SV433 @ SY2480 ) )
= SY2480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1239,plain,
! [SV251: $i,SV33: $i,SV434: $i] :
( ( ~ ( in @ SV434 @ SV33 )
| ! [SY2481: $i] :
( ~ ( in @ SY2481 @ SV251 )
| ( ( kfst @ ( kpair @ SV434 @ SY2481 ) )
= SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1240,plain,
! [SV34: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ SV34 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1241,plain,
! [SV252: $i,SV35: $i,SV436: $i] :
( ( ! [SY2482: $i] :
( ~ ( in @ ( kpair @ SV436 @ SY2482 ) @ ( cartprod @ SV35 @ SV252 ) )
| ( in @ SY2482 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1242,plain,
! [SV253: $i,SV36: $i,SV437: $i] :
( ( ! [SY2483: $i] :
~ ( in @ ( kpair @ SV437 @ SY2483 ) @ ( cartprod @ SV36 @ SV253 ) )
| ( in @ SV437 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1243,plain,
! [SV254: $i,SV37: $i,SV438: $i] :
( ( ~ ( in @ SV438 @ ( cartprod @ SV37 @ SV254 ) )
| ( in @ ( ksnd @ SV438 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1244,plain,
! [SV38: $i] :
( ( ( iskpair @ SV38 )
= $false )
| ( ( ( kpair @ ( kfst @ SV38 ) @ ( ksnd @ SV38 ) )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1245,plain,
! [SV40: $i] :
( ( ( iskpair @ SV40 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV40 )
@ ^ [SY1803: $i] :
( SV40
= ( kpair @ ( kfst @ SV40 ) @ SY1803 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1246,plain,
! [SV439: $i,SV256: $i,SV41: $i] :
( ( ! [SY2484: $i] :
( ( ( kpair @ SV41 @ SV256 )
!= ( kpair @ SV439 @ SY2484 ) )
| ( SV256 = SY2484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1247,plain,
! [SV440: $i,SV257: $i,SV42: $i] :
( ( ! [SY2485: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV257 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV440 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV440 @ ( setadjoin @ SY2485 @ emptyset ) ) @ emptyset ) ) )
| ( SV257 = SY2485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1248,plain,
! [SV258: $i,SV43: $i] :
( ( ( ! [SY2258: $i] :
( ( setadjoin @ SV43 @ ( setadjoin @ SV258 @ emptyset ) )
!= ( setadjoin @ SY2258 @ emptyset ) ) )
= $true )
| ( ( SV43 = SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1249,plain,
! [SV441: $i,SV259: $i,SV44: $i] :
( ( ! [SY2486: $i] :
( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SY2486 @ emptyset ) ) @ emptyset ) ) )
| ( SV441 != SY2486 )
| ( SV259 = SY2486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1250,plain,
! [SV260: $i,SV45: $i] :
( ( ( SV45 != SV260 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV45 @ ( setadjoin @ SV260 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1251,plain,
! [SV261: $i,SV46: $i] :
( ( ( SV46 != SV261 )
= $true )
| ( ( ( setadjoin @ SV46 @ ( setadjoin @ SV261 @ emptyset ) )
= ( setadjoin @ SV46 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1252,plain,
! [SV442: $i,SV262: $i,SV47: $i] :
( ( ! [SY2487: $i] :
( ( kpair @ SV47 @ SV262 )
!= ( kpair @ SV442 @ SY2487 ) )
| ( SV47 = SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1253,plain,
! [SV443: $i,SV263: $i,SV48: $i] :
( ( ! [SY2488: $i] :
( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV443 @ ( setadjoin @ SY2488 @ emptyset ) ) @ emptyset ) ) )
| ( SV48 = SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1254,plain,
! [SV264: $i,SV49: $i,SV444: $i] :
( ( ~ ( in @ SV444 @ ( cartprod @ SV49 @ SV264 ) )
| ( in @ ( kfst @ SV444 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1255,plain,
! [SV51: $i] :
( ( ( singleton @ SV51 )
= $false )
| ( ( in @ ( setunion @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1256,plain,
! [SV52: $i] :
( ( ( iskpair @ SV52 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV52 )
@ ^ [SY1826: $i] : ( in @ ( setadjoin @ SY1826 @ emptyset ) @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1257,plain,
! [SV266: $i,SV53: $i,SV445: $i] :
( ( ~ ( in @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV266 @ emptyset ) ) @ emptyset ) ) )
| ( SV53 = SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1258,plain,
! [SV267: $i,SV54: $i] :
( ( ( ( setadjoin @ SV54 @ emptyset )
!= ( setadjoin @ SV267 @ emptyset ) )
= $true )
| ( ( SV54 = SV267 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1259,plain,
! [SV268: $i,SV58: $i,SV446: $i] :
( ( ~ ( in @ SV446 @ ( cartprod @ SV58 @ SV268 ) )
| ( iskpair @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1260,plain,
! [SV269: $i,SV59: $i,SV447: $i] :
( ( ~ ( in @ SV447 @ SV59 )
| ! [SY2489: $i] :
( ~ ( in @ SY2489 @ SV269 )
| ( in @ ( kpair @ SV447 @ SY2489 ) @ ( cartprod @ SV59 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1261,plain,
! [SV270: $i,SV60: $i,SV448: $i] :
( ( ~ ( in @ SV448 @ SV60 )
| ! [SY2490: $i] :
( ~ ( in @ SY2490 @ SV270 )
| ( in @ ( kpair @ SV448 @ SY2490 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1262,plain,
! [SV271: $i,SV61: $i,SV449: $i] :
( ( ~ ( in @ SV449 @ SV61 )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SV271 )
| ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SY2491 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1263,plain,
! [SV272: $i,SV62: $i,SV450: $i] :
( ( ~ ( in @ SV450 @ SV62 )
| ! [SY2492: $i] :
( ~ ( in @ SY2492 @ SV272 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SY2492 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1264,plain,
! [SV273: $i,SV63: $i,SV451: $i] :
( ( ~ ( in @ SV451 @ SV63 )
| ! [SY2493: $i] :
( ~ ( in @ SY2493 @ SV273 )
| ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SY2493 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1265,plain,
! [SV274: $i,SV64: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ SV64 )
| ! [SY2494: $i] :
( ~ ( in @ SY2494 @ SV274 )
| ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SY2494 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1266,plain,
! [SV275: $i,SV65: $i,SV453: $i] :
( ( ~ ( in @ SV453 @ ( setadjoin @ SV65 @ ( setadjoin @ SV275 @ emptyset ) ) )
| ( SV453 = SV65 )
| ( SV453 = SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1267,plain,
! [SV276: $i,SV66: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ SV66 )
| ( in @ ( setadjoin @ SV454 @ emptyset ) @ ( powerset @ ( binunion @ SV66 @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1268,plain,
! [SV67: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV67 ) )
= $true )
| ( ( in @ ( setadjoin @ SV277 @ emptyset ) @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1269,plain,
! [SV68: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV68 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV278 @ emptyset ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1270,plain,
! [SV284: $i,SV74: $i,SV455: $i] :
( ( ( in @ SV455 @ SV74 )
| ( in @ SV455 @ SV284 )
| ~ ( in @ SV455 @ ( symdiff @ SV74 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1271,plain,
! [SV285: $i,SV75: $i,SV456: $i] :
( ( ~ ( in @ SV456 @ SV75 )
| ~ ( in @ SV456 @ SV285 )
| ~ ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1272,plain,
! [SV286: $i,SV76: $i,SV457: $i] :
( ( ( in @ SV457 @ SV76 )
| ~ ( in @ SV457 @ SV286 )
| ( in @ SV457 @ ( symdiff @ SV76 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1273,plain,
! [SV287: $i,SV77: $i,SV458: $i] :
( ( ~ ( in @ SV458 @ SV77 )
| ( in @ SV458 @ SV287 )
| ( in @ SV458 @ ( symdiff @ SV77 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1274,plain,
! [SV288: $i,SV78: $i] :
( ( ( ( setminus @ SV78 @ SV288 )
!= emptyset )
= $true )
| ( ( subset @ SV78 @ SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1275,plain,
! [SV80: $i,SV290: $i,SV459: $i] :
( ( ~ ( in @ SV459 @ SV290 )
| ~ ( in @ SV459 @ ( setminus @ SV80 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1276,plain,
! [SV291: $i,SV81: $i,SV460: $i] :
( ( ( in @ SV460 @ SV81 )
| ~ ( in @ SV460 @ ( setminus @ SV81 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1277,plain,
! [SV292: $i,SV82: $i,SV461: $i] :
( ( ( in @ SV461 @ ( setminus @ SV82 @ SV292 ) )
| ( in @ SV461 @ SV292 )
| ~ ( in @ SV461 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1278,plain,
! [SV293: $i,SV83: $i,SV462: $i] :
( ( ( in @ SV462 @ ( setminus @ SV83 @ SV293 ) )
| ~ ( in @ SV462 @ SV83 )
| ( in @ SV462 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1279,plain,
! [SV294: $i,SV84: $i] :
( ( ( ~ ( subset @ SV84 @ SV294 ) )
= $true )
| ( ( ( setminus @ SV84 @ SV294 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1280,plain,
! [SV295: $i,SV85: $i,SV463: $i] :
( ( ~ ( in @ SV463 @ ( setminus @ SV85 @ SV295 ) )
| ~ ( in @ SV463 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1281,plain,
! [SV296: $i,SV86: $i,SV464: $i] :
( ( ~ ( in @ SV464 @ ( setminus @ SV86 @ SV296 ) )
| ( in @ SV464 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1282,plain,
! [SV297: $i,SV87: $i,SV465: $i] :
( ( ~ ( in @ SV465 @ SV87 )
| ( in @ SV465 @ SV297 )
| ( in @ SV465 @ ( setminus @ SV87 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1283,plain,
! [SV466: $i,SV298: $i,SV88: $i] :
( ( ( binintersect @ SV88 @ ( binunion @ SV298 @ SV466 ) )
= ( binunion @ ( binintersect @ SV88 @ SV298 ) @ ( binintersect @ SV88 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1284,plain,
! [SV299: $i,SV89: $i] :
( ( ( ( binintersect @ SV89 @ SV299 )
!= SV89 )
= $true )
| ( ( subset @ SV89 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1285,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( subset @ SV300 @ SV90 ) )
= $true )
| ( ( ( binintersect @ SV90 @ SV300 )
= SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1286,plain,
! [SV302: $i,SV92: $i,SV467: $i] :
( ( ~ ( in @ SV467 @ ( binintersect @ SV92 @ SV302 ) )
| ( in @ SV467 @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1287,plain,
! [SV303: $i,SV93: $i] :
( ( ( ( binintersect @ SV93 @ SV303 )
!= SV303 )
= $true )
| ( ( subset @ SV303 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1288,plain,
! [SV304: $i,SV94: $i] :
( ( ( ~ ( subset @ SV94 @ SV304 ) )
= $true )
| ( ( ( binintersect @ SV94 @ SV304 )
= SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1289,plain,
! [SV306: $i,SV96: $i,SV468: $i] :
( ( ~ ( in @ SV468 @ ( binintersect @ SV96 @ SV306 ) )
| ( in @ SV468 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1290,plain,
! [SV307: $i,SV97: $i,SV469: $i] :
( ( ~ ( subset @ SV469 @ SV97 )
| ~ ( subset @ SV469 @ SV307 )
| ( subset @ SV469 @ ( binintersect @ SV97 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1291,plain,
! [SV308: $i,SV98: $i,SV470: $i] :
( ( ~ ( in @ SV470 @ SV98 )
| ~ ( in @ SV470 @ SV308 )
| ( in @ SV470 @ ( binintersect @ SV98 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1292,plain,
! [SV311: $i,SV101: $i,SV471: $i] :
( ( ~ ( in @ SV471 @ ( binunion @ SV101 @ SV311 ) )
| ( in @ SV471 @ SV101 )
| ( in @ SV471 @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1293,plain,
! [SV102: $i,SV312: $i,SV472: $i] :
( ( ~ ( in @ SV472 @ SV312 )
| ( in @ SV472 @ ( binunion @ SV102 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1294,plain,
! [SV314: $i,SV104: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ SV104 )
| ( in @ SV473 @ ( binunion @ SV104 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1295,plain,
! [SV317: $i,SV107: $i] :
( ( ( ~ ( subset @ SV107 @ SV317 ) )
= $true )
| ( ( subset @ ( powerset @ SV107 ) @ ( powerset @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1296,plain,
! [SV109: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ ( powerset @ SV109 ) ) )
= $true )
| ( ( subset @ SV318 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1297,plain,
! [SV110: $i,SV319: $i] :
( ( ( ~ ( subset @ SV319 @ SV110 ) )
= $true )
| ( ( in @ SV319 @ ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1298,plain,
! [SV111: $i] :
( ( ( subset @ SV111 @ emptyset )
= $false )
| ( ( SV111 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1299,plain,
! [SV320: $i,SV112: $i] :
( ( ( ~ ( subset @ SV112 @ SV320 ) )
= $true )
| ( ( ~ ( subset @ SV320 @ SV112 )
| ( SV112 = SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1300,plain,
! [SV321: $i,SV113: $i] :
( ( ( ~ ( subset @ SV113 @ SV321 ) )
= $true )
| ( ( in @ SV113 @ ( powerset @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1301,plain,
! [SV322: $i,SV474: $i,SV114: $i] :
( ( ~ ( subset @ SV114 @ SV474 )
| ( subset @ SV114 @ ( setadjoin @ SV322 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1302,plain,
! [SV324: $i,SV116: $i] :
( ( ( ~ ( subset @ SV116 @ SV324 ) )
= $true )
| ( ( ! [SY2304: $i] :
( ~ ( subset @ SV324 @ SY2304 )
| ( subset @ SV116 @ SY2304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1303,plain,
! [SV325: $i,SV118: $i,SV475: $i] :
( ( ~ ( in @ SV475 @ SV118 )
| ( in @ SV475 @ SV325 )
| ( SV118 != SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1304,plain,
! [SV326: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV326 )
= $true )
| ( ( SV119 != SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1305,plain,
! [SV327: $i,SV120: $i,SV476: $i] :
( ( ~ ( in @ SV476 @ SV120 )
| ( in @ SV476 @ SV327 )
| ~ ( subset @ SV120 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1306,plain,
! [SV328: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV328 ) )
= $true )
| ( ( ! [SY2307: $i] :
( ( in @ SY2307 @ SV328 )
| ~ ( in @ SY2307 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1307,plain,
! [SV329: $i,SV122: $i] :
( ( ( ~ ( subset @ SV122 @ SV329 ) )
= $true )
| ( ( ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV122 )
| ( in @ SY2308 @ SV329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1308,plain,
! [SV330: $i,SV124: $i] :
( ( ( SV124 != SV330 )
= $true )
| ( ( subset @ SV124 @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1309,plain,
! [SV331: $i,SV125: $i] :
( ( ( SV125 != SV331 )
= $true )
| ( ( subset @ SV331 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1310,plain,
! [SV332: $i,SV126: $i] :
( ( ( SV126 != SV332 )
= $true )
| ( ( ( setunion @ SV126 )
= ( setunion @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1311,plain,
! [SV333: $i,SV127: $i] :
( ( ( SV127 != SV333 )
= $true )
| ( ( ( powerset @ SV127 )
= ( powerset @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1312,plain,
! [SV334: $i,SV128: $i] :
( ( ( SV128 != SV334 )
= $true )
| ( ( ! [SY2309: $i,SY2310: $i] :
( ( SY2309 != SY2310 )
| ( ( setadjoin @ SV128 @ SY2309 )
= ( setadjoin @ SV334 @ SY2310 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1313,plain,
! [SV335: $i,SV129: $i] :
( ( ( SV129 != SV335 )
= $true )
| ( ( ! [SY2311: $i,SY2312: $i] :
( ( SY2311 != SY2312 )
| ~ ( in @ SY2311 @ SV129 )
| ( in @ SY2312 @ SV335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1314,plain,
! [SV130: $o] :
( ( SV130 = $false )
| ( ( set2prop @ ( prop2set @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1315,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1316,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1317,plain,
! [SV131: $o] :
( ( SV131 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1318,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1319,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1320,plain,
! [SV132: $i > $o,SV336: $i] :
( ( ( ~ ( in @ SV336 @ emptyset ) )
= $true )
| ( ( SV132 @ SV336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1321,plain,
! [SV133: $i,SV337: $i > $o] :
( ( ( ! [SY2313: $i] :
( ~ ( SV337 @ SY2313 )
| ~ ( in @ SY2313 @ SV133 ) ) )
= $true )
| ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1322,plain,
! [SV340: $i,SV136: $i,SV477: $i] :
( ( ~ ( in @ SV477 @ ( setadjoin @ SV136 @ ( setadjoin @ SV340 @ emptyset ) ) )
| ( SV477 = SV136 )
| ( SV477 = SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1323,plain,
! [SV341: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ ( setadjoin @ SV341 @ emptyset ) ) )
= $true )
| ( ( in @ SV341 @ ( setadjoin @ SV137 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1324,plain,
! [SV342: $i,SV138: $i] :
( ( ( SV138 != SV342 )
= $true )
| ( ( in @ SV138 @ ( setadjoin @ SV342 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1325,plain,
! [SV343: $i,SV139: $i] :
( ( ( SV139 = SV343 )
= $true )
| ( ( ~ ( in @ SV343 @ ( setadjoin @ SV139 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1326,plain,
! [SV344: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ ( setadjoin @ SV344 @ emptyset ) ) )
= $true )
| ( ( SV140 = SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1327,plain,
! [SV142: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ SV142 ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ ( setunion @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1328,plain,
! [SV143: $i,SV478: $i,SV346: $i] :
( ( ~ ( in @ SV346 @ SV478 )
| ~ ( in @ SV478 @ SV143 )
| ( in @ SV346 @ ( setunion @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1329,plain,
! [SV144: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( in @ SY2317 @ SV347 )
| ( in @ SY2317 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1330,plain,
! [SV348: $i,SV148: $i,SV479: $i] :
( ( ~ ( in @ SV479 @ ( setadjoin @ SV148 @ SV348 ) )
| ( SV479 = SV148 )
| ( in @ SV479 @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1331,plain,
! [SV149: $i,SV349: $i,SV480: $i] :
( ( ~ ( in @ SV480 @ SV349 )
| ( in @ SV480 @ ( setadjoin @ SV149 @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1332,plain,
! [SV151: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV151 ) )
= $true )
| ( ( SV151 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1333,plain,
! [SV351: $i > $o,SV152: $i,SV482: $i] :
( ( ~ ( in @ SV482 @ SV152 )
| ~ ( SV351 @ SV482 )
| ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1334,plain,
! [SV352: $i] :
( ( ( in @ SV352 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1335,plain,
! [SV158: $o,SV483: $i] :
( ( ( ~ ( in @ SV483 @ ( prop2set @ SV158 ) ) )
= $true )
| ( SV158 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1336,plain,
! [SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1337,plain,
! [SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1338,plain,
! [SV353: $i > $o,SV159: $i,SV486: $i] :
( ( ~ ( in @ SV486
@ ( dsetconstr @ SV159
@ ^ [SY2323: $i] : ( SV353 @ SY2323 ) ) )
| ( SV353 @ SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1339,plain,
! [SV354: $i > $o,SV160: $i,SV487: $i] :
( ( ~ ( in @ SV487
@ ( dsetconstr @ SV160
@ ^ [SY2325: $i] : ( SV354 @ SY2325 ) ) )
| ( in @ SV487 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1340,plain,
! [SV355: $i > $o,SV161: $i,SV488: $i] :
( ( ~ ( in @ SV488 @ SV161 )
| ~ ( SV355 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1341,plain,
! [SV162: $i] :
( ( ( in @ SV162 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV162 @ SV162 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1342,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( ~ ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
| ~ ( ( SV489
!= ( sK20_SY72 @ SV489 @ SV164 ) ) ) )
| ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1343,plain,
! [SV356: $i,SV165: $i] :
( ( ( SV165 != SV356 )
= $true )
| ( ( ~ ( ~ ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) )
| ~ ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1344,plain,
! [SV490: $i,SV357: $i,SV166: $i] :
( ( ~ ( func @ SV166 @ SV357 @ SV490 )
| ! [SY2499: $i] :
( ~ ( func @ SV166 @ SV357 @ SY2499 )
| ~ ( ~ ( in @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SY2499 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2500: $i] :
( ~ ( in @ SY2500 @ SV166 )
| ! [SY2501: $i] :
( ~ ( in @ SY2501 @ SV357 )
| ~ ( in @ ( kpair @ SY2500 @ SY2501 ) @ SY2499 )
| ( in @ ( kpair @ SY2500 @ SY2501 ) @ SV490 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1345,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ~ ( ~ ( in @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) @ SV167 )
| ~ ~ ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 ) )
| ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1346,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ~ ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1347,plain,
( ( in @ sK2_SY1624 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1348,plain,
( ( ~ ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1349,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( ~ ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
| ~ ( ( SV493
!= ( sK40_Xy @ SV493 @ SV169 ) ) ) )
| ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1350,plain,
! [SV170: $i] :
( ( ~ ! [SY2009: $i] :
( ~ ( ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SY2009 )
| ~ ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SV170 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2009 )
| ~ ( ~ ! [SY2011: $i] :
( ~ ( in @ SY2011 @ ( sK13_B @ SV170 ) )
| ! [SY2012: $i] :
( ~ ( in @ SY2012 @ SY2011 )
| ( in @ SY2012 @ ( sK15_SY1637 @ SY2009 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2011 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SY2009 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2009 ) )
| ~ ! [SY2013: $i] :
( ~ ( in @ SY2013 @ ( sK15_SY1637 @ SY2009 @ SV170 ) )
| ~ ( in @ SY2013 @ SY2009 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1351,plain,
! [SV170: $i] :
( ( ~ ~ ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) )
| ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1352,plain,
! [SV360: $i,SV171: $i,SV494: $i] :
( ( ~ ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
| ! [SY2512: $i] :
( ~ ( in @ SY2512 @ ( funcSet @ SV171 @ SV360 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SY2512 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SY2512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1353,plain,
! [SV172: $i,SV361: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV361 ) ) )
= $true )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1354,plain,
! [SV362: $i > $o,SV173: $i] :
( ( ( ! [SY2350: $i] :
( ~ ( in @ SY2350 @ SV173 )
| ( SV362 @ SY2350 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1355,plain,
! [SV174: $i] :
( ( ~ ! [SY2028: $i,SY2029: $i] :
( ~ ( in @ SY2029 @ ( setadjoin @ SV174 @ SY2028 ) )
| ( SY2029 = SV174 )
| ( in @ SY2029 @ SY2028 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1356,plain,
! [SV174: $i] :
( ( ~ ~ ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) )
| ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1357,plain,
! [SV363: $i > $o,SV175: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) )
| ~ ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1358,plain,
! [SV364: $i,SV176: $i,SV495: $i] :
( ( ~ ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
| ! [SY2513: $i] :
( ~ ( subset @ SY2513 @ ( cartprod @ SV176 @ SV364 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SY2513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1359,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ~ ( ~ ( in @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 ) )
| ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1360,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ~ ( ~ ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 ) )
| ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1361,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1362,plain,
! [SV368: $i > $o,SV180: $i] :
( ( ( ! [SY2362: $i] :
( ~ ( in @ SY2362 @ SV180 )
| ( SV368 @ SY2362 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1363,plain,
! [SV181: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( setunion @ SV181 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 )
| ~ ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1364,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
| ~ ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1365,plain,
! [SV183: $i,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV183 )
| ~ ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 ) ) )
= $true )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1366,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( ~ ( ~ ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
| ~ ( ( SV498
!= ( sK46_SY222 @ SV498 @ SV184 ) ) ) )
| ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1367,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( ~ ( ~ ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
| ~ ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1368,plain,
! [SV373: $i,SV186: $i,SV499: $i] :
( ( ~ ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
| ~ ( ~ ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
| ~ ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1369,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
| ~ ! [SY2365: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) )
| ~ ( ( SY2365
!= ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SY2365 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1370,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( ~ ( ~ ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
| ~ ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 ) ) )
= $true )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1371,plain,
! [SV189: $i,SV376: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV376 )
| ~ ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1372,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ~ ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) )
| ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1373,plain,
! [SV500: $i,SV378: $i,SV191: $i] :
( ( ~ ( func @ SV191 @ SV378 @ SV500 )
| ! [SY2518: $i] :
( ~ ( func @ SV191 @ SV378 @ SY2518 )
| ~ ( ~ ( in @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SY2518 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SY2518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1374,plain,
! [SV379: $i > $o,SV192: $i] :
( ( ( ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV192 )
| ( SV379 @ SY2380 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1375,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV501 ) )
= $true )
| ( ( ~ ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
| ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1376,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( ~ ( ~ ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
| ~ ( ( SV502
!= ( sK55_SY246 @ SV502 @ SV194 ) ) ) )
| ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1377,plain,
! [SV380: $o,SV195: $i,SV503: $i] :
( ( ~ ( in @ SV503 @ SV195 )
| ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV195 )
| SV380
| ( in @ SY2519
@ ( dsetconstr @ SV195
@ ^ [SY2520: $i] :
( ~ ( ~ SV380
| ( SY2520 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2520 != SY2519 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1378,plain,
! [SV195: $i,SV504: $i] :
( ( ~ ( in @ SV504 @ SV195 )
| ! [SY2521: $i] :
( ~ ( in @ SY2521 @ SV195 )
| $true
| ( in @ SY2521
@ ( dsetconstr @ SV195
@ ^ [SY2522: $i] :
( ~ ( ~ $true
| ( SY2522 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2522 != SY2521 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1379,plain,
! [SV195: $i,SV505: $i] :
( ( ~ ( in @ SV505 @ SV195 )
| ! [SY2523: $i] :
( ~ ( in @ SY2523 @ SV195 )
| $false
| ( in @ SY2523
@ ( dsetconstr @ SV195
@ ^ [SY2524: $i] :
( ~ ( ~ $false
| ( SY2524 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2524 != SY2523 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1380,plain,
! [SV381: $i,SV196: $i] :
( ( ( SV196 != SV381 )
= $true )
| ( ( ! [SY2384: $i > $o,SY2385: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) )
| ~ ( ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SX4: $i] : ( SY2384 @ SX4 ) )
= ( dsetconstr @ SV381
@ ^ [SX4: $i] : ( SY2385 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1381,plain,
! [SV382: $o,SV197: $i,SV506: $i] :
( ( ~ ( in @ SV506 @ SV197 )
| ! [SY2525: $i] :
( ~ ( in @ SY2525 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2526: $i] :
( ~ ( ~ SV382
| ( SY2526 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2526 != SY2525 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1382,plain,
! [SV197: $i,SV507: $i] :
( ( ~ ( in @ SV507 @ SV197 )
| ! [SY2527: $i] :
( ~ ( in @ SY2527 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2528: $i] :
( ~ ( ~ $true
| ( SY2528 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2528 != SY2527 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1383,plain,
! [SV197: $i,SV508: $i] :
( ( ~ ( in @ SV508 @ SV197 )
| ! [SY2529: $i] :
( ~ ( in @ SY2529 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2530: $i] :
( ~ ( ~ $false
| ( SY2530 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2530 != SY2529 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1384,plain,
! [SV198: $i,SV509: $i] :
( ( ( ! [SY2531: $i > $i] :
~ ( ~ ( in @ ( sK91_Xx @ SY2531 @ SV509 @ SV198 ) @ SV198 )
| ~ ~ ( in @ ( SY2531 @ ( sK91_Xx @ SY2531 @ SV509 @ SV198 ) ) @ SV509 ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1385,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1386,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1387,plain,
! [SV383: $o,SV199: $i,SV510: $i] :
( ( ~ ( in @ SV510 @ SV199 )
| ! [SY2532: $i] :
( ~ ( in @ SY2532 @ SV199 )
| ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2533: $i] :
( ~ ( ~ SV383
| ( SY2533 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2533 != SY2532 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1388,plain,
! [SV199: $i,SV511: $i] :
( ( ~ ( in @ SV511 @ SV199 )
| ! [SY2534: $i] :
( ~ ( in @ SY2534 @ SV199 )
| ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2535: $i] :
( ~ ( ~ $true
| ( SY2535 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2535 != SY2534 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1389,plain,
! [SV199: $i,SV512: $i] :
( ( ~ ( in @ SV512 @ SV199 )
| ! [SY2536: $i] :
( ~ ( in @ SY2536 @ SV199 )
| ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2537: $i] :
( ~ ( ~ $false
| ( SY2537 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2537 != SY2536 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1390,plain,
! [SV384: $i > $o,SV200: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ SV200 )
| ~ ( SV384 @ SV513 )
| ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1391,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ~ ( ~ ( in @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) @ SV201 )
| ~ ~ ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 ) )
| ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1392,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
| ~ ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) ) ) )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1393,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( ~ ( ~ ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) )
| ~ ( ( SV515
!= ( sK22_SY84 @ SV515 @ SV203 ) ) ) )
| ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1394,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1395,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ~ ( ~ ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
| ~ ~ ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 ) )
| ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1396,plain,
! [SV389: $i,SV206: $i,SV517: $i] :
( ( ~ ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
| ! [SY2542: $i] :
( ~ ( subset @ SY2542 @ ( cartprod @ SV206 @ SV389 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SY2542 ) ) ) )
| ( subset @ SV517 @ SY2542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1397,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) )
| ~ ( ( SV518
!= ( sK18_SY55 @ SV518 @ SV207 ) ) ) )
| ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1398,plain,
! [SV390: $i,SV208: $i,SV519: $i] :
( ( ~ ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
| ! [SY2543: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SY2543 @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
| ! [SY2544: $i] :
( ~ ( in @ SY2544 @ SV519 )
| ( SY2543 @ SY2544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1399,plain,
! [SV209: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV209 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 )
| ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1400,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK53_Xx @ SX1 @ SX0 )
!= ( sK54_SY1668 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK53_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK54_SY1668 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK52_SY231 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK51_SY233 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK51_SY233 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1401,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK49_Xx @ SX1 @ SX0 )
!= ( sK50_SY1666 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK49_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK50_SY1666 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK48_SY234 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK47_SY230 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK47_SY230 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1402,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
| ~ ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) ) ) )
= $true )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1403,plain,
! [SV211: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1404,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ~ ( ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
!= SV521 )
| ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
| ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
| ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1405,plain,
! [SV392: $o,SV213: $i,SV522: $i] :
( ( ~ ( in @ SV522 @ SV213 )
| ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV213 )
| SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2546: $i] :
( ~ ( ~ SV392
| ( SY2546 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2546 != SY2545 ) ) ) )
= ( setadjoin @ SY2545 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1406,plain,
! [SV213: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ SV213 )
| ! [SY2547: $i] :
( ~ ( in @ SY2547 @ SV213 )
| $true
| ( ( dsetconstr @ SV213
@ ^ [SY2548: $i] :
( ~ ( ~ $true
| ( SY2548 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2548 != SY2547 ) ) ) )
= ( setadjoin @ SY2547 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1407,plain,
! [SV213: $i,SV524: $i] :
( ( ~ ( in @ SV524 @ SV213 )
| ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV213 )
| $false
| ( ( dsetconstr @ SV213
@ ^ [SY2550: $i] :
( ~ ( ~ $false
| ( SY2550 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2550 != SY2549 ) ) ) )
= ( setadjoin @ SY2549 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1408,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ( ~ ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
| ~ ( ( SV525
!= ( sK31_SY140 @ SV525 @ SV214 ) ) ) )
| ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1409,plain,
! [SV215: $i,SV393: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV215 )
| ~ ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 ) ) )
= $true )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1410,plain,
! [SV394: $i,SV216: $i,SV526: $i] :
( ( ~ ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
| ! [SY2551: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SY2551 @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
| ! [SY2552: $i] :
( ~ ( in @ SY2552 @ SV526 )
| ( SY2551 @ SY2552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1411,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ~ ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
| ~ ( ~ ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1412,plain,
! [SV218: $i] :
( ( ~ ! [SY2157: $i > $o,SY2158: $i] :
( ~ ( in @ SY2158 @ SV218 )
| ~ ( SY2157 @ SY2158 )
| ( in @ SY2158
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2157 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1413,plain,
! [SV218: $i] :
( ( ~ ! [SY2160: $i > $o,SY2161: $i] :
( ~ ( in @ SY2161 @ SV218 )
| ~ ( in @ SY2161
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2160 @ SX3 ) ) )
| ( SY2160 @ SY2161 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1414,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( setunion @ SV219 ) ) )
= $true )
| ( ( ! [SY2420: $o] :
( ~ ( ~ ( in @ SV396 @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SY2420 ) )
| SY2420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1415,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ( ~ ( ( ( sK58_Xx @ SV397 @ SV220 )
!= ( sK59_SY1669 @ SV397 @ SV220 ) )
| ~ ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1416,plain,
! [SV398: $o,SV221: $i,SV528: $i] :
( ( ~ ( in @ SV528 @ SV221 )
| ! [SY2557: $i] :
( ~ ( in @ SY2557 @ SV221 )
| ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2558: $i] :
( ~ ( ~ SV398
| ( SY2558 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2558 != SY2557 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1417,plain,
! [SV221: $i,SV529: $i] :
( ( ~ ( in @ SV529 @ SV221 )
| ! [SY2559: $i] :
( ~ ( in @ SY2559 @ SV221 )
| ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2560: $i] :
( ~ ( ~ $true
| ( SY2560 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2560 != SY2559 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1418,plain,
! [SV221: $i,SV530: $i] :
( ( ~ ( in @ SV530 @ SV221 )
| ! [SY2561: $i] :
( ~ ( in @ SY2561 @ SV221 )
| ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2562: $i] :
( ~ ( ~ $false
| ( SY2562 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2562 != SY2561 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1419,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1420,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK6_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK6_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1421,plain,
! [SV1: $i,SV222: $i] :
( ( ( in @ SV222 @ ( powerset @ SV1 ) )
= $false )
| ( ( in @ ( powerset @ SV222 ) @ ( powerset @ ( powerset @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1422,plain,
! [SV2: $i,SV223: $i] :
( ( ( in @ SV223 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY2174: $i] :
( ~ ( in @ SY2174 @ ( powerset @ SV2 ) )
| ( in @ ( binunion @ SV223 @ SY2174 ) @ ( powerset @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1423,plain,
! [SV3: $i,SV224: $i] :
( ( ( in @ SV224 @ ( powerset @ SV3 ) )
= $false )
| ( ( ! [SY2175: $i] :
( ~ ( in @ SY2175 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV224 @ SY2175 ) @ ( powerset @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1424,plain,
! [SV225: $o,SV4: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ SV4 ) )
= $true )
| ( ( ! [SY2428: $i] :
( ~ ( in @ SY2428 @ SV4 )
| ( in @ ( if @ SV4 @ SV225 @ SV399 @ SY2428 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SY2428 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1425,plain,
! [SV4: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ SV4 ) )
= $true )
| ( ( ! [SY2429: $i] :
( ~ ( in @ SY2429 @ SV4 )
| ( in @ ( if @ SV4 @ $true @ SV400 @ SY2429 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SY2429 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1426,plain,
! [SV4: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV4 ) )
= $true )
| ( ( ! [SY2430: $i] :
( ~ ( in @ SY2430 @ SV4 )
| ( in @ ( if @ SV4 @ $false @ SV401 @ SY2430 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SY2430 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1427,plain,
! [SV226: $o,SV5: $i,SV402: $i] :
( ( ( ~ ( in @ SV402 @ SV5 ) )
= $true )
| ( ( ! [SY2431: $i] :
( ~ ( in @ SY2431 @ SV5 )
| SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SY2431 )
= SY2431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1428,plain,
! [SV5: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV5 ) )
= $true )
| ( ( ! [SY2432: $i] :
( ~ ( in @ SY2432 @ SV5 )
| $true
| ( ( if @ SV5 @ $true @ SV403 @ SY2432 )
= SY2432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1429,plain,
! [SV5: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV5 ) )
= $true )
| ( ( ! [SY2433: $i] :
( ~ ( in @ SY2433 @ SV5 )
| $false
| ( ( if @ SV5 @ $false @ SV404 @ SY2433 )
= SY2433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1430,plain,
! [SV227: $o,SV6: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV6 ) )
= $true )
| ( ( ! [SY2434: $i] :
( ~ ( in @ SY2434 @ SV6 )
| ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SY2434 )
= SV405 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1431,plain,
! [SV6: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV6 ) )
= $true )
| ( ( ! [SY2435: $i] :
( ~ ( in @ SY2435 @ SV6 )
| ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SY2435 )
= SV406 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1432,plain,
! [SV6: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV6 ) )
= $true )
| ( ( ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV6 )
| ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SY2436 )
= SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1433,plain,
! [SV7: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV7 )
| ( ( setunion @ SV7 )
= SV531 ) )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1434,plain,
! [SV228: $o,SV8: $i,SV408: $i] :
( ( ( ~ ( in @ SV408 @ SV8 ) )
= $true )
| ( ( ! [SY2437: $i] :
( ~ ( in @ SY2437 @ SV8 )
| ( in @ ( if @ SV8 @ SV228 @ SV408 @ SY2437 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1435,plain,
! [SV8: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ SV8 ) )
= $true )
| ( ( ! [SY2438: $i] :
( ~ ( in @ SY2438 @ SV8 )
| ( in @ ( if @ SV8 @ $true @ SV409 @ SY2438 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1436,plain,
! [SV8: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV8 ) )
= $true )
| ( ( ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV8 )
| ( in @ ( if @ SV8 @ $false @ SV410 @ SY2439 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1437,plain,
! [SV229: $i,SV9: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ ( funcSet @ SV9 @ SV229 ) ) )
= $true )
| ( ( ( lam @ SV9 @ SV229
@ ^ [SY2440: $i] : ( ap @ SV9 @ SV229 @ SV411 @ SY2440 ) )
= SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1438,plain,
! [SV412: $i,SV230: $i,SV10: $i] :
( ( ( ~ ( func @ SV10 @ SV230 @ SV412 ) )
= $true )
| ( ( ( lam @ SV10 @ SV230
@ ^ [SY2441: $i] : ( ap @ SV10 @ SV230 @ SV412 @ SY2441 ) )
= SV412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1439,plain,
! [SV532: $i,SV413: $i,SV11: $i] :
( ( ( ~ ( func @ SV11 @ SV413 @ SV532 ) )
= $true )
| ( ( ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1440,plain,
! [SV414: $i,SV12: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ ( funcSet @ SV12 @ SV414 ) ) )
= $true )
| ( ( ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1441,plain,
! [SV231: $i,SV13: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) ) )
= $true )
| ( ( ! [SY2444: $i] :
( ~ ( in @ SY2444 @ SV13 )
| ! [SY2445: $i] :
( ~ ( in @ SY2445 @ SV231 )
| ~ ( in @ ( kpair @ SY2444 @ SY2445 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SY2444 )
= SY2445 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1442,plain,
! [SV416: $i,SV232: $i,SV14: $i] :
( ( ( ~ ( func @ SV14 @ SV232 @ SV416 ) )
= $true )
| ( ( ! [SY2446: $i] :
( ~ ( in @ SY2446 @ SV14 )
| ! [SY2447: $i] :
( ~ ( in @ SY2447 @ SV232 )
| ~ ( in @ ( kpair @ SY2446 @ SY2447 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SY2446 )
= SY2447 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1443,plain,
! [SV233: $i,SV15: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) ) )
= $true )
| ( ( ! [SY2448: $i] :
( ~ ( in @ SY2448 @ SV15 )
| ( in @ ( kpair @ SY2448 @ ( ap @ SV15 @ SV233 @ SV417 @ SY2448 ) ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1444,plain,
! [SV418: $i,SV234: $i,SV16: $i] :
( ( ( ~ ( func @ SV16 @ SV234 @ SV418 ) )
= $true )
| ( ( ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SV16 )
| ( in @ ( kpair @ SY2449 @ ( ap @ SV16 @ SV234 @ SV418 @ SY2449 ) ) @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1445,plain,
! [SV235: $i > $o,SV17: $i] :
( ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false )
| ( ( ! [SY2199: $i] :
( ~ ( in @ SY2199 @ SV17 )
| ! [SY2200: $i] :
( ~ ( in @ SY2200 @ SV17 )
| ~ ( SV235 @ SY2199 )
| ~ ( SV235 @ SY2200 )
| ( SY2199 = SY2200 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1446,plain,
! [SV419: $i,SV236: $i,SV18: $i] :
( ( ( ~ ( func @ SV18 @ SV236 @ SV419 ) )
= $true )
| ( ( in @ SV419 @ ( funcSet @ SV18 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1447,plain,
! [SV237: $i,SV19: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) ) )
= $true )
| ( ( ! [SY2450: $i] :
( ~ ( in @ SY2450 @ SV19 )
| ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SY2450 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1448,plain,
! [SV238: $i,SV20: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ ( funcSet @ SV20 @ SV238 ) ) )
= $true )
| ( ( func @ SV20 @ SV238 @ SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1449,plain,
! [SV422: $i,SV239: $i,SV21: $i] :
( ( ( ~ ( func @ SV21 @ SV239 @ SV422 ) )
= $true )
| ( ( ! [SY2451: $i] :
( ~ ( in @ SY2451 @ SV21 )
| ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SY2451 ) @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1450,plain,
! [SV423: $i,SV240: $i,SV22: $i] :
( ( ( ~ ( func @ SV22 @ SV240 @ SV423 ) )
= $true )
| ( ( ! [SY2452: $i] :
( ~ ( in @ SY2452 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2453: $i] : ( in @ ( kpair @ SY2452 @ SY2453 ) @ SV423 ) ) )
@ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1451,plain,
! [SV424: $i,SV241: $i,SV23: $i] :
( ( ( ~ ( func @ SV23 @ SV241 @ SV424 ) )
= $true )
| ( ( ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SV23 )
| ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2455: $i] : ( in @ ( kpair @ SY2454 @ SY2455 ) @ SV424 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1452,plain,
! [SV425: $i > $i > $o,SV242: $i,SV24: $i,SV534: $i] :
( ( ! [SY2563: $i] :
( ~ ( in @ ( kpair @ SV534 @ SY2563 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [SY2458: $i,SY2459: $i] : ( SV425 @ SY2458 @ SY2459 ) ) )
| ( SV425 @ SV534 @ SY2563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1453,plain,
! [SV426: $i > $i > $o,SV243: $i,SV25: $i,SV535: $i] :
( ( ! [SY2566: $i] :
( ~ ( in @ ( kpair @ SV535 @ SY2566 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [SY2462: $i,SY2463: $i] : ( SV426 @ SY2462 @ SY2463 ) ) )
| ( in @ SY2566 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1454,plain,
! [SV427: $i > $i > $o,SV244: $i,SV26: $i,SV536: $i] :
( ( ! [SY2569: $i] :
~ ( in @ ( kpair @ SV536 @ SY2569 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [SY2466: $i,SY2467: $i] : ( SV427 @ SY2466 @ SY2467 ) ) )
| ( in @ SV536 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1455,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i,SV537: $i] :
( ( ~ ( in @ SV537 @ SV27 )
| ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV245 )
| ~ ( in @ ( kpair @ SV537 @ SY2572 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SY2572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1456,plain,
! [SV431: $i > $i > $o,SV248: $i,SV30: $i,SV538: $i] :
( ( ~ ( in @ SV538 @ SV30 )
| ! [SY2575: $i] :
( ~ ( in @ SY2575 @ SV248 )
| ~ ( SV431 @ SV538 @ SY2575 )
| ( in @ ( kpair @ SV538 @ SY2575 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1457,plain,
! [SV249: $i,SV31: $i,SV432: $i] :
( ( ( ~ ( in @ SV432 @ ( cartprod @ SV31 @ SV249 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV432 ) @ ( ksnd @ SV432 ) )
= SV432 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1458,plain,
! [SV250: $i,SV32: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ SV32 ) )
= $true )
| ( ( ! [SY2480: $i] :
( ~ ( in @ SY2480 @ SV250 )
| ( ( ksnd @ ( kpair @ SV433 @ SY2480 ) )
= SY2480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1459,plain,
! [SV251: $i,SV33: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV33 ) )
= $true )
| ( ( ! [SY2481: $i] :
( ~ ( in @ SY2481 @ SV251 )
| ( ( kfst @ ( kpair @ SV434 @ SY2481 ) )
= SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1460,plain,
! [SV34: $i,SV435: $i] :
( ( ( in @ SV435 @ SV34 )
= $false )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1461,plain,
! [SV252: $i,SV35: $i,SV539: $i,SV436: $i] :
( ( ~ ( in @ ( kpair @ SV436 @ SV539 ) @ ( cartprod @ SV35 @ SV252 ) )
| ( in @ SV539 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1462,plain,
! [SV253: $i,SV36: $i,SV437: $i] :
( ( ( ! [SY2483: $i] :
~ ( in @ ( kpair @ SV437 @ SY2483 ) @ ( cartprod @ SV36 @ SV253 ) ) )
= $true )
| ( ( in @ SV437 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1463,plain,
! [SV254: $i,SV37: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ ( cartprod @ SV37 @ SV254 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV438 ) @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1464,plain,
! [SV540: $i,SV439: $i,SV256: $i,SV41: $i] :
( ( ( ( kpair @ SV41 @ SV256 )
!= ( kpair @ SV439 @ SV540 ) )
| ( SV256 = SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1465,plain,
! [SV541: $i,SV440: $i,SV257: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV257 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV440 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV440 @ ( setadjoin @ SV541 @ emptyset ) ) @ emptyset ) ) )
| ( SV257 = SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1466,plain,
! [SV542: $i,SV258: $i,SV43: $i] :
( ( ( ( setadjoin @ SV43 @ ( setadjoin @ SV258 @ emptyset ) )
!= ( setadjoin @ SV542 @ emptyset ) )
= $true )
| ( ( SV43 = SV258 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1467,plain,
! [SV543: $i,SV441: $i,SV259: $i,SV44: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) ) )
| ( SV441 != SV543 )
| ( SV259 = SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1468,plain,
! [SV260: $i,SV45: $i] :
( ( ( SV45 = SV260 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV45 @ ( setadjoin @ SV260 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV45 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1469,plain,
! [SV261: $i,SV46: $i] :
( ( ( SV46 = SV261 )
= $false )
| ( ( ( setadjoin @ SV46 @ ( setadjoin @ SV261 @ emptyset ) )
= ( setadjoin @ SV46 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1470,plain,
! [SV442: $i,SV262: $i,SV47: $i] :
( ( ( ! [SY2487: $i] :
( ( kpair @ SV47 @ SV262 )
!= ( kpair @ SV442 @ SY2487 ) ) )
= $true )
| ( ( SV47 = SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1471,plain,
! [SV443: $i,SV263: $i,SV48: $i] :
( ( ( ! [SY2488: $i] :
( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV443 @ ( setadjoin @ SY2488 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV48 = SV443 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1472,plain,
! [SV264: $i,SV49: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( cartprod @ SV49 @ SV264 ) ) )
= $true )
| ( ( in @ ( kfst @ SV444 ) @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1473,plain,
! [SV266: $i,SV53: $i,SV445: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV266 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV53 = SV445 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1474,plain,
! [SV267: $i,SV54: $i] :
( ( ( ( setadjoin @ SV54 @ emptyset )
= ( setadjoin @ SV267 @ emptyset ) )
= $false )
| ( ( SV54 = SV267 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1475,plain,
! [SV268: $i,SV58: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ ( cartprod @ SV58 @ SV268 ) ) )
= $true )
| ( ( iskpair @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1476,plain,
! [SV269: $i,SV59: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ SV59 ) )
= $true )
| ( ( ! [SY2489: $i] :
( ~ ( in @ SY2489 @ SV269 )
| ( in @ ( kpair @ SV447 @ SY2489 ) @ ( cartprod @ SV59 @ SV269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1477,plain,
! [SV270: $i,SV60: $i,SV448: $i] :
( ( ( ~ ( in @ SV448 @ SV60 ) )
= $true )
| ( ( ! [SY2490: $i] :
( ~ ( in @ SY2490 @ SV270 )
| ( in @ ( kpair @ SV448 @ SY2490 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1478,plain,
! [SV271: $i,SV61: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ SV61 ) )
= $true )
| ( ( ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SV271 )
| ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SY2491 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1479,plain,
! [SV272: $i,SV62: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ SV62 ) )
= $true )
| ( ( ! [SY2492: $i] :
( ~ ( in @ SY2492 @ SV272 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SY2492 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1480,plain,
! [SV273: $i,SV63: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV63 ) )
= $true )
| ( ( ! [SY2493: $i] :
( ~ ( in @ SY2493 @ SV273 )
| ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SY2493 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1481,plain,
! [SV274: $i,SV64: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV64 ) )
= $true )
| ( ( ! [SY2494: $i] :
( ~ ( in @ SY2494 @ SV274 )
| ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SY2494 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1482,plain,
! [SV275: $i,SV65: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( setadjoin @ SV65 @ ( setadjoin @ SV275 @ emptyset ) ) ) )
= $true )
| ( ( ( SV453 = SV65 )
| ( SV453 = SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1483,plain,
! [SV276: $i,SV66: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ SV66 ) )
= $true )
| ( ( in @ ( setadjoin @ SV454 @ emptyset ) @ ( powerset @ ( binunion @ SV66 @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1484,plain,
! [SV67: $i,SV277: $i] :
( ( ( in @ SV277 @ SV67 )
= $false )
| ( ( in @ ( setadjoin @ SV277 @ emptyset ) @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1485,plain,
! [SV68: $i,SV278: $i] :
( ( ( in @ SV278 @ SV68 )
= $false )
| ( ( subset @ ( setadjoin @ SV278 @ emptyset ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1486,plain,
! [SV284: $i,SV74: $i,SV455: $i] :
( ( ( in @ SV455 @ SV74 )
= $true )
| ( ( ( in @ SV455 @ SV284 )
| ~ ( in @ SV455 @ ( symdiff @ SV74 @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1487,plain,
! [SV285: $i,SV75: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV456 @ SV285 )
| ~ ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1488,plain,
! [SV286: $i,SV76: $i,SV457: $i] :
( ( ( in @ SV457 @ SV76 )
= $true )
| ( ( ~ ( in @ SV457 @ SV286 )
| ( in @ SV457 @ ( symdiff @ SV76 @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1489,plain,
! [SV287: $i,SV77: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV77 ) )
= $true )
| ( ( ( in @ SV458 @ SV287 )
| ( in @ SV458 @ ( symdiff @ SV77 @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1490,plain,
! [SV288: $i,SV78: $i] :
( ( ( ( setminus @ SV78 @ SV288 )
= emptyset )
= $false )
| ( ( subset @ SV78 @ SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1491,plain,
! [SV80: $i,SV290: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV290 ) )
= $true )
| ( ( ~ ( in @ SV459 @ ( setminus @ SV80 @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1492,plain,
! [SV291: $i,SV81: $i,SV460: $i] :
( ( ( in @ SV460 @ SV81 )
= $true )
| ( ( ~ ( in @ SV460 @ ( setminus @ SV81 @ SV291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1493,plain,
! [SV292: $i,SV82: $i,SV461: $i] :
( ( ( in @ SV461 @ ( setminus @ SV82 @ SV292 ) )
= $true )
| ( ( ( in @ SV461 @ SV292 )
| ~ ( in @ SV461 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1494,plain,
! [SV293: $i,SV83: $i,SV462: $i] :
( ( ( in @ SV462 @ ( setminus @ SV83 @ SV293 ) )
= $true )
| ( ( ~ ( in @ SV462 @ SV83 )
| ( in @ SV462 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1495,plain,
! [SV294: $i,SV84: $i] :
( ( ( subset @ SV84 @ SV294 )
= $false )
| ( ( ( setminus @ SV84 @ SV294 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1496,plain,
! [SV295: $i,SV85: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ ( setminus @ SV85 @ SV295 ) ) )
= $true )
| ( ( ~ ( in @ SV463 @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1497,plain,
! [SV296: $i,SV86: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( setminus @ SV86 @ SV296 ) ) )
= $true )
| ( ( in @ SV464 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1498,plain,
! [SV297: $i,SV87: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV87 ) )
= $true )
| ( ( ( in @ SV465 @ SV297 )
| ( in @ SV465 @ ( setminus @ SV87 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1499,plain,
! [SV299: $i,SV89: $i] :
( ( ( ( binintersect @ SV89 @ SV299 )
= SV89 )
= $false )
| ( ( subset @ SV89 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1500,plain,
! [SV90: $i,SV300: $i] :
( ( ( subset @ SV300 @ SV90 )
= $false )
| ( ( ( binintersect @ SV90 @ SV300 )
= SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1501,plain,
! [SV302: $i,SV92: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ ( binintersect @ SV92 @ SV302 ) ) )
= $true )
| ( ( in @ SV467 @ SV302 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1502,plain,
! [SV303: $i,SV93: $i] :
( ( ( ( binintersect @ SV93 @ SV303 )
= SV303 )
= $false )
| ( ( subset @ SV303 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1503,plain,
! [SV304: $i,SV94: $i] :
( ( ( subset @ SV94 @ SV304 )
= $false )
| ( ( ( binintersect @ SV94 @ SV304 )
= SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1504,plain,
! [SV306: $i,SV96: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ ( binintersect @ SV96 @ SV306 ) ) )
= $true )
| ( ( in @ SV468 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1505,plain,
! [SV307: $i,SV97: $i,SV469: $i] :
( ( ( ~ ( subset @ SV469 @ SV97 ) )
= $true )
| ( ( ~ ( subset @ SV469 @ SV307 )
| ( subset @ SV469 @ ( binintersect @ SV97 @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1506,plain,
! [SV308: $i,SV98: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV98 ) )
= $true )
| ( ( ~ ( in @ SV470 @ SV308 )
| ( in @ SV470 @ ( binintersect @ SV98 @ SV308 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1507,plain,
! [SV311: $i,SV101: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ ( binunion @ SV101 @ SV311 ) ) )
= $true )
| ( ( ( in @ SV471 @ SV101 )
| ( in @ SV471 @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1508,plain,
! [SV102: $i,SV312: $i,SV472: $i] :
( ( ( ~ ( in @ SV472 @ SV312 ) )
= $true )
| ( ( in @ SV472 @ ( binunion @ SV102 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1509,plain,
! [SV314: $i,SV104: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV104 ) )
= $true )
| ( ( in @ SV473 @ ( binunion @ SV104 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1510,plain,
! [SV317: $i,SV107: $i] :
( ( ( subset @ SV107 @ SV317 )
= $false )
| ( ( subset @ ( powerset @ SV107 ) @ ( powerset @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1511,plain,
! [SV109: $i,SV318: $i] :
( ( ( in @ SV318 @ ( powerset @ SV109 ) )
= $false )
| ( ( subset @ SV318 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1512,plain,
! [SV110: $i,SV319: $i] :
( ( ( subset @ SV319 @ SV110 )
= $false )
| ( ( in @ SV319 @ ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1513,plain,
! [SV320: $i,SV112: $i] :
( ( ( subset @ SV112 @ SV320 )
= $false )
| ( ( ~ ( subset @ SV320 @ SV112 )
| ( SV112 = SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1514,plain,
! [SV321: $i,SV113: $i] :
( ( ( subset @ SV113 @ SV321 )
= $false )
| ( ( in @ SV113 @ ( powerset @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1515,plain,
! [SV322: $i,SV474: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ SV474 ) )
= $true )
| ( ( subset @ SV114 @ ( setadjoin @ SV322 @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1516,plain,
! [SV324: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV324 )
= $false )
| ( ( ! [SY2304: $i] :
( ~ ( subset @ SV324 @ SY2304 )
| ( subset @ SV116 @ SY2304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1517,plain,
! [SV325: $i,SV118: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV118 ) )
= $true )
| ( ( ( in @ SV475 @ SV325 )
| ( SV118 != SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1518,plain,
! [SV326: $i,SV119: $i] :
( ( ( SV119 = SV326 )
= $false )
| ( ( subset @ SV119 @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1519,plain,
! [SV327: $i,SV120: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ SV120 ) )
= $true )
| ( ( ( in @ SV476 @ SV327 )
| ~ ( subset @ SV120 @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1520,plain,
! [SV328: $i,SV121: $i] :
( ( ( subset @ SV121 @ SV328 )
= $false )
| ( ( ! [SY2307: $i] :
( ( in @ SY2307 @ SV328 )
| ~ ( in @ SY2307 @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1521,plain,
! [SV329: $i,SV122: $i] :
( ( ( subset @ SV122 @ SV329 )
= $false )
| ( ( ! [SY2308: $i] :
( ~ ( in @ SY2308 @ SV122 )
| ( in @ SY2308 @ SV329 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1522,plain,
! [SV330: $i,SV124: $i] :
( ( ( SV124 = SV330 )
= $false )
| ( ( subset @ SV124 @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1523,plain,
! [SV331: $i,SV125: $i] :
( ( ( SV125 = SV331 )
= $false )
| ( ( subset @ SV331 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1524,plain,
! [SV332: $i,SV126: $i] :
( ( ( SV126 = SV332 )
= $false )
| ( ( ( setunion @ SV126 )
= ( setunion @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1525,plain,
! [SV333: $i,SV127: $i] :
( ( ( SV127 = SV333 )
= $false )
| ( ( ( powerset @ SV127 )
= ( powerset @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1526,plain,
! [SV334: $i,SV128: $i] :
( ( ( SV128 = SV334 )
= $false )
| ( ( ! [SY2309: $i,SY2310: $i] :
( ( SY2309 != SY2310 )
| ( ( setadjoin @ SV128 @ SY2309 )
= ( setadjoin @ SV334 @ SY2310 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1527,plain,
! [SV335: $i,SV129: $i] :
( ( ( SV129 = SV335 )
= $false )
| ( ( ! [SY2311: $i,SY2312: $i] :
( ( SY2311 != SY2312 )
| ~ ( in @ SY2311 @ SV129 )
| ( in @ SY2312 @ SV335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1528,plain,
! [SV132: $i > $o,SV336: $i] :
( ( ( in @ SV336 @ emptyset )
= $false )
| ( ( SV132 @ SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1529,plain,
! [SV133: $i,SV544: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ SV544 )
| ~ ( in @ SV544 @ SV133 ) )
= $true )
| ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1530,plain,
! [SV340: $i,SV136: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ ( setadjoin @ SV136 @ ( setadjoin @ SV340 @ emptyset ) ) ) )
= $true )
| ( ( ( SV477 = SV136 )
| ( SV477 = SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1531,plain,
! [SV341: $i,SV137: $i] :
( ( ( in @ SV137 @ ( setadjoin @ SV341 @ emptyset ) )
= $false )
| ( ( in @ SV341 @ ( setadjoin @ SV137 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1532,plain,
! [SV342: $i,SV138: $i] :
( ( ( SV138 = SV342 )
= $false )
| ( ( in @ SV138 @ ( setadjoin @ SV342 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1533,plain,
! [SV139: $i,SV343: $i] :
( ( ( in @ SV343 @ ( setadjoin @ SV139 @ emptyset ) )
= $false )
| ( ( SV139 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1534,plain,
! [SV344: $i,SV140: $i] :
( ( ( in @ SV140 @ ( setadjoin @ SV344 @ emptyset ) )
= $false )
| ( ( SV140 = SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1535,plain,
! [SV142: $i,SV345: $i] :
( ( ( in @ SV345 @ SV142 )
= $false )
| ( ( in @ SV345 @ ( powerset @ ( setunion @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1536,plain,
! [SV143: $i,SV478: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ SV478 ) )
= $true )
| ( ( ~ ( in @ SV478 @ SV143 )
| ( in @ SV346 @ ( setunion @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1537,plain,
! [SV144: $i,SV347: $i] :
( ( ( in @ SV347 @ ( powerset @ SV144 ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( in @ SY2317 @ SV347 )
| ( in @ SY2317 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1538,plain,
! [SV348: $i,SV148: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( setadjoin @ SV148 @ SV348 ) ) )
= $true )
| ( ( ( SV479 = SV148 )
| ( in @ SV479 @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1539,plain,
! [SV149: $i,SV349: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV349 ) )
= $true )
| ( ( in @ SV480 @ ( setadjoin @ SV149 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1540,plain,
! [SV151: $i,SV481: $i] :
( ( ( in @ SV481 @ SV151 )
= $false )
| ( ( SV151 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1541,plain,
! [SV351: $i > $o,SV152: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV152 ) )
= $true )
| ( ( ~ ( SV351 @ SV482 )
| ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1542,plain,
! [SV352: $i,SV545: $o] :
( ( SV545 = $true )
| ( ( in @ SV352 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1334]) ).
thf(1543,plain,
! [SV352: $i] :
( ( $true = $true )
| ( ( in @ SV352 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1334]) ).
thf(1544,plain,
! [SV352: $i] :
( ( $false = $true )
| ( ( in @ SV352 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1334]) ).
thf(1545,plain,
! [SV158: $o,SV483: $i] :
( ( ( in @ SV483 @ ( prop2set @ SV158 ) )
= $false )
| ( SV158 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1546,plain,
! [SV484: $i] :
( ( ( in @ SV484 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1547,plain,
! [SV485: $i] :
( ( ( in @ SV485 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1548,plain,
! [SV353: $i > $o,SV159: $i,SV486: $i] :
( ( ( ~ ( in @ SV486
@ ( dsetconstr @ SV159
@ ^ [SY2323: $i] : ( SV353 @ SY2323 ) ) ) )
= $true )
| ( ( SV353 @ SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1549,plain,
! [SV354: $i > $o,SV160: $i,SV487: $i] :
( ( ( ~ ( in @ SV487
@ ( dsetconstr @ SV160
@ ^ [SY2325: $i] : ( SV354 @ SY2325 ) ) ) )
= $true )
| ( ( in @ SV487 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1550,plain,
! [SV355: $i > $o,SV161: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV161 ) )
= $true )
| ( ( ~ ( SV355 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1551,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( ~ ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
| ~ ( ( SV489
!= ( sK20_SY72 @ SV489 @ SV164 ) ) ) ) )
= $true )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1552,plain,
! [SV356: $i,SV165: $i] :
( ( ( SV165 = SV356 )
= $false )
| ( ( ~ ( ~ ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) )
| ~ ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1553,plain,
! [SV490: $i,SV357: $i,SV166: $i] :
( ( ( ~ ( func @ SV166 @ SV357 @ SV490 ) )
= $true )
| ( ( ! [SY2499: $i] :
( ~ ( func @ SV166 @ SV357 @ SY2499 )
| ~ ( ~ ( in @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SY2499 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2500: $i] :
( ~ ( in @ SY2500 @ SV166 )
| ! [SY2501: $i] :
( ~ ( in @ SY2501 @ SV357 )
| ~ ( in @ ( kpair @ SY2500 @ SY2501 ) @ SY2499 )
| ( in @ ( kpair @ SY2500 @ SY2501 ) @ SV490 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1554,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) @ SV167 )
| ~ ~ ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 ) ) )
= $true )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1555,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1556,plain,
( ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1557,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( ~ ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
| ~ ( ( SV493
!= ( sK40_Xy @ SV493 @ SV169 ) ) ) ) )
= $true )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1558,plain,
! [SV170: $i] :
( ( ! [SY2009: $i] :
( ~ ( ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SY2009 )
| ~ ~ ( in @ ( sK17_Xx @ SY2009 @ SV170 ) @ SV170 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2009 )
| ~ ( ~ ! [SY2011: $i] :
( ~ ( in @ SY2011 @ ( sK13_B @ SV170 ) )
| ! [SY2012: $i] :
( ~ ( in @ SY2012 @ SY2011 )
| ( in @ SY2012 @ ( sK15_SY1637 @ SY2009 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2011 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SY2009 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SY2009 @ SV170 ) @ SY2009 ) )
| ~ ! [SY2013: $i] :
( ~ ( in @ SY2013 @ ( sK15_SY1637 @ SY2009 @ SV170 ) )
| ~ ( in @ SY2013 @ SY2009 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1559,plain,
! [SV170: $i] :
( ( ~ ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) )
| ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1560,plain,
! [SV360: $i,SV171: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) ) )
= $true )
| ( ( ! [SY2512: $i] :
( ~ ( in @ SY2512 @ ( funcSet @ SV171 @ SV360 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SY2512 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SY2512 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1561,plain,
! [SV172: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV172 )
| ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV361 ) )
= $false )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1562,plain,
! [SV362: $i > $o,SV173: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV173 )
| ( SV362 @ SV546 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1563,plain,
! [SV174: $i] :
( ( ! [SY2028: $i,SY2029: $i] :
( ~ ( in @ SY2029 @ ( setadjoin @ SV174 @ SY2028 ) )
| ( SY2029 = SV174 )
| ( in @ SY2029 @ SY2028 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1564,plain,
! [SV174: $i] :
( ( ~ ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) )
| ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1565,plain,
! [SV363: $i > $o,SV175: $i] :
( ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false )
| ( ( ~ ( ~ ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) )
| ~ ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1566,plain,
! [SV364: $i,SV176: $i,SV495: $i] :
( ( ( ~ ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) ) )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( subset @ SY2513 @ ( cartprod @ SV176 @ SV364 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SY2513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1567,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 ) ) )
= $true )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1568,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 ) ) )
= $true )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1569,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1570,plain,
! [SV368: $i > $o,SV180: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV180 )
| ( SV368 @ SV547 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1571,plain,
! [SV181: $i,SV369: $i] :
( ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 )
| ~ ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1572,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
| ~ ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1573,plain,
! [SV183: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV183 )
| ~ ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 ) )
= $false )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1574,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( ~ ( ~ ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
| ~ ( ( SV498
!= ( sK46_SY222 @ SV498 @ SV184 ) ) ) ) )
= $true )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1575,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( ~ ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
| ~ ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 ) )
= $false )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1576,plain,
! [SV373: $i,SV186: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
| ~ ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1577,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
| ~ ! [SY2365: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) )
| ~ ( ( SY2365
!= ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SY2365 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1578,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( ~ ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
| ~ ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 ) )
= $false )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1370]) ).
thf(1579,plain,
! [SV189: $i,SV376: $i] :
( ( ( ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV376 )
| ~ ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1580,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ~ ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1581,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ~ ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) )
| ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1582,plain,
! [SV500: $i,SV378: $i,SV191: $i] :
( ( ( ~ ( func @ SV191 @ SV378 @ SV500 ) )
= $true )
| ( ( ! [SY2518: $i] :
( ~ ( func @ SV191 @ SV378 @ SY2518 )
| ~ ( ~ ( in @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SY2518 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SY2518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1583,plain,
! [SV379: $i > $o,SV192: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ SV192 )
| ( SV379 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1584,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ SV501 )
= $false )
| ( ( ~ ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
| ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1585,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( ~ ( ~ ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
| ~ ( ( SV502
!= ( sK55_SY246 @ SV502 @ SV194 ) ) ) ) )
= $true )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1586,plain,
! [SV380: $o,SV195: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV195 ) )
= $true )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV195 )
| SV380
| ( in @ SY2519
@ ( dsetconstr @ SV195
@ ^ [SY2520: $i] :
( ~ ( ~ SV380
| ( SY2520 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2520 != SY2519 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1587,plain,
! [SV195: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV195 ) )
= $true )
| ( ( ! [SY2521: $i] :
( ~ ( in @ SY2521 @ SV195 )
| $true
| ( in @ SY2521
@ ( dsetconstr @ SV195
@ ^ [SY2522: $i] :
( ~ ( ~ $true
| ( SY2522 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2522 != SY2521 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1588,plain,
! [SV195: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV195 ) )
= $true )
| ( ( ! [SY2523: $i] :
( ~ ( in @ SY2523 @ SV195 )
| $false
| ( in @ SY2523
@ ( dsetconstr @ SV195
@ ^ [SY2524: $i] :
( ~ ( ~ $false
| ( SY2524 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2524 != SY2523 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1589,plain,
! [SV381: $i,SV196: $i] :
( ( ( SV196 = SV381 )
= $false )
| ( ( ! [SY2384: $i > $o,SY2385: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ~ ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) )
| ~ ( ( SY2384 @ ( sK60_Xx @ SY2385 @ SY2384 @ SV381 @ SV196 ) )
| ( SY2385 @ ( sK61_SY1670 @ SY2385 @ SY2384 @ SV381 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SX4: $i] : ( SY2384 @ SX4 ) )
= ( dsetconstr @ SV381
@ ^ [SX4: $i] : ( SY2385 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1590,plain,
! [SV382: $o,SV197: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV197 ) )
= $true )
| ( ( ! [SY2525: $i] :
( ~ ( in @ SY2525 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2526: $i] :
( ~ ( ~ SV382
| ( SY2526 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2526 != SY2525 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1591,plain,
! [SV197: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV197 ) )
= $true )
| ( ( ! [SY2527: $i] :
( ~ ( in @ SY2527 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2528: $i] :
( ~ ( ~ $true
| ( SY2528 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2528 != SY2527 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1592,plain,
! [SV197: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV197 ) )
= $true )
| ( ( ! [SY2529: $i] :
( ~ ( in @ SY2529 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2530: $i] :
( ~ ( ~ $false
| ( SY2530 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2530 != SY2529 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1593,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) @ SV198 )
| ~ ~ ( in @ ( SV549 @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) ) @ SV509 ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1594,plain,
! [SV550: $i] :
( ( ! [SY2578: $i] :
( ~ ( ~ ( in @ ( sK5_Xx @ SY2578 @ SV550 ) @ SY2578 )
| ~ ~ ( in @ ( sK5_Xx @ SY2578 @ SV550 ) @ SV550 ) )
| ( in @ SY2578 @ ( powerset @ SV550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1595,plain,
! [SV551: $i] :
( ( ! [SY2579: $i] :
( ~ ( in @ SY2579 @ ( powerset @ SV551 ) )
| ! [SY2580: $i] :
( ~ ( in @ SY2580 @ SY2579 )
| ( in @ SY2580 @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1596,plain,
! [SV383: $o,SV199: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV199 ) )
= $true )
| ( ( ! [SY2532: $i] :
( ~ ( in @ SY2532 @ SV199 )
| ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2533: $i] :
( ~ ( ~ SV383
| ( SY2533 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2533 != SY2532 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1597,plain,
! [SV199: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV199 ) )
= $true )
| ( ( ! [SY2534: $i] :
( ~ ( in @ SY2534 @ SV199 )
| ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2535: $i] :
( ~ ( ~ $true
| ( SY2535 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2535 != SY2534 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1598,plain,
! [SV199: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV199 ) )
= $true )
| ( ( ! [SY2536: $i] :
( ~ ( in @ SY2536 @ SV199 )
| ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2537: $i] :
( ~ ( ~ $false
| ( SY2537 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2537 != SY2536 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1599,plain,
! [SV384: $i > $o,SV200: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV200 ) )
= $true )
| ( ( ~ ( SV384 @ SV513 )
| ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1600,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) @ SV201 )
| ~ ~ ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 ) ) )
= $true )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1601,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
| ~ ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) ) )
= $false )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1602,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( ~ ( ~ ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) )
| ~ ( ( SV515
!= ( sK22_SY84 @ SV515 @ SV203 ) ) ) ) )
= $true )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1603,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1604,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
| ~ ~ ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 ) ) )
= $true )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1605,plain,
! [SV389: $i,SV206: $i,SV517: $i] :
( ( ( ~ ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) ) )
= $true )
| ( ( ! [SY2542: $i] :
( ~ ( subset @ SY2542 @ ( cartprod @ SV206 @ SV389 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SY2542 ) ) ) )
| ( subset @ SV517 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1606,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) )
| ~ ( ( SV518
!= ( sK18_SY55 @ SV518 @ SV207 ) ) ) ) )
= $true )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1607,plain,
! [SV390: $i,SV208: $i,SV519: $i] :
( ( ( ~ ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) ) )
= $true )
| ( ( ! [SY2543: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SY2543 @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
| ! [SY2544: $i] :
( ~ ( in @ SY2544 @ SV519 )
| ( SY2543 @ SY2544 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1608,plain,
! [SV209: $i,SV520: $i] :
( ( ( in @ SV520 @ SV209 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 )
| ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1609,plain,
! [SV552: $i > $o] :
( ( ! [SY2581: $i > $o] :
( ~ ( ( ( sK53_Xx @ SY2581 @ SV552 )
!= ( sK54_SY1668 @ SY2581 @ SV552 ) )
| ~ ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SY2581 @ SV552 ) )
| ~ ( SY2581 @ ( sK54_SY1668 @ SY2581 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SY2581 @ SV552 ) )
| ( SY2581 @ ( sK54_SY1668 @ SY2581 @ SV552 ) ) ) ) )
| ! [SY2582: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2582 @ SY2581 @ SV552 ) )
| ~ ( ( SY2582
!= ( sK52_SY231 @ SY2582 @ SY2581 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2582 ) )
| ~ ( ~ ! [SY2583: $i] :
( ~ ( SY2581 @ SY2583 )
| ( ( sK51_SY233 @ SY2581 @ SV552 )
= SY2583 ) )
| ~ ( SY2581 @ ( sK51_SY233 @ SY2581 @ SV552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1610,plain,
! [SV553: $i > $o] :
( ( ! [SY2584: $i > $o] :
( ~ ( ( ( sK49_Xx @ SY2584 @ SV553 )
!= ( sK50_SY1666 @ SY2584 @ SV553 ) )
| ~ ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SY2584 @ SV553 ) )
| ~ ( SY2584 @ ( sK50_SY1666 @ SY2584 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SY2584 @ SV553 ) )
| ( SY2584 @ ( sK50_SY1666 @ SY2584 @ SV553 ) ) ) ) )
| ! [SY2585: $i] :
( ~ ( ~ ( SY2584 @ ( sK48_SY234 @ SY2585 @ SY2584 @ SV553 ) )
| ~ ( ( SY2585
!= ( sK48_SY234 @ SY2585 @ SY2584 @ SV553 ) ) ) )
| ~ ( SY2584 @ SY2585 ) )
| ~ ( ~ ! [SY2586: $i] :
( ~ ( SV553 @ SY2586 )
| ( ( sK47_SY230 @ SY2584 @ SV553 )
= SY2586 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SY2584 @ SV553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1611,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( ~ ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
| ~ ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) ) )
= $false )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1612,plain,
! [SV211: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1613,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
!= SV521 )
| ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
| ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
| ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1614,plain,
! [SV392: $o,SV213: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV213 ) )
= $true )
| ( ( ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV213 )
| SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2546: $i] :
( ~ ( ~ SV392
| ( SY2546 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2546 != SY2545 ) ) ) )
= ( setadjoin @ SY2545 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1615,plain,
! [SV213: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV213 ) )
= $true )
| ( ( ! [SY2547: $i] :
( ~ ( in @ SY2547 @ SV213 )
| $true
| ( ( dsetconstr @ SV213
@ ^ [SY2548: $i] :
( ~ ( ~ $true
| ( SY2548 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2548 != SY2547 ) ) ) )
= ( setadjoin @ SY2547 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1616,plain,
! [SV213: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ SV213 ) )
= $true )
| ( ( ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV213 )
| $false
| ( ( dsetconstr @ SV213
@ ^ [SY2550: $i] :
( ~ ( ~ $false
| ( SY2550 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2550 != SY2549 ) ) ) )
= ( setadjoin @ SY2549 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1617,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ( ~ ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
| ~ ( ( SV525
!= ( sK31_SY140 @ SV525 @ SV214 ) ) ) ) )
= $true )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1618,plain,
! [SV215: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV215 )
| ~ ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 ) )
= $false )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1619,plain,
! [SV394: $i,SV216: $i,SV526: $i] :
( ( ( ~ ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) ) )
= $true )
| ( ( ! [SY2551: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SY2551 @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
| ! [SY2552: $i] :
( ~ ( in @ SY2552 @ SV526 )
| ( SY2551 @ SY2552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1620,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1621,plain,
! [SV218: $i] :
( ( ! [SY2157: $i > $o,SY2158: $i] :
( ~ ( in @ SY2158 @ SV218 )
| ~ ( SY2157 @ SY2158 )
| ( in @ SY2158
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2157 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1622,plain,
! [SV218: $i] :
( ( ! [SY2160: $i > $o,SY2161: $i] :
( ~ ( in @ SY2161 @ SV218 )
| ~ ( in @ SY2161
@ ( dsetconstr @ SV218
@ ^ [SX3: $i] : ( SY2160 @ SX3 ) ) )
| ( SY2160 @ SY2161 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1623,plain,
! [SV219: $i,SV396: $i] :
( ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false )
| ( ( ! [SY2420: $o] :
( ~ ( ~ ( in @ SV396 @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SY2420 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SY2420 ) )
| SY2420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1624,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ( ( ( sK58_Xx @ SV397 @ SV220 )
!= ( sK59_SY1669 @ SV397 @ SV220 ) )
| ~ ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1625,plain,
! [SV398: $o,SV221: $i,SV528: $i] :
( ( ( ~ ( in @ SV528 @ SV221 ) )
= $true )
| ( ( ! [SY2557: $i] :
( ~ ( in @ SY2557 @ SV221 )
| ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2558: $i] :
( ~ ( ~ SV398
| ( SY2558 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2558 != SY2557 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1626,plain,
! [SV221: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV221 ) )
= $true )
| ( ( ! [SY2559: $i] :
( ~ ( in @ SY2559 @ SV221 )
| ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2560: $i] :
( ~ ( ~ $true
| ( SY2560 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2560 != SY2559 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1627,plain,
! [SV221: $i,SV530: $i] :
( ( ( ~ ( in @ SV530 @ SV221 ) )
= $true )
| ( ( ! [SY2561: $i] :
( ~ ( in @ SY2561 @ SV221 )
| ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2562: $i] :
( ~ ( ~ $false
| ( SY2562 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2562 != SY2561 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1628,plain,
! [SV554: $i] :
( ( ! [SY2587: $i] :
( ! [SY2588: $i] :
( ~ ( in @ SY2587 @ SY2588 )
| ~ ( in @ SY2588 @ SV554 ) )
| ( in @ SY2587 @ ( setunion @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1629,plain,
! [SV555: $i] :
( ( ! [SY2589: $i] :
( ~ ( in @ SY2589 @ ( setunion @ SV555 ) )
| ~ ( ~ ( in @ SY2589 @ ( sK6_B @ SY2589 @ SV555 ) )
| ~ ( in @ ( sK6_B @ SY2589 @ SV555 ) @ SV555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1630,plain,
! [SV223: $i,SV2: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ ( powerset @ SV2 ) )
| ( in @ ( binunion @ SV223 @ SV556 ) @ ( powerset @ SV2 ) ) )
= $true )
| ( ( in @ SV223 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1631,plain,
! [SV224: $i,SV3: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( powerset @ SV3 ) )
| ( in @ ( binintersect @ SV224 @ SV557 ) @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ SV224 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1632,plain,
! [SV225: $o,SV4: $i,SV399: $i] :
( ( ( in @ SV399 @ SV4 )
= $false )
| ( ( ! [SY2428: $i] :
( ~ ( in @ SY2428 @ SV4 )
| ( in @ ( if @ SV4 @ SV225 @ SV399 @ SY2428 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SY2428 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1633,plain,
! [SV4: $i,SV400: $i] :
( ( ( in @ SV400 @ SV4 )
= $false )
| ( ( ! [SY2429: $i] :
( ~ ( in @ SY2429 @ SV4 )
| ( in @ ( if @ SV4 @ $true @ SV400 @ SY2429 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SY2429 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1634,plain,
! [SV4: $i,SV401: $i] :
( ( ( in @ SV401 @ SV4 )
= $false )
| ( ( ! [SY2430: $i] :
( ~ ( in @ SY2430 @ SV4 )
| ( in @ ( if @ SV4 @ $false @ SV401 @ SY2430 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SY2430 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1635,plain,
! [SV226: $o,SV5: $i,SV402: $i] :
( ( ( in @ SV402 @ SV5 )
= $false )
| ( ( ! [SY2431: $i] :
( ~ ( in @ SY2431 @ SV5 )
| SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SY2431 )
= SY2431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1636,plain,
! [SV5: $i,SV403: $i] :
( ( ( in @ SV403 @ SV5 )
= $false )
| ( ( ! [SY2432: $i] :
( ~ ( in @ SY2432 @ SV5 )
| $true
| ( ( if @ SV5 @ $true @ SV403 @ SY2432 )
= SY2432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1637,plain,
! [SV5: $i,SV404: $i] :
( ( ( in @ SV404 @ SV5 )
= $false )
| ( ( ! [SY2433: $i] :
( ~ ( in @ SY2433 @ SV5 )
| $false
| ( ( if @ SV5 @ $false @ SV404 @ SY2433 )
= SY2433 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1638,plain,
! [SV227: $o,SV6: $i,SV405: $i] :
( ( ( in @ SV405 @ SV6 )
= $false )
| ( ( ! [SY2434: $i] :
( ~ ( in @ SY2434 @ SV6 )
| ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SY2434 )
= SV405 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1639,plain,
! [SV6: $i,SV406: $i] :
( ( ( in @ SV406 @ SV6 )
= $false )
| ( ( ! [SY2435: $i] :
( ~ ( in @ SY2435 @ SV6 )
| ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SY2435 )
= SV406 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1640,plain,
! [SV6: $i,SV407: $i] :
( ( ( in @ SV407 @ SV6 )
= $false )
| ( ( ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV6 )
| ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SY2436 )
= SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1641,plain,
! [SV7: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV7 ) )
= $true )
| ( ( ( setunion @ SV7 )
= SV531 )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1642,plain,
! [SV228: $o,SV8: $i,SV408: $i] :
( ( ( in @ SV408 @ SV8 )
= $false )
| ( ( ! [SY2437: $i] :
( ~ ( in @ SY2437 @ SV8 )
| ( in @ ( if @ SV8 @ SV228 @ SV408 @ SY2437 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1643,plain,
! [SV8: $i,SV409: $i] :
( ( ( in @ SV409 @ SV8 )
= $false )
| ( ( ! [SY2438: $i] :
( ~ ( in @ SY2438 @ SV8 )
| ( in @ ( if @ SV8 @ $true @ SV409 @ SY2438 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1644,plain,
! [SV8: $i,SV410: $i] :
( ( ( in @ SV410 @ SV8 )
= $false )
| ( ( ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV8 )
| ( in @ ( if @ SV8 @ $false @ SV410 @ SY2439 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1645,plain,
! [SV229: $i,SV9: $i,SV411: $i] :
( ( ( in @ SV411 @ ( funcSet @ SV9 @ SV229 ) )
= $false )
| ( ( ( lam @ SV9 @ SV229
@ ^ [SY2440: $i] : ( ap @ SV9 @ SV229 @ SV411 @ SY2440 ) )
= SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1646,plain,
! [SV412: $i,SV230: $i,SV10: $i] :
( ( ( func @ SV10 @ SV230 @ SV412 )
= $false )
| ( ( ( lam @ SV10 @ SV230
@ ^ [SY2441: $i] : ( ap @ SV10 @ SV230 @ SV412 @ SY2441 ) )
= SV412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1647,plain,
! [SV532: $i,SV413: $i,SV11: $i] :
( ( ( func @ SV11 @ SV413 @ SV532 )
= $false )
| ( ( ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1648,plain,
! [SV414: $i,SV12: $i,SV533: $i] :
( ( ( in @ SV533 @ ( funcSet @ SV12 @ SV414 ) )
= $false )
| ( ( ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1649,plain,
! [SV231: $i,SV13: $i,SV415: $i] :
( ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false )
| ( ( ! [SY2444: $i] :
( ~ ( in @ SY2444 @ SV13 )
| ! [SY2445: $i] :
( ~ ( in @ SY2445 @ SV231 )
| ~ ( in @ ( kpair @ SY2444 @ SY2445 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SY2444 )
= SY2445 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1650,plain,
! [SV416: $i,SV232: $i,SV14: $i] :
( ( ( func @ SV14 @ SV232 @ SV416 )
= $false )
| ( ( ! [SY2446: $i] :
( ~ ( in @ SY2446 @ SV14 )
| ! [SY2447: $i] :
( ~ ( in @ SY2447 @ SV232 )
| ~ ( in @ ( kpair @ SY2446 @ SY2447 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SY2446 )
= SY2447 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1651,plain,
! [SV233: $i,SV15: $i,SV417: $i] :
( ( ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) )
= $false )
| ( ( ! [SY2448: $i] :
( ~ ( in @ SY2448 @ SV15 )
| ( in @ ( kpair @ SY2448 @ ( ap @ SV15 @ SV233 @ SV417 @ SY2448 ) ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1652,plain,
! [SV418: $i,SV234: $i,SV16: $i] :
( ( ( func @ SV16 @ SV234 @ SV418 )
= $false )
| ( ( ! [SY2449: $i] :
( ~ ( in @ SY2449 @ SV16 )
| ( in @ ( kpair @ SY2449 @ ( ap @ SV16 @ SV234 @ SV418 @ SY2449 ) ) @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1653,plain,
! [SV235: $i > $o,SV17: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ SV17 )
| ! [SY2590: $i] :
( ~ ( in @ SY2590 @ SV17 )
| ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SY2590 )
| ( SV558 = SY2590 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1654,plain,
! [SV419: $i,SV236: $i,SV18: $i] :
( ( ( func @ SV18 @ SV236 @ SV419 )
= $false )
| ( ( in @ SV419 @ ( funcSet @ SV18 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1655,plain,
! [SV237: $i,SV19: $i,SV420: $i] :
( ( ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) )
= $false )
| ( ( ! [SY2450: $i] :
( ~ ( in @ SY2450 @ SV19 )
| ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SY2450 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1656,plain,
! [SV238: $i,SV20: $i,SV421: $i] :
( ( ( in @ SV421 @ ( funcSet @ SV20 @ SV238 ) )
= $false )
| ( ( func @ SV20 @ SV238 @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1657,plain,
! [SV422: $i,SV239: $i,SV21: $i] :
( ( ( func @ SV21 @ SV239 @ SV422 )
= $false )
| ( ( ! [SY2451: $i] :
( ~ ( in @ SY2451 @ SV21 )
| ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SY2451 ) @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1658,plain,
! [SV423: $i,SV240: $i,SV22: $i] :
( ( ( func @ SV22 @ SV240 @ SV423 )
= $false )
| ( ( ! [SY2452: $i] :
( ~ ( in @ SY2452 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2453: $i] : ( in @ ( kpair @ SY2452 @ SY2453 ) @ SV423 ) ) )
@ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1659,plain,
! [SV424: $i,SV241: $i,SV23: $i] :
( ( ( func @ SV23 @ SV241 @ SV424 )
= $false )
| ( ( ! [SY2454: $i] :
( ~ ( in @ SY2454 @ SV23 )
| ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2455: $i] : ( in @ ( kpair @ SY2454 @ SY2455 ) @ SV424 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1660,plain,
! [SV425: $i > $i > $o,SV242: $i,SV24: $i,SV559: $i,SV534: $i] :
( ( ~ ( in @ ( kpair @ SV534 @ SV559 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [SY2458: $i,SY2459: $i] : ( SV425 @ SY2458 @ SY2459 ) ) )
| ( SV425 @ SV534 @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1661,plain,
! [SV426: $i > $i > $o,SV243: $i,SV25: $i,SV560: $i,SV535: $i] :
( ( ~ ( in @ ( kpair @ SV535 @ SV560 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [SY2462: $i,SY2463: $i] : ( SV426 @ SY2462 @ SY2463 ) ) )
| ( in @ SV560 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1662,plain,
! [SV427: $i > $i > $o,SV244: $i,SV26: $i,SV536: $i] :
( ( ( ! [SY2569: $i] :
~ ( in @ ( kpair @ SV536 @ SY2569 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [SY2466: $i,SY2467: $i] : ( SV427 @ SY2466 @ SY2467 ) ) ) )
= $true )
| ( ( in @ SV536 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1663,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ SV27 ) )
= $true )
| ( ( ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV245 )
| ~ ( in @ ( kpair @ SV537 @ SY2572 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SY2572 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1664,plain,
! [SV431: $i > $i > $o,SV248: $i,SV30: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV30 ) )
= $true )
| ( ( ! [SY2575: $i] :
( ~ ( in @ SY2575 @ SV248 )
| ~ ( SV431 @ SV538 @ SY2575 )
| ( in @ ( kpair @ SV538 @ SY2575 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1665,plain,
! [SV249: $i,SV31: $i,SV432: $i] :
( ( ( in @ SV432 @ ( cartprod @ SV31 @ SV249 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV432 ) @ ( ksnd @ SV432 ) )
= SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1666,plain,
! [SV250: $i,SV32: $i,SV433: $i] :
( ( ( in @ SV433 @ SV32 )
= $false )
| ( ( ! [SY2480: $i] :
( ~ ( in @ SY2480 @ SV250 )
| ( ( ksnd @ ( kpair @ SV433 @ SY2480 ) )
= SY2480 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1667,plain,
! [SV251: $i,SV33: $i,SV434: $i] :
( ( ( in @ SV434 @ SV33 )
= $false )
| ( ( ! [SY2481: $i] :
( ~ ( in @ SY2481 @ SV251 )
| ( ( kfst @ ( kpair @ SV434 @ SY2481 ) )
= SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1668,plain,
! [SV34: $i,SV435: $i] :
( ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B ) )
= $true )
| ( $true = $true )
| ( ( in @ SV435 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1669,plain,
! [SV252: $i,SV35: $i,SV539: $i,SV436: $i] :
( ( ( ~ ( in @ ( kpair @ SV436 @ SV539 ) @ ( cartprod @ SV35 @ SV252 ) ) )
= $true )
| ( ( in @ SV539 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1670,plain,
! [SV253: $i,SV36: $i,SV561: $i,SV437: $i] :
( ( ( ~ ( in @ ( kpair @ SV437 @ SV561 ) @ ( cartprod @ SV36 @ SV253 ) ) )
= $true )
| ( ( in @ SV437 @ SV36 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1671,plain,
! [SV254: $i,SV37: $i,SV438: $i] :
( ( ( in @ SV438 @ ( cartprod @ SV37 @ SV254 ) )
= $false )
| ( ( in @ ( ksnd @ SV438 ) @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1672,plain,
! [SV540: $i,SV439: $i,SV256: $i,SV41: $i] :
( ( ( ( kpair @ SV41 @ SV256 )
!= ( kpair @ SV439 @ SV540 ) )
= $true )
| ( ( SV256 = SV540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1673,plain,
! [SV541: $i,SV440: $i,SV257: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV257 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV440 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV440 @ ( setadjoin @ SV541 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV257 = SV541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1674,plain,
! [SV542: $i,SV258: $i,SV43: $i] :
( ( ( ( setadjoin @ SV43 @ ( setadjoin @ SV258 @ emptyset ) )
= ( setadjoin @ SV542 @ emptyset ) )
= $false )
| ( ( SV43 = SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1675,plain,
! [SV543: $i,SV441: $i,SV259: $i,SV44: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV441 != SV543 )
| ( SV259 = SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1676,plain,
! [SV562: $i,SV442: $i,SV262: $i,SV47: $i] :
( ( ( ( kpair @ SV47 @ SV262 )
!= ( kpair @ SV442 @ SV562 ) )
= $true )
| ( ( SV47 = SV442 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1677,plain,
! [SV563: $i,SV443: $i,SV263: $i,SV48: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV443 @ ( setadjoin @ SV563 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV48 = SV443 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1678,plain,
! [SV264: $i,SV49: $i,SV444: $i] :
( ( ( in @ SV444 @ ( cartprod @ SV49 @ SV264 ) )
= $false )
| ( ( in @ ( kfst @ SV444 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1679,plain,
! [SV266: $i,SV53: $i,SV445: $i] :
( ( ( in @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV53 @ ( setadjoin @ SV266 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV53 = SV445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1680,plain,
! [SV268: $i,SV58: $i,SV446: $i] :
( ( ( in @ SV446 @ ( cartprod @ SV58 @ SV268 ) )
= $false )
| ( ( iskpair @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1681,plain,
! [SV269: $i,SV59: $i,SV447: $i] :
( ( ( in @ SV447 @ SV59 )
= $false )
| ( ( ! [SY2489: $i] :
( ~ ( in @ SY2489 @ SV269 )
| ( in @ ( kpair @ SV447 @ SY2489 ) @ ( cartprod @ SV59 @ SV269 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1682,plain,
! [SV270: $i,SV60: $i,SV448: $i] :
( ( ( in @ SV448 @ SV60 )
= $false )
| ( ( ! [SY2490: $i] :
( ~ ( in @ SY2490 @ SV270 )
| ( in @ ( kpair @ SV448 @ SY2490 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1683,plain,
! [SV271: $i,SV61: $i,SV449: $i] :
( ( ( in @ SV449 @ SV61 )
= $false )
| ( ( ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SV271 )
| ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SY2491 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1684,plain,
! [SV272: $i,SV62: $i,SV450: $i] :
( ( ( in @ SV450 @ SV62 )
= $false )
| ( ( ! [SY2492: $i] :
( ~ ( in @ SY2492 @ SV272 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SY2492 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1685,plain,
! [SV273: $i,SV63: $i,SV451: $i] :
( ( ( in @ SV451 @ SV63 )
= $false )
| ( ( ! [SY2493: $i] :
( ~ ( in @ SY2493 @ SV273 )
| ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SY2493 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1686,plain,
! [SV274: $i,SV64: $i,SV452: $i] :
( ( ( in @ SV452 @ SV64 )
= $false )
| ( ( ! [SY2494: $i] :
( ~ ( in @ SY2494 @ SV274 )
| ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SY2494 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1687,plain,
! [SV275: $i,SV65: $i,SV453: $i] :
( ( ( in @ SV453 @ ( setadjoin @ SV65 @ ( setadjoin @ SV275 @ emptyset ) ) )
= $false )
| ( ( ( SV453 = SV65 )
| ( SV453 = SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1688,plain,
! [SV276: $i,SV66: $i,SV454: $i] :
( ( ( in @ SV454 @ SV66 )
= $false )
| ( ( in @ ( setadjoin @ SV454 @ emptyset ) @ ( powerset @ ( binunion @ SV66 @ SV276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1689,plain,
! [SV74: $i,SV284: $i,SV455: $i] :
( ( ( in @ SV455 @ SV284 )
= $true )
| ( ( ~ ( in @ SV455 @ ( symdiff @ SV74 @ SV284 ) ) )
= $true )
| ( ( in @ SV455 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1690,plain,
! [SV285: $i,SV75: $i,SV456: $i] :
( ( ( in @ SV456 @ SV75 )
= $false )
| ( ( ~ ( in @ SV456 @ SV285 )
| ~ ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1691,plain,
! [SV76: $i,SV286: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV286 ) )
= $true )
| ( ( in @ SV457 @ ( symdiff @ SV76 @ SV286 ) )
= $true )
| ( ( in @ SV457 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1692,plain,
! [SV287: $i,SV77: $i,SV458: $i] :
( ( ( in @ SV458 @ SV77 )
= $false )
| ( ( ( in @ SV458 @ SV287 )
| ( in @ SV458 @ ( symdiff @ SV77 @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1693,plain,
! [SV80: $i,SV290: $i,SV459: $i] :
( ( ( in @ SV459 @ SV290 )
= $false )
| ( ( ~ ( in @ SV459 @ ( setminus @ SV80 @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1694,plain,
! [SV291: $i,SV81: $i,SV460: $i] :
( ( ( in @ SV460 @ ( setminus @ SV81 @ SV291 ) )
= $false )
| ( ( in @ SV460 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1695,plain,
! [SV82: $i,SV292: $i,SV461: $i] :
( ( ( in @ SV461 @ SV292 )
= $true )
| ( ( ~ ( in @ SV461 @ SV82 ) )
= $true )
| ( ( in @ SV461 @ ( setminus @ SV82 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1696,plain,
! [SV293: $i,SV83: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ SV83 ) )
= $true )
| ( ( in @ SV462 @ SV293 )
= $true )
| ( ( in @ SV462 @ ( setminus @ SV83 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1697,plain,
! [SV295: $i,SV85: $i,SV463: $i] :
( ( ( in @ SV463 @ ( setminus @ SV85 @ SV295 ) )
= $false )
| ( ( ~ ( in @ SV463 @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1698,plain,
! [SV296: $i,SV86: $i,SV464: $i] :
( ( ( in @ SV464 @ ( setminus @ SV86 @ SV296 ) )
= $false )
| ( ( in @ SV464 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1699,plain,
! [SV297: $i,SV87: $i,SV465: $i] :
( ( ( in @ SV465 @ SV87 )
= $false )
| ( ( ( in @ SV465 @ SV297 )
| ( in @ SV465 @ ( setminus @ SV87 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1700,plain,
! [SV302: $i,SV92: $i,SV467: $i] :
( ( ( in @ SV467 @ ( binintersect @ SV92 @ SV302 ) )
= $false )
| ( ( in @ SV467 @ SV302 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1701,plain,
! [SV306: $i,SV96: $i,SV468: $i] :
( ( ( in @ SV468 @ ( binintersect @ SV96 @ SV306 ) )
= $false )
| ( ( in @ SV468 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1702,plain,
! [SV307: $i,SV97: $i,SV469: $i] :
( ( ( subset @ SV469 @ SV97 )
= $false )
| ( ( ~ ( subset @ SV469 @ SV307 )
| ( subset @ SV469 @ ( binintersect @ SV97 @ SV307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1703,plain,
! [SV308: $i,SV98: $i,SV470: $i] :
( ( ( in @ SV470 @ SV98 )
= $false )
| ( ( ~ ( in @ SV470 @ SV308 )
| ( in @ SV470 @ ( binintersect @ SV98 @ SV308 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1704,plain,
! [SV311: $i,SV101: $i,SV471: $i] :
( ( ( in @ SV471 @ ( binunion @ SV101 @ SV311 ) )
= $false )
| ( ( ( in @ SV471 @ SV101 )
| ( in @ SV471 @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1705,plain,
! [SV102: $i,SV312: $i,SV472: $i] :
( ( ( in @ SV472 @ SV312 )
= $false )
| ( ( in @ SV472 @ ( binunion @ SV102 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1706,plain,
! [SV314: $i,SV104: $i,SV473: $i] :
( ( ( in @ SV473 @ SV104 )
= $false )
| ( ( in @ SV473 @ ( binunion @ SV104 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1707,plain,
! [SV112: $i,SV320: $i] :
( ( ( ~ ( subset @ SV320 @ SV112 ) )
= $true )
| ( ( SV112 = SV320 )
= $true )
| ( ( subset @ SV112 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1708,plain,
! [SV322: $i,SV474: $i,SV114: $i] :
( ( ( subset @ SV114 @ SV474 )
= $false )
| ( ( subset @ SV114 @ ( setadjoin @ SV322 @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1709,plain,
! [SV116: $i,SV564: $i,SV324: $i] :
( ( ( ~ ( subset @ SV324 @ SV564 )
| ( subset @ SV116 @ SV564 ) )
= $true )
| ( ( subset @ SV116 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1710,plain,
! [SV325: $i,SV118: $i,SV475: $i] :
( ( ( in @ SV475 @ SV118 )
= $false )
| ( ( ( in @ SV475 @ SV325 )
| ( SV118 != SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1711,plain,
! [SV327: $i,SV120: $i,SV476: $i] :
( ( ( in @ SV476 @ SV120 )
= $false )
| ( ( ( in @ SV476 @ SV327 )
| ~ ( subset @ SV120 @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1712,plain,
! [SV121: $i,SV328: $i,SV565: $i] :
( ( ( ( in @ SV565 @ SV328 )
| ~ ( in @ SV565 @ SV121 ) )
= $true )
| ( ( subset @ SV121 @ SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1713,plain,
! [SV329: $i,SV122: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV122 )
| ( in @ SV566 @ SV329 ) )
= $true )
| ( ( subset @ SV122 @ SV329 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1714,plain,
! [SV334: $i,SV128: $i,SV567: $i] :
( ( ( ! [SY2595: $i] :
( ( SV567 != SY2595 )
| ( ( setadjoin @ SV128 @ SV567 )
= ( setadjoin @ SV334 @ SY2595 ) ) ) )
= $true )
| ( ( SV128 = SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1715,plain,
! [SV335: $i,SV129: $i,SV568: $i] :
( ( ( ! [SY2596: $i] :
( ( SV568 != SY2596 )
| ~ ( in @ SV568 @ SV129 )
| ( in @ SY2596 @ SV335 ) ) )
= $true )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1716,plain,
! [SV133: $i,SV544: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ SV544 ) )
= $true )
| ( ( ~ ( in @ SV544 @ SV133 ) )
= $true )
| ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1717,plain,
! [SV340: $i,SV136: $i,SV477: $i] :
( ( ( in @ SV477 @ ( setadjoin @ SV136 @ ( setadjoin @ SV340 @ emptyset ) ) )
= $false )
| ( ( ( SV477 = SV136 )
| ( SV477 = SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1718,plain,
! [SV143: $i,SV478: $i,SV346: $i] :
( ( ( in @ SV346 @ SV478 )
= $false )
| ( ( ~ ( in @ SV478 @ SV143 )
| ( in @ SV346 @ ( setunion @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1719,plain,
! [SV144: $i,SV347: $i,SV569: $i] :
( ( ( ~ ( in @ SV569 @ SV347 )
| ( in @ SV569 @ SV144 ) )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1720,plain,
! [SV348: $i,SV148: $i,SV479: $i] :
( ( ( in @ SV479 @ ( setadjoin @ SV148 @ SV348 ) )
= $false )
| ( ( ( SV479 = SV148 )
| ( in @ SV479 @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1721,plain,
! [SV149: $i,SV349: $i,SV480: $i] :
( ( ( in @ SV480 @ SV349 )
= $false )
| ( ( in @ SV480 @ ( setadjoin @ SV149 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1722,plain,
! [SV481: $i,SV151: $i] :
( ( ( SV151 = emptyset )
= $false )
| ( ( in @ SV481 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1723,plain,
! [SV351: $i > $o,SV152: $i,SV482: $i] :
( ( ( in @ SV482 @ SV152 )
= $false )
| ( ( ~ ( SV351 @ SV482 )
| ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1724,plain,
! [SV353: $i > $o,SV159: $i,SV486: $i] :
( ( ( in @ SV486
@ ( dsetconstr @ SV159
@ ^ [SY2323: $i] : ( SV353 @ SY2323 ) ) )
= $false )
| ( ( SV353 @ SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1725,plain,
! [SV354: $i > $o,SV160: $i,SV487: $i] :
( ( ( in @ SV487
@ ( dsetconstr @ SV160
@ ^ [SY2325: $i] : ( SV354 @ SY2325 ) ) )
= $false )
| ( ( in @ SV487 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1726,plain,
! [SV355: $i > $o,SV161: $i,SV488: $i] :
( ( ( in @ SV488 @ SV161 )
= $false )
| ( ( ~ ( SV355 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1727,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
| ~ ( ( SV489
!= ( sK20_SY72 @ SV489 @ SV164 ) ) ) )
= $false )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1728,plain,
! [SV356: $i,SV165: $i] :
( ( ( ~ ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) )
| ~ ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1729,plain,
! [SV490: $i,SV357: $i,SV166: $i] :
( ( ( func @ SV166 @ SV357 @ SV490 )
= $false )
| ( ( ! [SY2499: $i] :
( ~ ( func @ SV166 @ SV357 @ SY2499 )
| ~ ( ~ ( in @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SY2499 @ ( sK81_Xx @ SY2499 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2500: $i] :
( ~ ( in @ SY2500 @ SV166 )
| ! [SY2501: $i] :
( ~ ( in @ SY2501 @ SV357 )
| ~ ( in @ ( kpair @ SY2500 @ SY2501 ) @ SY2499 )
| ( in @ ( kpair @ SY2500 @ SY2501 ) @ SV490 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1730,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( ~ ( in @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) @ SV167 )
| ~ ~ ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 ) )
= $false )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1731,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1732,plain,
( ( ~ ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1733,plain,
( ( ~ ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1734,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
| ~ ( ( SV493
!= ( sK40_Xy @ SV493 @ SV169 ) ) ) )
= $false )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1735,plain,
! [SV170: $i,SV570: $i] :
( ( ~ ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
| ~ ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) )
| ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 )
| ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1736,plain,
! [SV170: $i] :
( ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) )
| ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1737,plain,
! [SV360: $i,SV171: $i,SV494: $i] :
( ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( ! [SY2512: $i] :
( ~ ( in @ SY2512 @ ( funcSet @ SV171 @ SV360 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SY2512 @ ( sK89_Xx @ SY2512 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SY2512 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1738,plain,
! [SV172: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1739,plain,
! [SV172: $i,SV361: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV361 ) )
= $false )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1740,plain,
! [SV362: $i > $o,SV173: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV173 ) )
= $true )
| ( ( SV362 @ SV546 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1741,plain,
! [SV571: $i,SV174: $i] :
( ( ! [SY2601: $i] :
( ~ ( in @ SY2601 @ ( setadjoin @ SV174 @ SV571 ) )
| ( SY2601 = SV174 )
| ( in @ SY2601 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1742,plain,
! [SV174: $i] :
( ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) )
| ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1743,plain,
! [SV175: $i,SV363: $i > $o] :
( ( ( ~ ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) )
| ~ ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1744,plain,
! [SV364: $i,SV176: $i,SV495: $i] :
( ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( subset @ SY2513 @ ( cartprod @ SV176 @ SV364 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SY2513 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2513 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SY2513 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SY2513 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1745,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 ) )
= $false )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1746,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 ) )
= $false )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1747,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1748,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1569]) ).
thf(1749,plain,
! [SV368: $i > $o,SV180: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV180 ) )
= $true )
| ( ( SV368 @ SV547 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1750,plain,
! [SV181: $i,SV369: $i] :
( ( ( ~ ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 )
| ~ ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) ) )
= $false )
| ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1751,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1752,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1753,plain,
! [SV183: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV183 ) )
= $false )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1754,plain,
! [SV183: $i,SV371: $i] :
( ( ( ~ ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 ) )
= $false )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1573]) ).
thf(1755,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
| ~ ( ( SV498
!= ( sK46_SY222 @ SV498 @ SV184 ) ) ) )
= $false )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1756,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( ~ ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) ) )
= $false )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1757,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( ~ ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 ) )
= $false )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1758,plain,
! [SV373: $i,SV186: $i,SV499: $i] :
( ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
| ~ ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1759,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1760,plain,
! [SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2365: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) )
| ~ ( ( SY2365
!= ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SY2365 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1577]) ).
thf(1761,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( ~ ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) ) )
= $false )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1762,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( ~ ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 ) )
= $false )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1578]) ).
thf(1763,plain,
! [SV189: $i,SV376: $i] :
( ( ( ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV376 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1764,plain,
! [SV189: $i,SV376: $i] :
( ( ( ~ ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1579]) ).
thf(1765,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1766,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) )
| ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1767,plain,
! [SV500: $i,SV378: $i,SV191: $i] :
( ( ( func @ SV191 @ SV378 @ SV500 )
= $false )
| ( ( ! [SY2518: $i] :
( ~ ( func @ SV191 @ SV378 @ SY2518 )
| ~ ( ~ ( in @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SY2518 @ ( sK88_Xx @ SY2518 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1768,plain,
! [SV379: $i > $o,SV192: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ SV192 ) )
= $true )
| ( ( SV379 @ SV548 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1769,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1770,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
| ~ ( ( SV502
!= ( sK55_SY246 @ SV502 @ SV194 ) ) ) )
= $false )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1771,plain,
! [SV380: $o,SV195: $i,SV503: $i] :
( ( ( in @ SV503 @ SV195 )
= $false )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV195 )
| SV380
| ( in @ SY2519
@ ( dsetconstr @ SV195
@ ^ [SY2520: $i] :
( ~ ( ~ SV380
| ( SY2520 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2520 != SY2519 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1772,plain,
! [SV195: $i,SV504: $i] :
( ( ( in @ SV504 @ SV195 )
= $false )
| ( ( ! [SY2521: $i] :
( ~ ( in @ SY2521 @ SV195 )
| $true
| ( in @ SY2521
@ ( dsetconstr @ SV195
@ ^ [SY2522: $i] :
( ~ ( ~ $true
| ( SY2522 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2522 != SY2521 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1773,plain,
! [SV195: $i,SV505: $i] :
( ( ( in @ SV505 @ SV195 )
= $false )
| ( ( ! [SY2523: $i] :
( ~ ( in @ SY2523 @ SV195 )
| $false
| ( in @ SY2523
@ ( dsetconstr @ SV195
@ ^ [SY2524: $i] :
( ~ ( ~ $false
| ( SY2524 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2524 != SY2523 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1774,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o] :
( ( ( ! [SY2602: $i > $o] :
( ~ ( ~ ( in @ ( sK60_Xx @ SY2602 @ SV572 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SY2602 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SY2602 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SY2602 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SY2602 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SY2602 @ ( sK61_SY1670 @ SY2602 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SY2602 @ SV572 @ SV381 @ SV196 ) )
| ( SY2602 @ ( sK61_SY1670 @ SY2602 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SX4: $i] : ( SY2602 @ SX4 ) ) ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1775,plain,
! [SV382: $o,SV197: $i,SV506: $i] :
( ( ( in @ SV506 @ SV197 )
= $false )
| ( ( ! [SY2525: $i] :
( ~ ( in @ SY2525 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2526: $i] :
( ~ ( ~ SV382
| ( SY2526 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2526 != SY2525 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1776,plain,
! [SV197: $i,SV507: $i] :
( ( ( in @ SV507 @ SV197 )
= $false )
| ( ( ! [SY2527: $i] :
( ~ ( in @ SY2527 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2528: $i] :
( ~ ( ~ $true
| ( SY2528 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2528 != SY2527 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1777,plain,
! [SV197: $i,SV508: $i] :
( ( ( in @ SV508 @ SV197 )
= $false )
| ( ( ! [SY2529: $i] :
( ~ ( in @ SY2529 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2530: $i] :
( ~ ( ~ $false
| ( SY2530 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2530 != SY2529 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1778,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( ~ ( in @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) @ SV198 )
| ~ ~ ( in @ ( SV549 @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) ) @ SV509 ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1779,plain,
! [SV550: $i,SV573: $i] :
( ( ~ ( ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV573 )
| ~ ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 ) )
| ( in @ SV573 @ ( powerset @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1780,plain,
! [SV551: $i,SV574: $i] :
( ( ~ ( in @ SV574 @ ( powerset @ SV551 ) )
| ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV574 )
| ( in @ SY2605 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1781,plain,
! [SV383: $o,SV199: $i,SV510: $i] :
( ( ( in @ SV510 @ SV199 )
= $false )
| ( ( ! [SY2532: $i] :
( ~ ( in @ SY2532 @ SV199 )
| ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2533: $i] :
( ~ ( ~ SV383
| ( SY2533 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2533 != SY2532 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1782,plain,
! [SV199: $i,SV511: $i] :
( ( ( in @ SV511 @ SV199 )
= $false )
| ( ( ! [SY2534: $i] :
( ~ ( in @ SY2534 @ SV199 )
| ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2535: $i] :
( ~ ( ~ $true
| ( SY2535 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2535 != SY2534 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1783,plain,
! [SV199: $i,SV512: $i] :
( ( ( in @ SV512 @ SV199 )
= $false )
| ( ( ! [SY2536: $i] :
( ~ ( in @ SY2536 @ SV199 )
| ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2537: $i] :
( ~ ( ~ $false
| ( SY2537 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2537 != SY2536 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1784,plain,
! [SV384: $i > $o,SV200: $i,SV513: $i] :
( ( ( in @ SV513 @ SV200 )
= $false )
| ( ( ~ ( SV384 @ SV513 )
| ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1785,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( ~ ( in @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) @ SV201 )
| ~ ~ ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 ) )
= $false )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1786,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) ) )
= $false )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1787,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) ) )
= $false )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1601]) ).
thf(1788,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( ~ ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) )
| ~ ( ( SV515
!= ( sK22_SY84 @ SV515 @ SV203 ) ) ) )
= $false )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1789,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1790,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1791,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( ~ ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
| ~ ~ ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 ) )
= $false )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1792,plain,
! [SV389: $i,SV206: $i,SV517: $i] :
( ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( ! [SY2542: $i] :
( ~ ( subset @ SY2542 @ ( cartprod @ SV206 @ SV389 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SY2542 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SY2542 @ SV517 @ SV389 @ SV206 ) ) @ SY2542 ) ) ) )
| ( subset @ SV517 @ SY2542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1793,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) )
| ~ ( ( SV518
!= ( sK18_SY55 @ SV518 @ SV207 ) ) ) )
= $false )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1794,plain,
! [SV390: $i,SV208: $i,SV519: $i] :
( ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false )
| ( ( ! [SY2543: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SY2543 @ ( kpair @ ( sK77_Xx @ SY2543 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SY2543 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
| ! [SY2544: $i] :
( ~ ( in @ SY2544 @ SV519 )
| ( SY2543 @ SY2544 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1795,plain,
! [SV520: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 )
| ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) )
= $false )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1796,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ~ ( ( ( sK53_Xx @ SV575 @ SV552 )
!= ( sK54_SY1668 @ SV575 @ SV552 ) )
| ~ ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) ) )
| ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1797,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ~ ( ( ( sK49_Xx @ SV576 @ SV553 )
!= ( sK50_SY1666 @ SV576 @ SV553 ) )
| ~ ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) ) )
| ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1798,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( ~ ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 ) )
= $false )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1799,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( ~ ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) ) )
= $false )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1800,plain,
! [SV211: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1801,plain,
! [SV211: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1802,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
!= SV521 )
| ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1803,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ~ ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
| ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1804,plain,
! [SV392: $o,SV213: $i,SV522: $i] :
( ( ( in @ SV522 @ SV213 )
= $false )
| ( ( ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV213 )
| SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2546: $i] :
( ~ ( ~ SV392
| ( SY2546 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2546 != SY2545 ) ) ) )
= ( setadjoin @ SY2545 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1805,plain,
! [SV213: $i,SV523: $i] :
( ( ( in @ SV523 @ SV213 )
= $false )
| ( ( ! [SY2547: $i] :
( ~ ( in @ SY2547 @ SV213 )
| $true
| ( ( dsetconstr @ SV213
@ ^ [SY2548: $i] :
( ~ ( ~ $true
| ( SY2548 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2548 != SY2547 ) ) ) )
= ( setadjoin @ SY2547 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1806,plain,
! [SV213: $i,SV524: $i] :
( ( ( in @ SV524 @ SV213 )
= $false )
| ( ( ! [SY2549: $i] :
( ~ ( in @ SY2549 @ SV213 )
| $false
| ( ( dsetconstr @ SV213
@ ^ [SY2550: $i] :
( ~ ( ~ $false
| ( SY2550 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2550 != SY2549 ) ) ) )
= ( setadjoin @ SY2549 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1807,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
| ~ ( ( SV525
!= ( sK31_SY140 @ SV525 @ SV214 ) ) ) )
= $false )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1808,plain,
! [SV215: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV215 ) )
= $false )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1809,plain,
! [SV215: $i,SV393: $i] :
( ( ( ~ ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 ) )
= $false )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1618]) ).
thf(1810,plain,
! [SV394: $i,SV216: $i,SV526: $i] :
( ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false )
| ( ( ! [SY2551: $i > $o] :
( ~ ( ~ ( in @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SY2551 @ ( kpair @ ( sK79_Xx @ SY2551 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SY2551 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
| ! [SY2552: $i] :
( ~ ( in @ SY2552 @ SV526 )
| ( SY2551 @ SY2552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1811,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1812,plain,
! [SV577: $i > $o,SV218: $i] :
( ( ! [SY2610: $i] :
( ~ ( in @ SY2610 @ SV218 )
| ~ ( SV577 @ SY2610 )
| ( in @ SY2610
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1813,plain,
! [SV578: $i > $o,SV218: $i] :
( ( ! [SY2612: $i] :
( ~ ( in @ SY2612 @ SV218 )
| ~ ( in @ SY2612
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) )
| ( SV578 @ SY2612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1814,plain,
! [SV219: $i,SV579: $o,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ SV579 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 ) )
| SV579 )
= $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1623]) ).
thf(1815,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ $true @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true ) )
| $true )
= $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1623]) ).
thf(1816,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ $false @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false ) )
| $false )
= $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1623]) ).
thf(1817,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ( ( sK58_Xx @ SV397 @ SV220 )
!= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1818,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1819,plain,
! [SV398: $o,SV221: $i,SV528: $i] :
( ( ( in @ SV528 @ SV221 )
= $false )
| ( ( ! [SY2557: $i] :
( ~ ( in @ SY2557 @ SV221 )
| ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2558: $i] :
( ~ ( ~ SV398
| ( SY2558 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2558 != SY2557 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1820,plain,
! [SV221: $i,SV529: $i] :
( ( ( in @ SV529 @ SV221 )
= $false )
| ( ( ! [SY2559: $i] :
( ~ ( in @ SY2559 @ SV221 )
| ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2560: $i] :
( ~ ( ~ $true
| ( SY2560 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2560 != SY2559 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1821,plain,
! [SV221: $i,SV530: $i] :
( ( ( in @ SV530 @ SV221 )
= $false )
| ( ( ! [SY2561: $i] :
( ~ ( in @ SY2561 @ SV221 )
| ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2562: $i] :
( ~ ( ~ $false
| ( SY2562 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2562 != SY2561 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1822,plain,
! [SV554: $i,SV580: $i] :
( ( ! [SY2614: $i] :
( ~ ( in @ SV580 @ SY2614 )
| ~ ( in @ SY2614 @ SV554 ) )
| ( in @ SV580 @ ( setunion @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1823,plain,
! [SV555: $i,SV581: $i] :
( ( ~ ( in @ SV581 @ ( setunion @ SV555 ) )
| ~ ( ~ ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) )
| ~ ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1824,plain,
! [SV223: $i,SV2: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( in @ ( binunion @ SV223 @ SV556 ) @ ( powerset @ SV2 ) )
= $true )
| ( ( in @ SV223 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1825,plain,
! [SV224: $i,SV3: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV224 @ SV557 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV224 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1826,plain,
! [SV399: $i,SV225: $o,SV4: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ SV4 )
| ( in @ ( if @ SV4 @ SV225 @ SV399 @ SV582 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SV582 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV399 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1827,plain,
! [SV400: $i,SV4: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV4 )
| ( in @ ( if @ SV4 @ $true @ SV400 @ SV583 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SV583 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV400 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1828,plain,
! [SV401: $i,SV4: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV4 )
| ( in @ ( if @ SV4 @ $false @ SV401 @ SV584 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SV584 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV401 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1829,plain,
! [SV402: $i,SV226: $o,SV5: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV5 )
| SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SV585 )
= SV585 ) )
= $true )
| ( ( in @ SV402 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1830,plain,
! [SV403: $i,SV5: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV5 )
| $true
| ( ( if @ SV5 @ $true @ SV403 @ SV586 )
= SV586 ) )
= $true )
| ( ( in @ SV403 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1831,plain,
! [SV404: $i,SV5: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV5 )
| $false
| ( ( if @ SV5 @ $false @ SV404 @ SV587 )
= SV587 ) )
= $true )
| ( ( in @ SV404 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1832,plain,
! [SV405: $i,SV227: $o,SV6: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV6 )
| ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SV588 )
= SV405 ) )
= $true )
| ( ( in @ SV405 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1833,plain,
! [SV406: $i,SV6: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV6 )
| ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SV589 )
= SV406 ) )
= $true )
| ( ( in @ SV406 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1834,plain,
! [SV407: $i,SV6: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV6 )
| ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SV590 )
= SV407 ) )
= $true )
| ( ( in @ SV407 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1835,plain,
! [SV7: $i,SV531: $i] :
( ( ( in @ SV531 @ SV7 )
= $false )
| ( ( ( setunion @ SV7 )
= SV531 )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1836,plain,
! [SV408: $i,SV228: $o,SV8: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV8 )
| ( in @ ( if @ SV8 @ SV228 @ SV408 @ SV591 ) @ SV8 ) )
= $true )
| ( ( in @ SV408 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1837,plain,
! [SV409: $i,SV8: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV8 )
| ( in @ ( if @ SV8 @ $true @ SV409 @ SV592 ) @ SV8 ) )
= $true )
| ( ( in @ SV409 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1838,plain,
! [SV410: $i,SV8: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ SV8 )
| ( in @ ( if @ SV8 @ $false @ SV410 @ SV593 ) @ SV8 ) )
= $true )
| ( ( in @ SV410 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1839,plain,
! [SV532: $i,SV413: $i,SV11: $i] :
( ( ( ! [SY1705: $i] :
~ ( in @ SY1705 @ SV11 ) )
= $true )
| ( $true = $true )
| ( ( func @ SV11 @ SV413 @ SV532 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1840,plain,
! [SV414: $i,SV533: $i,SV12: $i] :
( ( ( ! [SY1708: $i] :
~ ( in @ SY1708 @ SV12 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV533 @ ( funcSet @ SV12 @ SV414 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1841,plain,
! [SV415: $i,SV231: $i,SV13: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV13 )
| ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV231 )
| ~ ( in @ ( kpair @ SV594 @ SY2615 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SY2615 ) ) )
= $true )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1842,plain,
! [SV416: $i,SV232: $i,SV14: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV14 )
| ! [SY2616: $i] :
( ~ ( in @ SY2616 @ SV232 )
| ~ ( in @ ( kpair @ SV595 @ SY2616 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SY2616 ) ) )
= $true )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1843,plain,
! [SV417: $i,SV233: $i,SV15: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV15 )
| ( in @ ( kpair @ SV596 @ ( ap @ SV15 @ SV233 @ SV417 @ SV596 ) ) @ SV417 ) )
= $true )
| ( ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1844,plain,
! [SV418: $i,SV234: $i,SV16: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV16 )
| ( in @ ( kpair @ SV597 @ ( ap @ SV16 @ SV234 @ SV418 @ SV597 ) ) @ SV418 ) )
= $true )
| ( ( func @ SV16 @ SV234 @ SV418 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1845,plain,
! [SV235: $i > $o,SV17: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ SV17 ) )
= $true )
| ( ( ! [SY2590: $i] :
( ~ ( in @ SY2590 @ SV17 )
| ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SY2590 )
| ( SV558 = SY2590 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1846,plain,
! [SV420: $i,SV237: $i,SV19: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV19 )
| ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SV598 ) @ SV237 ) )
= $true )
| ( ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1847,plain,
! [SV422: $i,SV239: $i,SV21: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV21 )
| ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SV599 ) @ SV239 ) )
= $true )
| ( ( func @ SV21 @ SV239 @ SV422 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1848,plain,
! [SV423: $i,SV240: $i,SV22: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV22 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2617: $i] : ( in @ ( kpair @ SV600 @ SY2617 ) @ SV423 ) ) )
@ SV240 ) )
= $true )
| ( ( func @ SV22 @ SV240 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1849,plain,
! [SV424: $i,SV241: $i,SV23: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV23 )
| ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2618: $i] : ( in @ ( kpair @ SV601 @ SY2618 ) @ SV424 ) ) ) )
= $true )
| ( ( func @ SV23 @ SV241 @ SV424 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1850,plain,
! [SV425: $i > $i > $o,SV242: $i,SV24: $i,SV559: $i,SV534: $i] :
( ( ( ~ ( in @ ( kpair @ SV534 @ SV559 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [SY2458: $i,SY2459: $i] : ( SV425 @ SY2458 @ SY2459 ) ) ) )
= $true )
| ( ( SV425 @ SV534 @ SV559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1851,plain,
! [SV426: $i > $i > $o,SV243: $i,SV25: $i,SV560: $i,SV535: $i] :
( ( ( ~ ( in @ ( kpair @ SV535 @ SV560 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [SY2462: $i,SY2463: $i] : ( SV426 @ SY2462 @ SY2463 ) ) ) )
= $true )
| ( ( in @ SV560 @ SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1852,plain,
! [SV427: $i > $i > $o,SV244: $i,SV26: $i,SV602: $i,SV536: $i] :
( ( ( ~ ( in @ ( kpair @ SV536 @ SV602 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [SY2466: $i,SY2467: $i] : ( SV427 @ SY2466 @ SY2467 ) ) ) )
= $true )
| ( ( in @ SV536 @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1853,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i,SV537: $i] :
( ( ( in @ SV537 @ SV27 )
= $false )
| ( ( ! [SY2572: $i] :
( ~ ( in @ SY2572 @ SV245 )
| ~ ( in @ ( kpair @ SV537 @ SY2572 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SY2572 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1854,plain,
! [SV431: $i > $i > $o,SV248: $i,SV30: $i,SV538: $i] :
( ( ( in @ SV538 @ SV30 )
= $false )
| ( ( ! [SY2575: $i] :
( ~ ( in @ SY2575 @ SV248 )
| ~ ( SV431 @ SV538 @ SY2575 )
| ( in @ ( kpair @ SV538 @ SY2575 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1855,plain,
! [SV32: $i,SV433: $i,SV250: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV250 )
| ( ( ksnd @ ( kpair @ SV433 @ SV603 ) )
= SV603 ) )
= $true )
| ( ( in @ SV433 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1856,plain,
! [SV33: $i,SV434: $i,SV251: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ SV251 )
| ( ( kfst @ ( kpair @ SV434 @ SV604 ) )
= SV434 ) )
= $true )
| ( ( in @ SV434 @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1857,plain,
! [SV34: $i,SV435: $i,SV605: $i] :
( ( ( ! [SY2621: $i] :
~ ( in @ SY2621 @ SV605 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV435 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1858,plain,
! [SV252: $i,SV35: $i,SV539: $i,SV436: $i] :
( ( ( in @ ( kpair @ SV436 @ SV539 ) @ ( cartprod @ SV35 @ SV252 ) )
= $false )
| ( ( in @ SV539 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1859,plain,
! [SV253: $i,SV36: $i,SV561: $i,SV437: $i] :
( ( ( in @ ( kpair @ SV437 @ SV561 ) @ ( cartprod @ SV36 @ SV253 ) )
= $false )
| ( ( in @ SV437 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1860,plain,
! [SV540: $i,SV439: $i,SV256: $i,SV41: $i] :
( ( ( ( kpair @ SV41 @ SV256 )
= ( kpair @ SV439 @ SV540 ) )
= $false )
| ( ( SV256 = SV540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1861,plain,
! [SV541: $i,SV440: $i,SV257: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV257 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV440 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV440 @ ( setadjoin @ SV541 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV257 = SV541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1862,plain,
! [SV543: $i,SV441: $i,SV259: $i,SV44: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV441 != SV543 )
| ( SV259 = SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1863,plain,
! [SV562: $i,SV442: $i,SV262: $i,SV47: $i] :
( ( ( ( kpair @ SV47 @ SV262 )
= ( kpair @ SV442 @ SV562 ) )
= $false )
| ( ( SV47 = SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1864,plain,
! [SV563: $i,SV443: $i,SV263: $i,SV48: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV443 @ ( setadjoin @ SV563 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV48 = SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1865,plain,
! [SV59: $i,SV447: $i,SV269: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV269 )
| ( in @ ( kpair @ SV447 @ SV606 ) @ ( cartprod @ SV59 @ SV269 ) ) )
= $true )
| ( ( in @ SV447 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1866,plain,
! [SV60: $i,SV448: $i,SV270: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV270 )
| ( in @ ( kpair @ SV448 @ SV607 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) ) )
= $true )
| ( ( in @ SV448 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1867,plain,
! [SV61: $i,SV449: $i,SV271: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV271 )
| ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SV608 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) ) )
= $true )
| ( ( in @ SV449 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1868,plain,
! [SV62: $i,SV450: $i,SV272: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV272 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SV609 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) ) )
= $true )
| ( ( in @ SV450 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(1869,plain,
! [SV63: $i,SV451: $i,SV273: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV273 )
| ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SV610 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) ) )
= $true )
| ( ( in @ SV451 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1870,plain,
! [SV64: $i,SV452: $i,SV274: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV274 )
| ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SV611 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) ) )
= $true )
| ( ( in @ SV452 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1871,plain,
! [SV275: $i,SV65: $i,SV453: $i] :
( ( ( SV453 = SV65 )
= $true )
| ( ( SV453 = SV275 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV65 @ ( setadjoin @ SV275 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1872,plain,
! [SV284: $i,SV74: $i,SV455: $i] :
( ( ( in @ SV455 @ ( symdiff @ SV74 @ SV284 ) )
= $false )
| ( ( in @ SV455 @ SV284 )
= $true )
| ( ( in @ SV455 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1873,plain,
! [SV75: $i,SV285: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV285 ) )
= $true )
| ( ( ~ ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) ) )
= $true )
| ( ( in @ SV456 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1874,plain,
! [SV76: $i,SV286: $i,SV457: $i] :
( ( ( in @ SV457 @ SV286 )
= $false )
| ( ( in @ SV457 @ ( symdiff @ SV76 @ SV286 ) )
= $true )
| ( ( in @ SV457 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1875,plain,
! [SV77: $i,SV287: $i,SV458: $i] :
( ( ( in @ SV458 @ SV287 )
= $true )
| ( ( in @ SV458 @ ( symdiff @ SV77 @ SV287 ) )
= $true )
| ( ( in @ SV458 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1876,plain,
! [SV290: $i,SV80: $i,SV459: $i] :
( ( ( in @ SV459 @ ( setminus @ SV80 @ SV290 ) )
= $false )
| ( ( in @ SV459 @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1877,plain,
! [SV292: $i,SV82: $i,SV461: $i] :
( ( ( in @ SV461 @ SV82 )
= $false )
| ( ( in @ SV461 @ SV292 )
= $true )
| ( ( in @ SV461 @ ( setminus @ SV82 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1878,plain,
! [SV293: $i,SV83: $i,SV462: $i] :
( ( ( in @ SV462 @ SV83 )
= $false )
| ( ( in @ SV462 @ SV293 )
= $true )
| ( ( in @ SV462 @ ( setminus @ SV83 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1879,plain,
! [SV85: $i,SV295: $i,SV463: $i] :
( ( ( in @ SV463 @ SV295 )
= $false )
| ( ( in @ SV463 @ ( setminus @ SV85 @ SV295 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1880,plain,
! [SV87: $i,SV297: $i,SV465: $i] :
( ( ( in @ SV465 @ SV297 )
= $true )
| ( ( in @ SV465 @ ( setminus @ SV87 @ SV297 ) )
= $true )
| ( ( in @ SV465 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1881,plain,
! [SV97: $i,SV307: $i,SV469: $i] :
( ( ( ~ ( subset @ SV469 @ SV307 ) )
= $true )
| ( ( subset @ SV469 @ ( binintersect @ SV97 @ SV307 ) )
= $true )
| ( ( subset @ SV469 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1882,plain,
! [SV98: $i,SV308: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV308 ) )
= $true )
| ( ( in @ SV470 @ ( binintersect @ SV98 @ SV308 ) )
= $true )
| ( ( in @ SV470 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1883,plain,
! [SV311: $i,SV101: $i,SV471: $i] :
( ( ( in @ SV471 @ SV101 )
= $true )
| ( ( in @ SV471 @ SV311 )
= $true )
| ( ( in @ SV471 @ ( binunion @ SV101 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1884,plain,
! [SV112: $i,SV320: $i] :
( ( ( subset @ SV320 @ SV112 )
= $false )
| ( ( SV112 = SV320 )
= $true )
| ( ( subset @ SV112 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1885,plain,
! [SV116: $i,SV564: $i,SV324: $i] :
( ( ( ~ ( subset @ SV324 @ SV564 ) )
= $true )
| ( ( subset @ SV116 @ SV564 )
= $true )
| ( ( subset @ SV116 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1886,plain,
! [SV118: $i,SV325: $i,SV475: $i] :
( ( ( in @ SV475 @ SV325 )
= $true )
| ( ( SV118 != SV325 )
= $true )
| ( ( in @ SV475 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1887,plain,
! [SV120: $i,SV327: $i,SV476: $i] :
( ( ( in @ SV476 @ SV327 )
= $true )
| ( ( ~ ( subset @ SV120 @ SV327 ) )
= $true )
| ( ( in @ SV476 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1888,plain,
! [SV121: $i,SV328: $i,SV565: $i] :
( ( ( in @ SV565 @ SV328 )
= $true )
| ( ( ~ ( in @ SV565 @ SV121 ) )
= $true )
| ( ( subset @ SV121 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(1889,plain,
! [SV329: $i,SV122: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV122 ) )
= $true )
| ( ( in @ SV566 @ SV329 )
= $true )
| ( ( subset @ SV122 @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1890,plain,
! [SV334: $i,SV128: $i,SV612: $i,SV567: $i] :
( ( ( ( SV567 != SV612 )
| ( ( setadjoin @ SV128 @ SV567 )
= ( setadjoin @ SV334 @ SV612 ) ) )
= $true )
| ( ( SV128 = SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1891,plain,
! [SV335: $i,SV129: $i,SV613: $i,SV568: $i] :
( ( ( ( SV568 != SV613 )
| ~ ( in @ SV568 @ SV129 )
| ( in @ SV613 @ SV335 ) )
= $true )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1892,plain,
! [SV133: $i,SV544: $i,SV337: $i > $o] :
( ( ( SV337 @ SV544 )
= $false )
| ( ( ~ ( in @ SV544 @ SV133 ) )
= $true )
| ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1893,plain,
! [SV340: $i,SV136: $i,SV477: $i] :
( ( ( SV477 = SV136 )
= $true )
| ( ( SV477 = SV340 )
= $true )
| ( ( in @ SV477 @ ( setadjoin @ SV136 @ ( setadjoin @ SV340 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1894,plain,
! [SV346: $i,SV143: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV143 ) )
= $true )
| ( ( in @ SV346 @ ( setunion @ SV143 ) )
= $true )
| ( ( in @ SV346 @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1895,plain,
! [SV144: $i,SV347: $i,SV569: $i] :
( ( ( ~ ( in @ SV569 @ SV347 ) )
= $true )
| ( ( in @ SV569 @ SV144 )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1896,plain,
! [SV348: $i,SV148: $i,SV479: $i] :
( ( ( SV479 = SV148 )
= $true )
| ( ( in @ SV479 @ SV348 )
= $true )
| ( ( in @ SV479 @ ( setadjoin @ SV148 @ SV348 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1897,plain,
! [SV152: $i,SV482: $i,SV351: $i > $o] :
( ( ( ~ ( SV351 @ SV482 ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset )
= $true )
| ( ( in @ SV482 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1898,plain,
! [SV161: $i,SV488: $i,SV355: $i > $o] :
( ( ( ~ ( SV355 @ SV488 ) )
= $true )
| ( ( in @ SV488
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) )
= $true )
| ( ( in @ SV488 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1899,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) ) )
= $false )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1900,plain,
! [SV164: $i > $o,SV489: $i] :
( ( ( ~ ( ( SV489
!= ( sK20_SY72 @ SV489 @ SV164 ) ) ) )
= $false )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1901,plain,
! [SV356: $i,SV165: $i] :
( ( ( ~ ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) ) )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1902,plain,
! [SV165: $i,SV356: $i] :
( ( ( ~ ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1728]) ).
thf(1903,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i] :
( ( ( ~ ( func @ SV166 @ SV357 @ SV614 )
| ~ ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(1904,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( ~ ( in @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) @ SV167 ) )
= $false )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1905,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( ~ ~ ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 ) )
= $false )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1730]) ).
thf(1906,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1907,plain,
( ( in @ sK3_SY1626 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1908,plain,
( ( ~ ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1733]) ).
thf(1909,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) ) )
= $false )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1910,plain,
! [SV169: $i > $o,SV493: $i] :
( ( ( ~ ( ( SV493
!= ( sK40_Xy @ SV493 @ SV169 ) ) ) )
= $false )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1911,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
| ~ ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) )
| ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1912,plain,
! [SV170: $i] :
( ( ~ ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1913,plain,
! [SV170: $i] :
( ( ~ ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1736]) ).
thf(1914,plain,
! [SV494: $i,SV360: $i,SV171: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
| ~ ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SV615 ) )
= $true )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1915,plain,
! [SV172: $i,SV361: $i] :
( ( ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV172 )
= $true )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1916,plain,
! [SV172: $i,SV361: $i] :
( ( ( in @ ( sK64_Xx @ SV361 @ SV172 ) @ SV361 )
= $true )
| ( ( ( binintersect @ SV172 @ SV361 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1917,plain,
! [SV362: $i > $o,SV173: $i,SV546: $i] :
( ( ( in @ SV546 @ SV173 )
= $false )
| ( ( SV362 @ SV546 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1918,plain,
! [SV571: $i,SV174: $i,SV616: $i] :
( ( ~ ( in @ SV616 @ ( setadjoin @ SV174 @ SV571 ) )
| ( SV616 = SV174 )
| ( in @ SV616 @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1919,plain,
! [SV174: $i] :
( ( ~ ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1920,plain,
! [SV174: $i] :
( ( ~ ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1742]) ).
thf(1921,plain,
! [SV175: $i,SV363: $i > $o] :
( ( ( ~ ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1922,plain,
! [SV175: $i,SV363: $i > $o] :
( ( ( ~ ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1923,plain,
! [SV495: $i,SV364: $i,SV176: $i,SV617: $i] :
( ( ( ~ ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
| ~ ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1924,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) @ SV177 ) )
= $false )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1925,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( ~ ~ ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 ) )
= $false )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1926,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 ) )
= $false )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1927,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 ) )
= $false )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1928,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1929,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1930,plain,
! [SV368: $i > $o,SV180: $i,SV547: $i] :
( ( ( in @ SV547 @ SV180 )
= $false )
| ( ( SV368 @ SV547 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1931,plain,
! [SV181: $i,SV369: $i] :
( ( ( ~ ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 ) )
= $false )
| ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1932,plain,
! [SV181: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) ) )
= $false )
| ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1750]) ).
thf(1933,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1934,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1935,plain,
! [SV183: $i,SV371: $i] :
( ( ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV183 )
= $true )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1936,plain,
! [SV183: $i,SV371: $i] :
( ( ( ~ ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 ) )
= $true )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1937,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) ) )
= $false )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1938,plain,
! [SV184: $i > $o,SV498: $i] :
( ( ( ~ ( ( SV498
!= ( sK46_SY222 @ SV498 @ SV184 ) ) ) )
= $false )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(1939,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
= $true )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1940,plain,
! [SV185: $i,SV372: $i > $o] :
( ( ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 )
= $true )
| ( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ SV185 )
| ~ ( SV372 @ SY2363 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1941,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ~ ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
| ~ ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1942,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1943,plain,
! [SV374: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2365: $i] :
( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) )
| ~ ( ( SY2365
!= ( sK11_SY1632 @ SY2365 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SY2365 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1944,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
= $true )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1945,plain,
! [SV188: $i,SV375: $i > $o] :
( ( ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 )
= $true )
| ( ( ! [SY2369: $i] :
( ~ ( in @ SY2369 @ SV188 )
| ~ ( SV375 @ SY2369 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1946,plain,
! [SV189: $i,SV376: $i] :
( ( ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV376 )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1947,plain,
! [SV189: $i,SV376: $i] :
( ( ( ~ ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 ) )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1948,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1949,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) )
| ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1950,plain,
! [SV500: $i,SV618: $i,SV378: $i,SV191: $i] :
( ( ( ~ ( func @ SV191 @ SV378 @ SV618 )
| ~ ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SV618 ) )
= $true )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1951,plain,
! [SV379: $i > $o,SV192: $i,SV548: $i] :
( ( ( in @ SV548 @ SV192 )
= $false )
| ( ( SV379 @ SV548 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1952,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) )
| ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1953,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) ) )
= $false )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1954,plain,
! [SV194: $i > $o,SV502: $i] :
( ( ( ~ ( ( SV502
!= ( sK55_SY246 @ SV502 @ SV194 ) ) ) )
= $false )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1955,plain,
! [SV503: $i,SV380: $o,SV195: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ SV195 )
| SV380
| ( in @ SV619
@ ( dsetconstr @ SV195
@ ^ [SY2624: $i] :
( ~ ( ~ SV380
| ( SY2624 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2624 != SV619 ) ) ) ) ) )
= $true )
| ( ( in @ SV503 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(1956,plain,
! [SV504: $i,SV195: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ SV195 )
| $true
| ( in @ SV620
@ ( dsetconstr @ SV195
@ ^ [SY2625: $i] :
( ~ ( ~ $true
| ( SY2625 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2625 != SV620 ) ) ) ) ) )
= $true )
| ( ( in @ SV504 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1957,plain,
! [SV505: $i,SV195: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV195 )
| $false
| ( in @ SV621
@ ( dsetconstr @ SV195
@ ^ [SY2626: $i] :
( ~ ( ~ $false
| ( SY2626 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2626 != SV621 ) ) ) ) ) )
= $true )
| ( ( in @ SV505 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(1958,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(1959,plain,
! [SV506: $i,SV382: $o,SV197: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2629: $i] :
( ~ ( ~ SV382
| ( SY2629 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2629 != SV623 ) ) ) ) ) )
= $true )
| ( ( in @ SV506 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1960,plain,
! [SV507: $i,SV197: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2630: $i] :
( ~ ( ~ $true
| ( SY2630 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2630 != SV624 ) ) ) ) ) )
= $true )
| ( ( in @ SV507 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1961,plain,
! [SV508: $i,SV197: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV197 )
| ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2631: $i] :
( ~ ( ~ $false
| ( SY2631 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2631 != SV625 ) ) ) ) ) )
= $true )
| ( ( in @ SV508 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(1962,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( ~ ( in @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) @ SV198 ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1963,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( ~ ~ ( in @ ( SV549 @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) ) @ SV509 ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1964,plain,
! [SV550: $i,SV573: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV573 )
| ~ ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 ) ) )
= $true )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1965,plain,
! [SV551: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ ( powerset @ SV551 ) ) )
= $true )
| ( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV574 )
| ( in @ SY2605 @ SV551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1966,plain,
! [SV510: $i,SV383: $o,SV199: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV199 )
| ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2632: $i] :
( ~ ( ~ SV383
| ( SY2632 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2632 != SV626 ) ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(1967,plain,
! [SV511: $i,SV199: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV199 )
| ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2633: $i] :
( ~ ( ~ $true
| ( SY2633 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2633 != SV627 ) ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1968,plain,
! [SV512: $i,SV199: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ SV199 )
| ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2634: $i] :
( ~ ( ~ $false
| ( SY2634 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2634 != SV628 ) ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1969,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( ~ ( SV384 @ SV513 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) )
= $true )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1970,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( ~ ( in @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) @ SV201 ) )
= $false )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1785]) ).
thf(1971,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( ~ ~ ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 ) )
= $false )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1785]) ).
thf(1972,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1973,plain,
! [SV202: $i,SV386: $i] :
( ( ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
| ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1974,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( ~ ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) ) )
= $false )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1975,plain,
! [SV203: $i > $o,SV515: $i] :
( ( ( ~ ( ( SV515
!= ( sK22_SY84 @ SV515 @ SV203 ) ) ) )
= $false )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1976,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1977,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1978,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( ~ ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 ) )
= $false )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1979,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( ~ ~ ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 ) )
= $false )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1980,plain,
! [SV517: $i,SV389: $i,SV206: $i,SV629: $i] :
( ( ( ~ ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
| ~ ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
| ( subset @ SV517 @ SV629 ) )
= $true )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1981,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) ) )
= $false )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1982,plain,
! [SV207: $i > $o,SV518: $i] :
( ( ( ~ ( ( SV518
!= ( sK18_SY55 @ SV518 @ SV207 ) ) ) )
= $false )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1983,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
| ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(1984,plain,
! [SV520: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK12_B @ SV209 ) @ SV209 ) )
= $false )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1985,plain,
! [SV520: $i,SV209: $i] :
( ( ( ~ ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) )
= $false )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1986,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( ( ( sK53_Xx @ SV575 @ SV552 )
!= ( sK54_SY1668 @ SV575 @ SV552 ) )
| ~ ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(1987,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ~ ( ( ( sK49_Xx @ SV576 @ SV553 )
!= ( sK50_SY1666 @ SV576 @ SV553 ) )
| ~ ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1988,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
= $true )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1989,plain,
! [SV210: $i,SV391: $i > $o] :
( ( ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) )
= $true )
| ( ( ! [SY2408: $i] :
( ~ ( SV391 @ SY2408 )
| ~ ( in @ SY2408 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1990,plain,
! [SV211: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1991,plain,
! [SV211: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1992,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ( ( sK45_Xy @ SV521 @ SV212 )
!= SV521 )
| ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1993,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
| ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1994,plain,
! [SV522: $i,SV392: $o,SV213: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV213 )
| SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2636: $i] :
( ~ ( ~ SV392
| ( SY2636 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2636 != SV631 ) ) ) )
= ( setadjoin @ SV631 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1995,plain,
! [SV523: $i,SV213: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV213 )
| $true
| ( ( dsetconstr @ SV213
@ ^ [SY2637: $i] :
( ~ ( ~ $true
| ( SY2637 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2637 != SV632 ) ) ) )
= ( setadjoin @ SV632 @ emptyset ) ) )
= $true )
| ( ( in @ SV523 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1996,plain,
! [SV524: $i,SV213: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV213 )
| $false
| ( ( dsetconstr @ SV213
@ ^ [SY2638: $i] :
( ~ ( ~ $false
| ( SY2638 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2638 != SV633 ) ) ) )
= ( setadjoin @ SV633 @ emptyset ) ) )
= $true )
| ( ( in @ SV524 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(1997,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) ) )
= $false )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1998,plain,
! [SV214: $i > $o,SV525: $i] :
( ( ( ~ ( ( SV525
!= ( sK31_SY140 @ SV525 @ SV214 ) ) ) )
= $false )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1807]) ).
thf(1999,plain,
! [SV215: $i,SV393: $i] :
( ( ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV215 )
= $true )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(2000,plain,
! [SV215: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 ) )
= $true )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(2001,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
| ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2002,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(2003,plain,
! [SV577: $i > $o,SV218: $i,SV635: $i] :
( ( ~ ( in @ SV635 @ SV218 )
| ~ ( SV577 @ SV635 )
| ( in @ SV635
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2004,plain,
! [SV578: $i > $o,SV218: $i,SV636: $i] :
( ( ~ ( in @ SV636 @ SV218 )
| ~ ( in @ SV636
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) )
| ( SV578 @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2005,plain,
! [SV219: $i,SV579: $o,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ SV579 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 ) ) )
= $true )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(2006,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ $true @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true ) ) )
= $true )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2007,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ SV396 @ ( sK29_B @ $false @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false ) ) )
= $true )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2008,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(2009,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(2010,plain,
! [SV528: $i,SV398: $o,SV221: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ SV221 )
| ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2642: $i] :
( ~ ( ~ SV398
| ( SY2642 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2642 != SV637 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) )
= $true )
| ( ( in @ SV528 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2011,plain,
! [SV529: $i,SV221: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV221 )
| ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2643: $i] :
( ~ ( ~ $true
| ( SY2643 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2643 != SV638 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) )
= $true )
| ( ( in @ SV529 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2012,plain,
! [SV530: $i,SV221: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV221 )
| ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2644: $i] :
( ~ ( ~ $false
| ( SY2644 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2644 != SV639 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) )
= $true )
| ( ( in @ SV530 @ SV221 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2013,plain,
! [SV554: $i,SV580: $i] :
( ( ( ! [SY2614: $i] :
( ~ ( in @ SV580 @ SY2614 )
| ~ ( in @ SY2614 @ SV554 ) ) )
= $true )
| ( ( in @ SV580 @ ( setunion @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2014,plain,
! [SV555: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ ( setunion @ SV555 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) )
| ~ ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2015,plain,
! [SV223: $i,SV2: $i,SV556: $i] :
( ( ( in @ SV556 @ ( powerset @ SV2 ) )
= $false )
| ( ( in @ ( binunion @ SV223 @ SV556 ) @ ( powerset @ SV2 ) )
= $true )
| ( ( in @ SV223 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2016,plain,
! [SV224: $i,SV3: $i,SV557: $i] :
( ( ( in @ SV557 @ ( powerset @ SV3 ) )
= $false )
| ( ( in @ ( binintersect @ SV224 @ SV557 ) @ ( powerset @ SV3 ) )
= $true )
| ( ( in @ SV224 @ ( powerset @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2017,plain,
! [SV399: $i,SV225: $o,SV4: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ SV4 ) )
= $true )
| ( ( in @ ( if @ SV4 @ SV225 @ SV399 @ SV582 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SV582 @ emptyset ) ) )
= $true )
| ( ( in @ SV399 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2018,plain,
! [SV400: $i,SV4: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV4 ) )
= $true )
| ( ( in @ ( if @ SV4 @ $true @ SV400 @ SV583 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SV583 @ emptyset ) ) )
= $true )
| ( ( in @ SV400 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2019,plain,
! [SV401: $i,SV4: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV4 ) )
= $true )
| ( ( in @ ( if @ SV4 @ $false @ SV401 @ SV584 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SV584 @ emptyset ) ) )
= $true )
| ( ( in @ SV401 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2020,plain,
! [SV402: $i,SV226: $o,SV5: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV5 ) )
= $true )
| ( ( SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SV585 )
= SV585 ) )
= $true )
| ( ( in @ SV402 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2021,plain,
! [SV403: $i,SV5: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV5 ) )
= $true )
| ( ( $true
| ( ( if @ SV5 @ $true @ SV403 @ SV586 )
= SV586 ) )
= $true )
| ( ( in @ SV403 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2022,plain,
! [SV404: $i,SV5: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV5 ) )
= $true )
| ( ( $false
| ( ( if @ SV5 @ $false @ SV404 @ SV587 )
= SV587 ) )
= $true )
| ( ( in @ SV404 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2023,plain,
! [SV405: $i,SV227: $o,SV6: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV6 ) )
= $true )
| ( ( ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SV588 )
= SV405 ) )
= $true )
| ( ( in @ SV405 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2024,plain,
! [SV406: $i,SV6: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV6 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SV589 )
= SV406 ) )
= $true )
| ( ( in @ SV406 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2025,plain,
! [SV407: $i,SV6: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV6 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SV590 )
= SV407 ) )
= $true )
| ( ( in @ SV407 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2026,plain,
! [SV408: $i,SV228: $o,SV8: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV8 ) )
= $true )
| ( ( in @ ( if @ SV8 @ SV228 @ SV408 @ SV591 ) @ SV8 )
= $true )
| ( ( in @ SV408 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2027,plain,
! [SV409: $i,SV8: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV8 ) )
= $true )
| ( ( in @ ( if @ SV8 @ $true @ SV409 @ SV592 ) @ SV8 )
= $true )
| ( ( in @ SV409 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2028,plain,
! [SV410: $i,SV8: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ SV8 ) )
= $true )
| ( ( in @ ( if @ SV8 @ $false @ SV410 @ SV593 ) @ SV8 )
= $true )
| ( ( in @ SV410 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(2029,plain,
! [SV532: $i,SV413: $i,SV11: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV11 ) )
= $true )
| ( $true = $true )
| ( ( func @ SV11 @ SV413 @ SV532 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2030,plain,
! [SV414: $i,SV533: $i,SV12: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV12 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV533 @ ( funcSet @ SV12 @ SV414 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2031,plain,
! [SV415: $i,SV231: $i,SV13: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV13 ) )
= $true )
| ( ( ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV231 )
| ~ ( in @ ( kpair @ SV594 @ SY2615 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SY2615 ) ) )
= $true )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2032,plain,
! [SV416: $i,SV232: $i,SV14: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV14 ) )
= $true )
| ( ( ! [SY2616: $i] :
( ~ ( in @ SY2616 @ SV232 )
| ~ ( in @ ( kpair @ SV595 @ SY2616 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SY2616 ) ) )
= $true )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2033,plain,
! [SV417: $i,SV233: $i,SV15: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV15 ) )
= $true )
| ( ( in @ ( kpair @ SV596 @ ( ap @ SV15 @ SV233 @ SV417 @ SV596 ) ) @ SV417 )
= $true )
| ( ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2034,plain,
! [SV418: $i,SV234: $i,SV16: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV16 ) )
= $true )
| ( ( in @ ( kpair @ SV597 @ ( ap @ SV16 @ SV234 @ SV418 @ SV597 ) ) @ SV418 )
= $true )
| ( ( func @ SV16 @ SV234 @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2035,plain,
! [SV235: $i > $o,SV17: $i,SV558: $i] :
( ( ( in @ SV558 @ SV17 )
= $false )
| ( ( ! [SY2590: $i] :
( ~ ( in @ SY2590 @ SV17 )
| ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SY2590 )
| ( SV558 = SY2590 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(2036,plain,
! [SV420: $i,SV237: $i,SV19: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV19 ) )
= $true )
| ( ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SV598 ) @ SV237 )
= $true )
| ( ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2037,plain,
! [SV422: $i,SV239: $i,SV21: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV21 ) )
= $true )
| ( ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SV599 ) @ SV239 )
= $true )
| ( ( func @ SV21 @ SV239 @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2038,plain,
! [SV423: $i,SV240: $i,SV22: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV22 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2617: $i] : ( in @ ( kpair @ SV600 @ SY2617 ) @ SV423 ) ) )
@ SV240 )
= $true )
| ( ( func @ SV22 @ SV240 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2039,plain,
! [SV424: $i,SV241: $i,SV23: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV23 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2618: $i] : ( in @ ( kpair @ SV601 @ SY2618 ) @ SV424 ) ) )
= $true )
| ( ( func @ SV23 @ SV241 @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2040,plain,
! [SV425: $i > $i > $o,SV242: $i,SV24: $i,SV559: $i,SV534: $i] :
( ( ( in @ ( kpair @ SV534 @ SV559 )
@ ( dpsetconstr @ SV24 @ SV242
@ ^ [SY2458: $i,SY2459: $i] : ( SV425 @ SY2458 @ SY2459 ) ) )
= $false )
| ( ( SV425 @ SV534 @ SV559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2041,plain,
! [SV426: $i > $i > $o,SV243: $i,SV25: $i,SV560: $i,SV535: $i] :
( ( ( in @ ( kpair @ SV535 @ SV560 )
@ ( dpsetconstr @ SV25 @ SV243
@ ^ [SY2462: $i,SY2463: $i] : ( SV426 @ SY2462 @ SY2463 ) ) )
= $false )
| ( ( in @ SV560 @ SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2042,plain,
! [SV427: $i > $i > $o,SV244: $i,SV26: $i,SV602: $i,SV536: $i] :
( ( ( in @ ( kpair @ SV536 @ SV602 )
@ ( dpsetconstr @ SV26 @ SV244
@ ^ [SY2466: $i,SY2467: $i] : ( SV427 @ SY2466 @ SY2467 ) ) )
= $false )
| ( ( in @ SV536 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2043,plain,
! [SV428: $i > $i > $o,SV27: $i,SV537: $i,SV245: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV245 )
| ~ ( in @ ( kpair @ SV537 @ SV642 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SV642 ) )
= $true )
| ( ( in @ SV537 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2044,plain,
! [SV30: $i,SV538: $i,SV431: $i > $i > $o,SV248: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV248 )
| ~ ( SV431 @ SV538 @ SV643 )
| ( in @ ( kpair @ SV538 @ SV643 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) )
= $true )
| ( ( in @ SV538 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2045,plain,
! [SV32: $i,SV433: $i,SV250: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV250 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV433 @ SV603 ) )
= SV603 )
= $true )
| ( ( in @ SV433 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2046,plain,
! [SV33: $i,SV434: $i,SV251: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ SV251 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV434 @ SV604 ) )
= SV434 )
= $true )
| ( ( in @ SV434 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(2047,plain,
! [SV34: $i,SV435: $i,SV605: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV605 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV435 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2048,plain,
! [SV44: $i,SV259: $i,SV543: $i,SV441: $i] :
( ( ( SV441 != SV543 )
= $true )
| ( ( SV259 = SV543 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2049,plain,
! [SV59: $i,SV447: $i,SV269: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV269 ) )
= $true )
| ( ( in @ ( kpair @ SV447 @ SV606 ) @ ( cartprod @ SV59 @ SV269 ) )
= $true )
| ( ( in @ SV447 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2050,plain,
! [SV60: $i,SV448: $i,SV270: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV270 ) )
= $true )
| ( ( in @ ( kpair @ SV448 @ SV607 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) )
= $true )
| ( ( in @ SV448 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2051,plain,
! [SV61: $i,SV449: $i,SV271: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV271 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SV608 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) )
= $true )
| ( ( in @ SV449 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2052,plain,
! [SV62: $i,SV450: $i,SV272: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV272 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SV609 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) )
= $true )
| ( ( in @ SV450 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2053,plain,
! [SV63: $i,SV451: $i,SV273: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV273 ) )
= $true )
| ( ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SV610 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) )
= $true )
| ( ( in @ SV451 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2054,plain,
! [SV64: $i,SV452: $i,SV274: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV274 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SV611 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) )
= $true )
| ( ( in @ SV452 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2055,plain,
! [SV75: $i,SV285: $i,SV456: $i] :
( ( ( in @ SV456 @ SV285 )
= $false )
| ( ( ~ ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) ) )
= $true )
| ( ( in @ SV456 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(2056,plain,
! [SV97: $i,SV307: $i,SV469: $i] :
( ( ( subset @ SV469 @ SV307 )
= $false )
| ( ( subset @ SV469 @ ( binintersect @ SV97 @ SV307 ) )
= $true )
| ( ( subset @ SV469 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2057,plain,
! [SV98: $i,SV308: $i,SV470: $i] :
( ( ( in @ SV470 @ SV308 )
= $false )
| ( ( in @ SV470 @ ( binintersect @ SV98 @ SV308 ) )
= $true )
| ( ( in @ SV470 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(2058,plain,
! [SV116: $i,SV564: $i,SV324: $i] :
( ( ( subset @ SV324 @ SV564 )
= $false )
| ( ( subset @ SV116 @ SV564 )
= $true )
| ( ( subset @ SV116 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(2059,plain,
! [SV475: $i,SV325: $i,SV118: $i] :
( ( ( SV118 = SV325 )
= $false )
| ( ( in @ SV475 @ SV325 )
= $true )
| ( ( in @ SV475 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2060,plain,
! [SV476: $i,SV327: $i,SV120: $i] :
( ( ( subset @ SV120 @ SV327 )
= $false )
| ( ( in @ SV476 @ SV327 )
= $true )
| ( ( in @ SV476 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2061,plain,
! [SV328: $i,SV121: $i,SV565: $i] :
( ( ( in @ SV565 @ SV121 )
= $false )
| ( ( in @ SV565 @ SV328 )
= $true )
| ( ( subset @ SV121 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2062,plain,
! [SV329: $i,SV122: $i,SV566: $i] :
( ( ( in @ SV566 @ SV122 )
= $false )
| ( ( in @ SV566 @ SV329 )
= $true )
| ( ( subset @ SV122 @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2063,plain,
! [SV334: $i,SV128: $i,SV612: $i,SV567: $i] :
( ( ( SV567 != SV612 )
= $true )
| ( ( ( setadjoin @ SV128 @ SV567 )
= ( setadjoin @ SV334 @ SV612 ) )
= $true )
| ( ( SV128 = SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2064,plain,
! [SV335: $i,SV129: $i,SV613: $i,SV568: $i] :
( ( ( SV568 != SV613 )
= $true )
| ( ( ~ ( in @ SV568 @ SV129 )
| ( in @ SV613 @ SV335 ) )
= $true )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2065,plain,
! [SV337: $i > $o,SV133: $i,SV544: $i] :
( ( ( in @ SV544 @ SV133 )
= $false )
| ( ( SV337 @ SV544 )
= $false )
| ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2066,plain,
! [SV346: $i,SV143: $i,SV478: $i] :
( ( ( in @ SV478 @ SV143 )
= $false )
| ( ( in @ SV346 @ ( setunion @ SV143 ) )
= $true )
| ( ( in @ SV346 @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2067,plain,
! [SV144: $i,SV347: $i,SV569: $i] :
( ( ( in @ SV569 @ SV347 )
= $false )
| ( ( in @ SV569 @ SV144 )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2068,plain,
! [SV152: $i,SV482: $i,SV351: $i > $o] :
( ( ( SV351 @ SV482 )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
!= emptyset )
= $true )
| ( ( in @ SV482 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2069,plain,
! [SV161: $i,SV488: $i,SV355: $i > $o] :
( ( ( SV355 @ SV488 )
= $false )
| ( ( in @ SV488
@ ( dsetconstr @ SV161
@ ^ [SY2327: $i] : ( SV355 @ SY2327 ) ) )
= $true )
| ( ( in @ SV488 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2070,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2071,plain,
! [SV164: $i > $o,SV489: $i] :
( ( ( SV489
!= ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2072,plain,
! [SV356: $i,SV165: $i] :
( ( ( ! [SY2328: $i,SY2329: $i] :
( ( SY2328 != SY2329 )
| ~ ( in @ SY2328 @ SV165 )
| ( in @ SY2329 @ SV356 ) ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2073,plain,
! [SV165: $i,SV356: $i] :
( ( ( ! [SY2330: $i,SY2331: $i] :
( ( SY2330 != SY2331 )
| ~ ( in @ SY2331 @ SV356 )
| ( in @ SY2330 @ SV165 ) ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(2074,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i] :
( ( ( ~ ( func @ SV166 @ SV357 @ SV614 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2075,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( in @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) @ SV167 )
= $true )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2076,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( ~ ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 ) )
= $true )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(2077,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2078,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2079,plain,
( ( in @ ( setminus @ sK2_SY1624 @ sK3_SY1626 ) @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2080,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(2081,plain,
! [SV169: $i > $o,SV493: $i] :
( ( ( SV493
!= ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(2082,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
| ~ ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) ) )
= $true )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2083,plain,
! [SV170: $i] :
( ( ! [SY2014: $i,SY2015: $i] :
( ~ ( in @ SY2014 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2015 @ ( sK13_B @ SV170 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2014 )
| ( in @ SX3 @ SY2015 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2015 )
| ( in @ SX3 @ SY2014 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(2084,plain,
! [SV170: $i] :
( ( ~ ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2085,plain,
! [SV494: $i,SV360: $i,SV171: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SV615 ) )
= $true )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2086,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
| ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) )
= $false )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2087,plain,
! [SV571: $i,SV174: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ ( setadjoin @ SV174 @ SV571 ) ) )
= $true )
| ( ( ( SV616 = SV174 )
| ( in @ SV616 @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2088,plain,
! [SV174: $i] :
( ( ! [SY2030: $i,SY2031: $i] :
( ( SY2031 != SV174 )
| ( in @ SY2031 @ ( setadjoin @ SV174 @ SY2030 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(2089,plain,
! [SV174: $i] :
( ( ! [SY2032: $i,SY2033: $i] :
( ~ ( in @ SY2033 @ SY2032 )
| ( in @ SY2033 @ ( setadjoin @ SV174 @ SY2032 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(2090,plain,
! [SV175: $i,SV363: $i > $o] :
( ( ( SV363 @ ( sK70_Xx @ SV363 @ SV175 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1921]) ).
thf(2091,plain,
! [SV175: $i,SV363: $i > $o] :
( ( ( in @ ( sK70_Xx @ SV363 @ SV175 ) @ SV175 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV175
@ ^ [SY2351: $i] : ( SV363 @ SY2351 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(2092,plain,
! [SV495: $i,SV364: $i,SV176: $i,SV617: $i] :
( ( ( ~ ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2093,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( in @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) @ SV177 )
= $true )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(2094,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 ) )
= $true )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2095,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
= $true )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2096,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 ) )
= $true )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2097,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2098,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
| ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2099,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
| ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) )
= $false )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2100,plain,
! [SV181: $i,SV369: $i] :
( ( ( in @ ( sK67_X @ SV369 @ SV181 ) @ SV181 )
= $true )
| ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(2101,plain,
! [SV181: $i,SV369: $i] :
( ( ( in @ SV369 @ ( sK67_X @ SV369 @ SV181 ) )
= $true )
| ( ( in @ SV369 @ ( setunion @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(2102,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2103,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
| ( SV182 = SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2104,plain,
! [SV183: $i,SV371: $i] :
( ( ( in @ ( sK62_Xx @ SV371 @ SV183 ) @ SV371 )
= $false )
| ( ( subset @ SV183 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2105,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2106,plain,
! [SV184: $i > $o,SV498: $i] :
( ( ( SV498
!= ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(2107,plain,
! [SV372: $i > $o,SV185: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV185 )
| ~ ( SV372 @ SV645 ) )
= $true )
| ( ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2108,plain,
! [SV372: $i > $o,SV185: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV185 )
| ~ ( SV372 @ SV646 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2109,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ~ ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2110,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2111,plain,
! [SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2112,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
| ~ ( ( SV647
!= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) ) ) )
| ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2113,plain,
! [SV375: $i > $o,SV188: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV188 )
| ~ ( SV375 @ SV648 ) )
= $true )
| ( ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2114,plain,
! [SV375: $i > $o,SV188: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ SV188 )
| ~ ( SV375 @ SV649 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2115,plain,
! [SV189: $i,SV376: $i] :
( ( ( in @ ( sK28_Xx @ SV376 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2116,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2117,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2118,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(2119,plain,
! [SV377: $i,SV190: $i] :
( ( ~ ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(2120,plain,
! [SV500: $i,SV618: $i,SV378: $i,SV191: $i] :
( ( ( ~ ( func @ SV191 @ SV378 @ SV618 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SV618 ) )
= $true )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2121,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
| ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) )
= $false )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2122,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK42_Xx @ SV193 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2123,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1952]) ).
thf(2124,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2125,plain,
! [SV194: $i > $o,SV502: $i] :
( ( ( SV502
!= ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(2126,plain,
! [SV503: $i,SV380: $o,SV195: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ SV195 ) )
= $true )
| ( ( SV380
| ( in @ SV619
@ ( dsetconstr @ SV195
@ ^ [SY2624: $i] :
( ~ ( ~ SV380
| ( SY2624 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2624 != SV619 ) ) ) ) ) )
= $true )
| ( ( in @ SV503 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2127,plain,
! [SV504: $i,SV195: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ SV195 ) )
= $true )
| ( ( $true
| ( in @ SV620
@ ( dsetconstr @ SV195
@ ^ [SY2625: $i] :
( ~ ( ~ $true
| ( SY2625 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2625 != SV620 ) ) ) ) ) )
= $true )
| ( ( in @ SV504 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2128,plain,
! [SV505: $i,SV195: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ SV195 ) )
= $true )
| ( ( $false
| ( in @ SV621
@ ( dsetconstr @ SV195
@ ^ [SY2626: $i] :
( ~ ( ~ $false
| ( SY2626 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2626 != SV621 ) ) ) ) ) )
= $true )
| ( ( in @ SV505 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2129,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2130,plain,
! [SV506: $i,SV382: $o,SV197: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ SV197 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2629: $i] :
( ~ ( ~ SV382
| ( SY2629 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2629 != SV623 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2131,plain,
! [SV507: $i,SV197: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ SV197 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2630: $i] :
( ~ ( ~ $true
| ( SY2630 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2630 != SV624 ) ) ) ) )
= $true )
| ( ( in @ SV507 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2132,plain,
! [SV508: $i,SV197: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV197 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2631: $i] :
( ~ ( ~ $false
| ( SY2631 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2631 != SV625 ) ) ) ) )
= $true )
| ( ( in @ SV508 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2133,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( in @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) @ SV198 )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2134,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( ~ ( in @ ( SV549 @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) ) @ SV509 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2135,plain,
! [SV550: $i,SV573: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV573 )
| ~ ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 ) )
= $false )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2136,plain,
! [SV551: $i,SV574: $i] :
( ( ( in @ SV574 @ ( powerset @ SV551 ) )
= $false )
| ( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV574 )
| ( in @ SY2605 @ SV551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2137,plain,
! [SV510: $i,SV383: $o,SV199: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV199 ) )
= $true )
| ( ( ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2632: $i] :
( ~ ( ~ SV383
| ( SY2632 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2632 != SV626 ) ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2138,plain,
! [SV511: $i,SV199: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV199 ) )
= $true )
| ( ( ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2633: $i] :
( ~ ( ~ $true
| ( SY2633 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2633 != SV627 ) ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2139,plain,
! [SV512: $i,SV199: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ SV199 ) )
= $true )
| ( ( ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2634: $i] :
( ~ ( ~ $false
| ( SY2634 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2634 != SV628 ) ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2140,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( SV384 @ SV513 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
| ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) ) )
= $true )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2141,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( in @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) @ SV201 )
= $true )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2142,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( ~ ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 ) )
= $true )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2143,plain,
! [SV202: $i,SV386: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 ) )
= $true )
| ( ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2144,plain,
! [SV202: $i,SV386: $i] :
( ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
= $true )
| ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2145,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) )
= $true )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2146,plain,
! [SV203: $i > $o,SV515: $i] :
( ( ( SV515
!= ( sK22_SY84 @ SV515 @ SV203 ) )
= $true )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2147,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2148,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
| ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2149,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
= $true )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2150,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( ~ ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 ) )
= $true )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1979]) ).
thf(2151,plain,
! [SV517: $i,SV389: $i,SV206: $i,SV629: $i] :
( ( ( ~ ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
| ( subset @ SV517 @ SV629 ) )
= $true )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2152,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) )
= $true )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1981]) ).
thf(2153,plain,
! [SV207: $i > $o,SV518: $i] :
( ( ( SV518
!= ( sK18_SY55 @ SV518 @ SV207 ) )
= $true )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2154,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2155,plain,
! [SV520: $i,SV209: $i] :
( ( ( in @ ( sK12_B @ SV209 ) @ SV209 )
= $true )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2156,plain,
! [SV520: $i,SV209: $i] :
( ( ( ! [SY2133: $i] :
( ~ ( in @ SY2133 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SY2133 @ SV209 ) ) )
= $true )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2157,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ( ( ( sK53_Xx @ SV575 @ SV552 )
!= ( sK54_SY1668 @ SV575 @ SV552 ) )
| ~ ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2158,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ( ( sK49_Xx @ SV576 @ SV553 )
!= ( sK50_SY1666 @ SV576 @ SV553 ) )
| ~ ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2159,plain,
! [SV210: $i,SV650: $i,SV391: $i > $o] :
( ( ( ~ ( SV391 @ SV650 )
| ~ ( in @ SV650 @ SV210 ) )
= $true )
| ( ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2160,plain,
! [SV210: $i,SV651: $i,SV391: $i > $o] :
( ( ( ~ ( SV391 @ SV651 )
| ~ ( in @ SV651 @ SV210 ) )
= $true )
| ( ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2161,plain,
! [SV211: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega )
| ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2162,plain,
! [SV211: $i] :
( ( ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2163,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ( sK45_Xy @ SV521 @ SV212 )
!= SV521 )
= $true )
| ( ( ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2164,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2165,plain,
! [SV522: $i,SV392: $o,SV213: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV213 ) )
= $true )
| ( ( SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2636: $i] :
( ~ ( ~ SV392
| ( SY2636 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2636 != SV631 ) ) ) )
= ( setadjoin @ SV631 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2166,plain,
! [SV523: $i,SV213: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV213 ) )
= $true )
| ( ( $true
| ( ( dsetconstr @ SV213
@ ^ [SY2637: $i] :
( ~ ( ~ $true
| ( SY2637 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2637 != SV632 ) ) ) )
= ( setadjoin @ SV632 @ emptyset ) ) )
= $true )
| ( ( in @ SV523 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2167,plain,
! [SV524: $i,SV213: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV213 ) )
= $true )
| ( ( $false
| ( ( dsetconstr @ SV213
@ ^ [SY2638: $i] :
( ~ ( ~ $false
| ( SY2638 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2638 != SV633 ) ) ) )
= ( setadjoin @ SV633 @ emptyset ) ) )
= $true )
| ( ( in @ SV524 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2168,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2169,plain,
! [SV214: $i > $o,SV525: $i] :
( ( ( SV525
!= ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2170,plain,
! [SV215: $i,SV393: $i] :
( ( ( in @ ( sK63_Xx @ SV393 @ SV215 ) @ SV393 )
= $false )
| ( ( subset @ SV215 @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2171,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2172,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2173,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2174,plain,
! [SV577: $i > $o,SV218: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV218 ) )
= $true )
| ( ( ~ ( SV577 @ SV635 )
| ( in @ SV635
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2175,plain,
! [SV578: $i > $o,SV218: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV218 ) )
= $true )
| ( ( ~ ( in @ SV636
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) )
| ( SV578 @ SV636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2004]) ).
thf(2176,plain,
! [SV219: $i,SV579: $o,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ SV579 @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 ) )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2177,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ $true @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2178,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ $false @ SV396 @ SV219 ) )
| ~ ~ ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2179,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2180,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
| ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2181,plain,
! [SV528: $i,SV398: $o,SV221: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ SV221 ) )
= $true )
| ( ( ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2642: $i] :
( ~ ( ~ SV398
| ( SY2642 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2642 != SV637 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) )
= $true )
| ( ( in @ SV528 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2182,plain,
! [SV529: $i,SV221: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV221 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2643: $i] :
( ~ ( ~ $true
| ( SY2643 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2643 != SV638 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) )
= $true )
| ( ( in @ SV529 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2183,plain,
! [SV530: $i,SV221: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV221 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2644: $i] :
( ~ ( ~ $false
| ( SY2644 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2644 != SV639 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) )
= $true )
| ( ( in @ SV530 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2184,plain,
! [SV554: $i,SV652: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ SV652 )
| ~ ( in @ SV652 @ SV554 ) )
= $true )
| ( ( in @ SV580 @ ( setunion @ SV554 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2185,plain,
! [SV555: $i,SV581: $i] :
( ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) )
| ~ ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2186,plain,
! [SV399: $i,SV225: $o,SV4: $i,SV582: $i] :
( ( ( in @ SV582 @ SV4 )
= $false )
| ( ( in @ ( if @ SV4 @ SV225 @ SV399 @ SV582 ) @ ( setadjoin @ SV399 @ ( setadjoin @ SV582 @ emptyset ) ) )
= $true )
| ( ( in @ SV399 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2187,plain,
! [SV400: $i,SV4: $i,SV583: $i] :
( ( ( in @ SV583 @ SV4 )
= $false )
| ( ( in @ ( if @ SV4 @ $true @ SV400 @ SV583 ) @ ( setadjoin @ SV400 @ ( setadjoin @ SV583 @ emptyset ) ) )
= $true )
| ( ( in @ SV400 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2188,plain,
! [SV401: $i,SV4: $i,SV584: $i] :
( ( ( in @ SV584 @ SV4 )
= $false )
| ( ( in @ ( if @ SV4 @ $false @ SV401 @ SV584 ) @ ( setadjoin @ SV401 @ ( setadjoin @ SV584 @ emptyset ) ) )
= $true )
| ( ( in @ SV401 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2189,plain,
! [SV402: $i,SV226: $o,SV5: $i,SV585: $i] :
( ( ( in @ SV585 @ SV5 )
= $false )
| ( ( SV226
| ( ( if @ SV5 @ SV226 @ SV402 @ SV585 )
= SV585 ) )
= $true )
| ( ( in @ SV402 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2190,plain,
! [SV403: $i,SV5: $i,SV586: $i] :
( ( ( in @ SV586 @ SV5 )
= $false )
| ( ( $true
| ( ( if @ SV5 @ $true @ SV403 @ SV586 )
= SV586 ) )
= $true )
| ( ( in @ SV403 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2191,plain,
! [SV404: $i,SV5: $i,SV587: $i] :
( ( ( in @ SV587 @ SV5 )
= $false )
| ( ( $false
| ( ( if @ SV5 @ $false @ SV404 @ SV587 )
= SV587 ) )
= $true )
| ( ( in @ SV404 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2192,plain,
! [SV405: $i,SV227: $o,SV6: $i,SV588: $i] :
( ( ( in @ SV588 @ SV6 )
= $false )
| ( ( ~ SV227
| ( ( if @ SV6 @ SV227 @ SV405 @ SV588 )
= SV405 ) )
= $true )
| ( ( in @ SV405 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2193,plain,
! [SV406: $i,SV6: $i,SV589: $i] :
( ( ( in @ SV589 @ SV6 )
= $false )
| ( ( ~ $true
| ( ( if @ SV6 @ $true @ SV406 @ SV589 )
= SV406 ) )
= $true )
| ( ( in @ SV406 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2194,plain,
! [SV407: $i,SV6: $i,SV590: $i] :
( ( ( in @ SV590 @ SV6 )
= $false )
| ( ( ~ $false
| ( ( if @ SV6 @ $false @ SV407 @ SV590 )
= SV407 ) )
= $true )
| ( ( in @ SV407 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2195,plain,
! [SV408: $i,SV228: $o,SV8: $i,SV591: $i] :
( ( ( in @ SV591 @ SV8 )
= $false )
| ( ( in @ ( if @ SV8 @ SV228 @ SV408 @ SV591 ) @ SV8 )
= $true )
| ( ( in @ SV408 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2196,plain,
! [SV409: $i,SV8: $i,SV592: $i] :
( ( ( in @ SV592 @ SV8 )
= $false )
| ( ( in @ ( if @ SV8 @ $true @ SV409 @ SV592 ) @ SV8 )
= $true )
| ( ( in @ SV409 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2197,plain,
! [SV410: $i,SV8: $i,SV593: $i] :
( ( ( in @ SV593 @ SV8 )
= $false )
| ( ( in @ ( if @ SV8 @ $false @ SV410 @ SV593 ) @ SV8 )
= $true )
| ( ( in @ SV410 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2198,plain,
! [SV532: $i,SV413: $i,SV11: $i,SV640: $i] :
( ( ( in @ SV640 @ SV11 )
= $false )
| ( $true = $true )
| ( ( func @ SV11 @ SV413 @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2199,plain,
! [SV414: $i,SV533: $i,SV12: $i,SV641: $i] :
( ( ( in @ SV641 @ SV12 )
= $false )
| ( $true = $true )
| ( ( in @ SV533 @ ( funcSet @ SV12 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2200,plain,
! [SV415: $i,SV231: $i,SV13: $i,SV594: $i] :
( ( ( in @ SV594 @ SV13 )
= $false )
| ( ( ! [SY2615: $i] :
( ~ ( in @ SY2615 @ SV231 )
| ~ ( in @ ( kpair @ SV594 @ SY2615 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SY2615 ) ) )
= $true )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2201,plain,
! [SV416: $i,SV232: $i,SV14: $i,SV595: $i] :
( ( ( in @ SV595 @ SV14 )
= $false )
| ( ( ! [SY2616: $i] :
( ~ ( in @ SY2616 @ SV232 )
| ~ ( in @ ( kpair @ SV595 @ SY2616 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SY2616 ) ) )
= $true )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2202,plain,
! [SV417: $i,SV233: $i,SV15: $i,SV596: $i] :
( ( ( in @ SV596 @ SV15 )
= $false )
| ( ( in @ ( kpair @ SV596 @ ( ap @ SV15 @ SV233 @ SV417 @ SV596 ) ) @ SV417 )
= $true )
| ( ( in @ SV417 @ ( funcSet @ SV15 @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2203,plain,
! [SV418: $i,SV234: $i,SV16: $i,SV597: $i] :
( ( ( in @ SV597 @ SV16 )
= $false )
| ( ( in @ ( kpair @ SV597 @ ( ap @ SV16 @ SV234 @ SV418 @ SV597 ) ) @ SV418 )
= $true )
| ( ( func @ SV16 @ SV234 @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2204,plain,
! [SV558: $i,SV235: $i > $o,SV17: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ SV17 )
| ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SV653 )
| ( SV558 = SV653 ) )
= $true )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2205,plain,
! [SV420: $i,SV237: $i,SV19: $i,SV598: $i] :
( ( ( in @ SV598 @ SV19 )
= $false )
| ( ( in @ ( ap @ SV19 @ SV237 @ SV420 @ SV598 ) @ SV237 )
= $true )
| ( ( in @ SV420 @ ( funcSet @ SV19 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2206,plain,
! [SV422: $i,SV239: $i,SV21: $i,SV599: $i] :
( ( ( in @ SV599 @ SV21 )
= $false )
| ( ( in @ ( ap @ SV21 @ SV239 @ SV422 @ SV599 ) @ SV239 )
= $true )
| ( ( func @ SV21 @ SV239 @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2207,plain,
! [SV423: $i,SV240: $i,SV22: $i,SV600: $i] :
( ( ( in @ SV600 @ SV22 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV240
@ ^ [SY2617: $i] : ( in @ ( kpair @ SV600 @ SY2617 ) @ SV423 ) ) )
@ SV240 )
= $true )
| ( ( func @ SV22 @ SV240 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2208,plain,
! [SV424: $i,SV241: $i,SV23: $i,SV601: $i] :
( ( ( in @ SV601 @ SV23 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV241
@ ^ [SY2618: $i] : ( in @ ( kpair @ SV601 @ SY2618 ) @ SV424 ) ) )
= $true )
| ( ( func @ SV23 @ SV241 @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2209,plain,
! [SV428: $i > $i > $o,SV27: $i,SV537: $i,SV245: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV245 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV537 @ SV642 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SV642 ) )
= $true )
| ( ( in @ SV537 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2210,plain,
! [SV30: $i,SV538: $i,SV431: $i > $i > $o,SV248: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV248 ) )
= $true )
| ( ( ~ ( SV431 @ SV538 @ SV643 )
| ( in @ ( kpair @ SV538 @ SV643 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) )
= $true )
| ( ( in @ SV538 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2211,plain,
! [SV32: $i,SV433: $i,SV250: $i,SV603: $i] :
( ( ( in @ SV603 @ SV250 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV433 @ SV603 ) )
= SV603 )
= $true )
| ( ( in @ SV433 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2212,plain,
! [SV33: $i,SV434: $i,SV251: $i,SV604: $i] :
( ( ( in @ SV604 @ SV251 )
= $false )
| ( ( ( kfst @ ( kpair @ SV434 @ SV604 ) )
= SV434 )
= $true )
| ( ( in @ SV434 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2213,plain,
! [SV34: $i,SV435: $i,SV605: $i,SV644: $i] :
( ( ( in @ SV644 @ SV605 )
= $false )
| ( $true = $true )
| ( ( in @ SV435 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2214,plain,
! [SV44: $i,SV259: $i,SV543: $i,SV441: $i] :
( ( ( SV441 = SV543 )
= $false )
| ( ( SV259 = SV543 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV44 @ ( setadjoin @ SV259 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV441 @ ( setadjoin @ SV543 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2215,plain,
! [SV59: $i,SV447: $i,SV269: $i,SV606: $i] :
( ( ( in @ SV606 @ SV269 )
= $false )
| ( ( in @ ( kpair @ SV447 @ SV606 ) @ ( cartprod @ SV59 @ SV269 ) )
= $true )
| ( ( in @ SV447 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2216,plain,
! [SV60: $i,SV448: $i,SV270: $i,SV607: $i] :
( ( ( in @ SV607 @ SV270 )
= $false )
| ( ( in @ ( kpair @ SV448 @ SV607 ) @ ( powerset @ ( powerset @ ( binunion @ SV60 @ SV270 ) ) ) )
= $true )
| ( ( in @ SV448 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2217,plain,
! [SV61: $i,SV449: $i,SV271: $i,SV608: $i] :
( ( ( in @ SV608 @ SV271 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV449 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV449 @ ( setadjoin @ SV608 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV61 @ SV271 ) ) ) )
= $true )
| ( ( in @ SV449 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2218,plain,
! [SV62: $i,SV450: $i,SV272: $i,SV609: $i] :
( ( ( in @ SV609 @ SV272 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV450 @ ( setadjoin @ SV609 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV62 @ SV272 ) ) )
= $true )
| ( ( in @ SV450 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2219,plain,
! [SV63: $i,SV451: $i,SV273: $i,SV610: $i] :
( ( ( in @ SV610 @ SV273 )
= $false )
| ( ( in @ ( setadjoin @ SV451 @ ( setadjoin @ SV610 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV273 ) ) )
= $true )
| ( ( in @ SV451 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2220,plain,
! [SV64: $i,SV452: $i,SV274: $i,SV611: $i] :
( ( ( in @ SV611 @ SV274 )
= $false )
| ( ( subset @ ( setadjoin @ SV452 @ ( setadjoin @ SV611 @ emptyset ) ) @ ( binunion @ SV64 @ SV274 ) )
= $true )
| ( ( in @ SV452 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2221,plain,
! [SV285: $i,SV75: $i,SV456: $i] :
( ( ( in @ SV456 @ ( symdiff @ SV75 @ SV285 ) )
= $false )
| ( ( in @ SV456 @ SV285 )
= $false )
| ( ( in @ SV456 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2222,plain,
! [SV334: $i,SV128: $i,SV612: $i,SV567: $i] :
( ( ( SV567 = SV612 )
= $false )
| ( ( ( setadjoin @ SV128 @ SV567 )
= ( setadjoin @ SV334 @ SV612 ) )
= $true )
| ( ( SV128 = SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2223,plain,
! [SV335: $i,SV129: $i,SV613: $i,SV568: $i] :
( ( ( SV568 = SV613 )
= $false )
| ( ( ~ ( in @ SV568 @ SV129 )
| ( in @ SV613 @ SV335 ) )
= $true )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2224,plain,
! [SV544: $i,SV337: $i > $o,SV133: $i] :
( ( ( ( dsetconstr @ SV133
@ ^ [SY2314: $i] : ( SV337 @ SY2314 ) )
= emptyset )
= $false )
| ( ( SV337 @ SV544 )
= $false )
| ( ( in @ SV544 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2225,plain,
! [SV482: $i,SV351: $i > $o,SV152: $i] :
( ( ( ( dsetconstr @ SV152
@ ^ [SY2321: $i] : ( SV351 @ SY2321 ) )
= emptyset )
= $false )
| ( ( SV351 @ SV482 )
= $false )
| ( ( in @ SV482 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2226,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( SV164 @ SV489 )
= $false )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2227,plain,
! [SV164: $i > $o,SV489: $i] :
( ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( ~ ( SV164 @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2228,plain,
! [SV356: $i,SV165: $i,SV654: $i] :
( ( ( ! [SY2649: $i] :
( ( SV654 != SY2649 )
| ~ ( in @ SV654 @ SV165 )
| ( in @ SY2649 @ SV356 ) ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2229,plain,
! [SV165: $i,SV356: $i,SV655: $i] :
( ( ( ! [SY2650: $i] :
( ( SV655 != SY2650 )
| ~ ( in @ SY2650 @ SV356 )
| ( in @ SV655 @ SV165 ) ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2230,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i] :
( ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) )
| ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2231,plain,
! [SV167: $i,SV358: $i,SV491: $i > $i] :
( ( ( in @ ( SV491 @ ( sK76_Xx @ SV491 @ SV358 @ SV167 ) ) @ SV358 )
= $false )
| ( ( in
@ ( lam @ SV167 @ SV358
@ ^ [SY2502: $i] : ( SV491 @ SY2502 ) )
@ ( funcSet @ SV167 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2232,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2233,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2234,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( SV169 @ SV493 )
= $false )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2235,plain,
! [SV169: $i > $o,SV493: $i] :
( ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( ~ ( SV169 @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2236,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
| ~ ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) )
= $false )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2237,plain,
! [SV170: $i,SV656: $i] :
( ( ! [SY2651: $i] :
( ~ ( in @ SV656 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SY2651 @ ( sK13_B @ SV170 ) )
| ! [SY2652: $i] :
( ~ ( in @ SY2652 @ SV656 )
| ( in @ SY2652 @ SY2651 ) )
| ! [SY2653: $i] :
( ~ ( in @ SY2653 @ SY2651 )
| ( in @ SY2653 @ SV656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2238,plain,
! [SV170: $i] :
( ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) )
| ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2239,plain,
! [SV494: $i,SV360: $i,SV171: $i,SV615: $i] :
( ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) )
| ( SV494 = SV615 ) )
= $true )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2240,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( ~ ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 ) )
= $false )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2241,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( ~ ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) )
= $false )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2086]) ).
thf(2242,plain,
! [SV571: $i,SV174: $i,SV616: $i] :
( ( ( in @ SV616 @ ( setadjoin @ SV174 @ SV571 ) )
= $false )
| ( ( ( SV616 = SV174 )
| ( in @ SV616 @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2243,plain,
! [SV657: $i,SV174: $i] :
( ( ! [SY2654: $i] :
( ( SY2654 != SV174 )
| ( in @ SY2654 @ ( setadjoin @ SV174 @ SV657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2244,plain,
! [SV174: $i,SV658: $i] :
( ( ! [SY2655: $i] :
( ~ ( in @ SY2655 @ SV658 )
| ( in @ SY2655 @ ( setadjoin @ SV174 @ SV658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2245,plain,
! [SV495: $i,SV364: $i,SV176: $i,SV617: $i] :
( ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
| ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2246,plain,
! [SV177: $i,SV365: $i,SV496: $i > $i] :
( ( ( in @ ( SV496 @ ( sK74_Xx @ SV496 @ SV365 @ SV177 ) ) @ SV365 )
= $false )
| ( ( func @ SV177 @ SV365
@ ( dpsetconstr @ SV177 @ SV365
@ ^ [SY2514: $i,SY2515: $i] :
( ( SV496 @ SY2514 )
= SY2515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2247,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV659 )
= ( SV497 @ SV659 ) ) )
= $true )
| ( ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2248,plain,
! [SV178: $i,SV366: $i,SV497: $i > $i] :
( ( ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 )
= $false )
| ( ( ! [SY2516: $i] :
( ~ ( in @ SY2516 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SY2516 )
= ( SV497 @ SY2516 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2249,plain,
! [SV179: $i,SV660: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV660 )
| ~ ( in @ SV660 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2250,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2251,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2252,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( ~ ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 ) )
= $false )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2253,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( ~ ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) )
= $false )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2099]) ).
thf(2254,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2255,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) ) )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2256,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( SV184 @ SV498 )
= $false )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2257,plain,
! [SV184: $i > $o,SV498: $i] :
( ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( ~ ( SV184 @ SV498 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2258,plain,
! [SV372: $i > $o,SV185: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV185 ) )
= $true )
| ( ( ~ ( SV372 @ SV645 ) )
= $true )
| ( ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2259,plain,
! [SV372: $i > $o,SV185: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV185 ) )
= $true )
| ( ( ~ ( SV372 @ SV646 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2260,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ~ ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) ) )
= $true )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2261,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( in @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2262,plain,
! [SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2263,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2111]) ).
thf(2264,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
| ~ ( ( SV647
!= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2265,plain,
! [SV375: $i > $o,SV188: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV188 ) )
= $true )
| ( ( ~ ( SV375 @ SV648 ) )
= $true )
| ( ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2266,plain,
! [SV375: $i > $o,SV188: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ SV188 ) )
= $true )
| ( ( ~ ( SV375 @ SV649 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2267,plain,
! [SV377: $i,SV190: $i] :
( ( ! [SY2370: $i] :
( ~ ( in @ SY2370 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2370 @ SV190 )
| ( in @ SY2370 @ SV377 )
| ! [SX3: $o] : SX3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2268,plain,
! [SV377: $i,SV190: $i] :
( ( ! [SY2372: $i] :
( ~ ( in @ SY2372 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SY2372 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2269,plain,
! [SV377: $i,SV190: $i] :
( ( ! [SY2374: $i] :
( ~ ( in @ SY2374 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2375: $o] :
( ~ SY2375
| ( in @ SY2374 @ SV377 )
| SY2375 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2118]) ).
thf(2270,plain,
! [SV377: $i,SV190: $i] :
( ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2271,plain,
! [SV500: $i,SV618: $i,SV378: $i,SV191: $i] :
( ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) )
| ( SV500 = SV618 ) )
= $true )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2272,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( ~ ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 ) )
= $false )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2273,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( ~ ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) )
= $false )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2274,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2275,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2123]) ).
thf(2276,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( SV194 @ SV502 )
= $false )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2277,plain,
! [SV194: $i > $o,SV502: $i] :
( ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( ~ ( SV194 @ SV502 ) )
= $true )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2278,plain,
! [SV503: $i,SV380: $o,SV195: $i,SV619: $i] :
( ( ( in @ SV619 @ SV195 )
= $false )
| ( ( SV380
| ( in @ SV619
@ ( dsetconstr @ SV195
@ ^ [SY2624: $i] :
( ~ ( ~ SV380
| ( SY2624 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2624 != SV619 ) ) ) ) ) )
= $true )
| ( ( in @ SV503 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2279,plain,
! [SV504: $i,SV195: $i,SV620: $i] :
( ( ( in @ SV620 @ SV195 )
= $false )
| ( ( $true
| ( in @ SV620
@ ( dsetconstr @ SV195
@ ^ [SY2625: $i] :
( ~ ( ~ $true
| ( SY2625 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2625 != SV620 ) ) ) ) ) )
= $true )
| ( ( in @ SV504 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2280,plain,
! [SV505: $i,SV195: $i,SV621: $i] :
( ( ( in @ SV621 @ SV195 )
= $false )
| ( ( $false
| ( in @ SV621
@ ( dsetconstr @ SV195
@ ^ [SY2626: $i] :
( ~ ( ~ $false
| ( SY2626 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2626 != SV621 ) ) ) ) ) )
= $true )
| ( ( in @ SV505 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2281,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( in @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV196 )
| ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2282,plain,
! [SV506: $i,SV382: $o,SV197: $i,SV623: $i] :
( ( ( in @ SV623 @ SV197 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2629: $i] :
( ~ ( ~ SV382
| ( SY2629 != SV506 ) )
| ~ ( ~ ~ SV382
| ( SY2629 != SV623 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2283,plain,
! [SV507: $i,SV197: $i,SV624: $i] :
( ( ( in @ SV624 @ SV197 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2630: $i] :
( ~ ( ~ $true
| ( SY2630 != SV507 ) )
| ~ ( ~ ~ $true
| ( SY2630 != SV624 ) ) ) ) )
= $true )
| ( ( in @ SV507 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2284,plain,
! [SV508: $i,SV197: $i,SV625: $i] :
( ( ( in @ SV625 @ SV197 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV197
@ ^ [SY2631: $i] :
( ~ ( ~ $false
| ( SY2631 != SV508 ) )
| ~ ( ~ ~ $false
| ( SY2631 != SV625 ) ) ) ) )
= $true )
| ( ( in @ SV508 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2285,plain,
! [SV198: $i,SV509: $i,SV549: $i > $i] :
( ( ( in @ ( SV549 @ ( sK91_Xx @ SV549 @ SV509 @ SV198 ) ) @ SV509 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2286,plain,
! [SV550: $i,SV573: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV573 ) )
= $false )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2287,plain,
! [SV550: $i,SV573: $i] :
( ( ( ~ ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 ) )
= $false )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2288,plain,
! [SV551: $i,SV574: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV574 )
| ( in @ SV661 @ SV551 ) )
= $true )
| ( ( in @ SV574 @ ( powerset @ SV551 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2289,plain,
! [SV510: $i,SV383: $o,SV199: $i,SV626: $i] :
( ( ( in @ SV626 @ SV199 )
= $false )
| ( ( ~ SV383
| ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2632: $i] :
( ~ ( ~ SV383
| ( SY2632 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2632 != SV626 ) ) ) ) ) )
= $true )
| ( ( in @ SV510 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2290,plain,
! [SV511: $i,SV199: $i,SV627: $i] :
( ( ( in @ SV627 @ SV199 )
= $false )
| ( ( ~ $true
| ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2633: $i] :
( ~ ( ~ $true
| ( SY2633 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2633 != SV627 ) ) ) ) ) )
= $true )
| ( ( in @ SV511 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2291,plain,
! [SV512: $i,SV199: $i,SV628: $i] :
( ( ( in @ SV628 @ SV199 )
= $false )
| ( ( ~ $false
| ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2634: $i] :
( ~ ( ~ $false
| ( SY2634 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2634 != SV628 ) ) ) ) ) )
= $true )
| ( ( in @ SV512 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2292,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2293,plain,
! [SV201: $i,SV385: $i,SV514: $i > $i] :
( ( ( in @ ( SV514 @ ( sK75_Xx @ SV514 @ SV385 @ SV201 ) ) @ SV385 )
= $false )
| ( ( func @ SV201 @ SV385
@ ( lam @ SV201 @ SV385
@ ^ [SY2539: $i] : ( SV514 @ SY2539 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2294,plain,
! [SV202: $i,SV386: $i] :
( ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
= $false )
| ( ( ~ ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 ) )
= $true )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2295,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( SV203 @ SV515 )
= $false )
| ( ( SV203 @ ( sK22_SY84 @ SV515 @ SV203 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2296,plain,
! [SV203: $i > $o,SV515: $i] :
( ( ( SV515
= ( sK22_SY84 @ SV515 @ SV203 ) )
= $false )
| ( ( ~ ( SV203 @ SV515 ) )
= $true )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2297,plain,
! [SV204: $i,SV662: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV662 )
| ~ ( in @ SV662 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2298,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2148]) ).
thf(2299,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2148]) ).
thf(2300,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV663 )
= ( SV516 @ SV663 ) ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2301,plain,
! [SV205: $i,SV388: $i,SV516: $i > $i] :
( ( ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 )
= $false )
| ( ( ! [SY2540: $i] :
( ~ ( in @ SY2540 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SY2540 )
= ( SV516 @ SY2540 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2302,plain,
! [SV517: $i,SV389: $i,SV206: $i,SV629: $i] :
( ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
| ( subset @ SV517 @ SV629 ) )
= $true )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2303,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( SV207 @ SV518 )
= $false )
| ( ( SV207 @ ( sK18_SY55 @ SV518 @ SV207 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2304,plain,
! [SV207: $i > $o,SV518: $i] :
( ( ( SV518
= ( sK18_SY55 @ SV518 @ SV207 ) )
= $false )
| ( ( ~ ( SV207 @ SV518 ) )
= $true )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2305,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
| ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2306,plain,
! [SV520: $i,SV209: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ ( sK12_B @ SV209 ) )
| ~ ( in @ SV664 @ SV209 ) )
= $true )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2307,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ( ( sK53_Xx @ SV575 @ SV552 )
!= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2308,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2309,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ( sK49_Xx @ SV576 @ SV553 )
!= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2310,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2311,plain,
! [SV210: $i,SV650: $i,SV391: $i > $o] :
( ( ( ~ ( SV391 @ SV650 ) )
= $true )
| ( ( ~ ( in @ SV650 @ SV210 ) )
= $true )
| ( ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2312,plain,
! [SV210: $i,SV651: $i,SV391: $i > $o] :
( ( ( ~ ( SV391 @ SV651 ) )
= $true )
| ( ( ~ ( in @ SV651 @ SV210 ) )
= $true )
| ( ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2313,plain,
! [SV211: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV211 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2314,plain,
! [SV211: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV211 ) @ SV211 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2315,plain,
! [SV211: $i] :
( ( ( in @ emptyset @ SV211 )
= $false )
| ( ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 )
= $false )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2316,plain,
! [SV212: $i > $o,SV521: $i] :
( ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( ~ ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2317,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2318,plain,
! [SV522: $i,SV392: $o,SV213: $i,SV631: $i] :
( ( ( in @ SV631 @ SV213 )
= $false )
| ( ( SV392
| ( ( dsetconstr @ SV213
@ ^ [SY2636: $i] :
( ~ ( ~ SV392
| ( SY2636 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2636 != SV631 ) ) ) )
= ( setadjoin @ SV631 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2319,plain,
! [SV523: $i,SV213: $i,SV632: $i] :
( ( ( in @ SV632 @ SV213 )
= $false )
| ( ( $true
| ( ( dsetconstr @ SV213
@ ^ [SY2637: $i] :
( ~ ( ~ $true
| ( SY2637 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2637 != SV632 ) ) ) )
= ( setadjoin @ SV632 @ emptyset ) ) )
= $true )
| ( ( in @ SV523 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2320,plain,
! [SV524: $i,SV213: $i,SV633: $i] :
( ( ( in @ SV633 @ SV213 )
= $false )
| ( ( $false
| ( ( dsetconstr @ SV213
@ ^ [SY2638: $i] :
( ~ ( ~ $false
| ( SY2638 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2638 != SV633 ) ) ) )
= ( setadjoin @ SV633 @ emptyset ) ) )
= $true )
| ( ( in @ SV524 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2321,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( SV214 @ SV525 )
= $false )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2322,plain,
! [SV214: $i > $o,SV525: $i] :
( ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( ~ ( SV214 @ SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2323,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
| ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2324,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2172]) ).
thf(2325,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2173]) ).
thf(2326,plain,
! [SV577: $i > $o,SV218: $i,SV635: $i] :
( ( ( in @ SV635 @ SV218 )
= $false )
| ( ( ~ ( SV577 @ SV635 )
| ( in @ SV635
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2327,plain,
! [SV578: $i > $o,SV218: $i,SV636: $i] :
( ( ( in @ SV636 @ SV218 )
= $false )
| ( ( ~ ( in @ SV636
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) )
| ( SV578 @ SV636 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2328,plain,
! [SV219: $i,SV579: $o,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ SV579 @ SV396 @ SV219 ) ) )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2329,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 ) )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2330,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ $true @ SV396 @ SV219 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2331,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2332,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( sK29_B @ $false @ SV396 @ SV219 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2333,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2334,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
| ~ ( ( SV665
!= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2335,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2336,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2337,plain,
! [SV528: $i,SV398: $o,SV221: $i,SV637: $i] :
( ( ( in @ SV637 @ SV221 )
= $false )
| ( ( ~ SV398
| ( ( dsetconstr @ SV221
@ ^ [SY2642: $i] :
( ~ ( ~ SV398
| ( SY2642 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2642 != SV637 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) ) )
= $true )
| ( ( in @ SV528 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2338,plain,
! [SV529: $i,SV221: $i,SV638: $i] :
( ( ( in @ SV638 @ SV221 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV221
@ ^ [SY2643: $i] :
( ~ ( ~ $true
| ( SY2643 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2643 != SV638 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) ) )
= $true )
| ( ( in @ SV529 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2339,plain,
! [SV530: $i,SV221: $i,SV639: $i] :
( ( ( in @ SV639 @ SV221 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV221
@ ^ [SY2644: $i] :
( ~ ( ~ $false
| ( SY2644 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2644 != SV639 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) ) )
= $true )
| ( ( in @ SV530 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2340,plain,
! [SV554: $i,SV652: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ SV652 ) )
= $true )
| ( ( ~ ( in @ SV652 @ SV554 ) )
= $true )
| ( ( in @ SV580 @ ( setunion @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2341,plain,
! [SV555: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) )
| ~ ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 ) )
= $false )
| ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2342,plain,
! [SV585: $i,SV402: $i,SV5: $i,SV226: $o] :
( ( SV226 = $true )
| ( ( ( if @ SV5 @ SV226 @ SV402 @ SV585 )
= SV585 )
= $true )
| ( ( in @ SV585 @ SV5 )
= $false )
| ( ( in @ SV402 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2343,plain,
! [SV586: $i,SV403: $i,SV5: $i] :
( ( $true = $true )
| ( ( ( if @ SV5 @ $true @ SV403 @ SV586 )
= SV586 )
= $true )
| ( ( in @ SV586 @ SV5 )
= $false )
| ( ( in @ SV403 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2344,plain,
! [SV587: $i,SV404: $i,SV5: $i] :
( ( $false = $true )
| ( ( ( if @ SV5 @ $false @ SV404 @ SV587 )
= SV587 )
= $true )
| ( ( in @ SV587 @ SV5 )
= $false )
| ( ( in @ SV404 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2345,plain,
! [SV588: $i,SV405: $i,SV6: $i,SV227: $o] :
( ( ( ~ SV227 ) = $true )
| ( ( ( if @ SV6 @ SV227 @ SV405 @ SV588 )
= SV405 )
= $true )
| ( ( in @ SV588 @ SV6 )
= $false )
| ( ( in @ SV405 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2346,plain,
! [SV589: $i,SV406: $i,SV6: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV6 @ $true @ SV406 @ SV589 )
= SV406 )
= $true )
| ( ( in @ SV589 @ SV6 )
= $false )
| ( ( in @ SV406 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2347,plain,
! [SV590: $i,SV407: $i,SV6: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV6 @ $false @ SV407 @ SV590 )
= SV407 )
= $true )
| ( ( in @ SV590 @ SV6 )
= $false )
| ( ( in @ SV407 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2348,plain,
! [SV13: $i,SV415: $i,SV594: $i,SV231: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV231 )
| ~ ( in @ ( kpair @ SV594 @ SV666 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SV666 ) )
= $true )
| ( ( in @ SV594 @ SV13 )
= $false )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2349,plain,
! [SV14: $i,SV416: $i,SV595: $i,SV232: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV232 )
| ~ ( in @ ( kpair @ SV595 @ SV667 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SV667 ) )
= $true )
| ( ( in @ SV595 @ SV14 )
= $false )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2350,plain,
! [SV558: $i,SV235: $i > $o,SV17: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ SV17 ) )
= $true )
| ( ( ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SV653 )
| ( SV558 = SV653 ) )
= $true )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2351,plain,
! [SV428: $i > $i > $o,SV27: $i,SV537: $i,SV245: $i,SV642: $i] :
( ( ( in @ SV642 @ SV245 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV537 @ SV642 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
| ( SV428 @ SV537 @ SV642 ) )
= $true )
| ( ( in @ SV537 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2352,plain,
! [SV30: $i,SV538: $i,SV431: $i > $i > $o,SV248: $i,SV643: $i] :
( ( ( in @ SV643 @ SV248 )
= $false )
| ( ( ~ ( SV431 @ SV538 @ SV643 )
| ( in @ ( kpair @ SV538 @ SV643 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) ) )
= $true )
| ( ( in @ SV538 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2353,plain,
! [SV335: $i,SV613: $i,SV129: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ SV129 ) )
= $true )
| ( ( in @ SV613 @ SV335 )
= $true )
| ( ( SV568 = SV613 )
= $false )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2354,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) )
= $false )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2355,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( SV164 @ SV489 )
= $false )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( ~ ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2356,plain,
! [SV356: $i,SV165: $i,SV668: $i,SV654: $i] :
( ( ( ( SV654 != SV668 )
| ~ ( in @ SV654 @ SV165 )
| ( in @ SV668 @ SV356 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2357,plain,
! [SV165: $i,SV356: $i,SV669: $i,SV655: $i] :
( ( ( ( SV655 != SV669 )
| ~ ( in @ SV669 @ SV356 )
| ( in @ SV655 @ SV165 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2358,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) ) )
= $true )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2359,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2360,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2361,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) )
= $false )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2362,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( SV169 @ SV493 )
= $false )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( ~ ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2363,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 ) )
= $false )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2236]) ).
thf(2364,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) )
= $false )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2236]) ).
thf(2365,plain,
! [SV670: $i,SV170: $i,SV656: $i] :
( ( ~ ( in @ SV656 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SV670 @ ( sK13_B @ SV170 ) )
| ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) )
| ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2366,plain,
! [SV170: $i] :
( ( ~ ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2238]) ).
thf(2367,plain,
! [SV170: $i] :
( ( ~ ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2238]) ).
thf(2368,plain,
! [SV171: $i,SV360: $i,SV494: $i,SV615: $i] :
( ( ( ~ ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) ) )
= $true )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2369,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( in @ ( sK33_Xx @ SV362 @ SV173 ) @ SV173 )
= $true )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2370,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) ) )
= $true )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2371,plain,
! [SV571: $i,SV174: $i,SV616: $i] :
( ( ( SV616 = SV174 )
= $true )
| ( ( in @ SV616 @ SV571 )
= $true )
| ( ( in @ SV616 @ ( setadjoin @ SV174 @ SV571 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2372,plain,
! [SV657: $i,SV174: $i,SV671: $i] :
( ( ( SV671 != SV174 )
| ( in @ SV671 @ ( setadjoin @ SV174 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2373,plain,
! [SV174: $i,SV658: $i,SV672: $i] :
( ( ~ ( in @ SV672 @ SV658 )
| ( in @ SV672 @ ( setadjoin @ SV174 @ SV658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2374,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2375,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV178 ) )
= $true )
| ( ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV659 )
= ( SV497 @ SV659 ) )
= $true )
| ( ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2376,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV178 )
| ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV673 )
= ( SV497 @ SV673 ) ) )
= $true )
| ( ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2377,plain,
! [SV179: $i,SV660: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV660 ) )
= $true )
| ( ( ~ ( in @ SV660 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2378,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2379,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2380,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( in @ ( sK38_Xx @ SV368 @ SV180 ) @ SV180 )
= $true )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2381,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( ~ ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) ) )
= $true )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2382,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2383,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2384,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
| ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2385,plain,
! [SV498: $i,SV674: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV674 )
| ! [SY2661: $i] :
( ~ ( SV184 @ SY2661 )
| ( SV674 = SY2661 ) ) )
= $true )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2386,plain,
! [SV498: $i,SV184: $i > $o] :
( ( ( SV184 @ SV498 )
= $false )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( ! [SY2056: $i] :
( ~ ( SV184 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV184 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2387,plain,
! [SV372: $i > $o,SV185: $i,SV645: $i] :
( ( ( in @ SV645 @ SV185 )
= $false )
| ( ( ~ ( SV372 @ SV645 ) )
= $true )
| ( ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2388,plain,
! [SV372: $i > $o,SV185: $i,SV646: $i] :
( ( ( in @ SV646 @ SV185 )
= $false )
| ( ( ~ ( SV372 @ SV646 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2389,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
| ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2390,plain,
! [SV374: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2391,plain,
! [SV187: $i > $i > $o,SV374: $i] :
( ( ( ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2263]) ).
thf(2392,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
| ~ ( ( SV647
!= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2393,plain,
! [SV375: $i > $o,SV188: $i,SV648: $i] :
( ( ( in @ SV648 @ SV188 )
= $false )
| ( ( ~ ( SV375 @ SV648 ) )
= $true )
| ( ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2394,plain,
! [SV375: $i > $o,SV188: $i,SV649: $i] :
( ( ( in @ SV649 @ SV188 )
= $false )
| ( ( ~ ( SV375 @ SV649 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2395,plain,
! [SV377: $i,SV190: $i,SV675: $i] :
( ( ~ ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SV675 @ SV190 )
| ( in @ SV675 @ SV377 )
| ! [SX3: $o] : SX3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2396,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ~ ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
| ( in @ SV676 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2397,plain,
! [SV377: $i,SV190: $i,SV677: $i] :
( ( ~ ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
| ! [SY2664: $o] :
( ~ SY2664
| ( in @ SV677 @ SV377 )
| SY2664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2398,plain,
! [SV377: $i,SV190: $i] :
( ( ( ! [SY2376: $i] :
~ ( in @ SY2376 @ ( binunion @ SV190 @ SV377 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2399,plain,
! [SV191: $i,SV378: $i,SV500: $i,SV618: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) ) )
= $true )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2400,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( in @ ( sK36_Xx @ SV379 @ SV192 ) @ SV192 )
= $true )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2401,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( ~ ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) ) )
= $true )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2273]) ).
thf(2402,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2403,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) )
| ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2404,plain,
! [SV502: $i,SV678: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV678 )
| ! [SY2665: $i] :
( ~ ( SV194 @ SY2665 )
| ( SV678 = SY2665 ) ) )
= $true )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2405,plain,
! [SV502: $i,SV194: $i > $o] :
( ( ( SV194 @ SV502 )
= $false )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( ! [SY2087: $i] :
( ~ ( SV194 @ SY2087 )
| ! [SY2088: $i] :
( ~ ( SV194 @ SY2088 )
| ( SY2087 = SY2088 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2406,plain,
! [SV503: $i,SV195: $i,SV619: $i,SV380: $o] :
( ( SV380 = $true )
| ( ( in @ SV619
@ ( dsetconstr @ SV195
@ ^ [SY2624: $i] :
( ~ ( ~ SV380
| ( SY2624 != SV503 ) )
| ~ ( ~ ~ SV380
| ( SY2624 != SV619 ) ) ) ) )
= $true )
| ( ( in @ SV619 @ SV195 )
= $false )
| ( ( in @ SV503 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2407,plain,
! [SV504: $i,SV195: $i,SV620: $i] :
( ( $true = $true )
| ( ( in @ SV620
@ ( dsetconstr @ SV195
@ ^ [SY2625: $i] :
( ~ ( ~ $true
| ( SY2625 != SV504 ) )
| ~ ( ~ ~ $true
| ( SY2625 != SV620 ) ) ) ) )
= $true )
| ( ( in @ SV620 @ SV195 )
= $false )
| ( ( in @ SV504 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2408,plain,
! [SV505: $i,SV195: $i,SV621: $i] :
( ( $false = $true )
| ( ( in @ SV621
@ ( dsetconstr @ SV195
@ ^ [SY2626: $i] :
( ~ ( ~ $false
| ( SY2626 != SV505 ) )
| ~ ( ~ ~ $false
| ( SY2626 != SV621 ) ) ) ) )
= $true )
| ( ( in @ SV621 @ SV195 )
= $false )
| ( ( in @ SV505 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2409,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( in @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV196 ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2410,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2411,plain,
! [SV550: $i,SV573: $i] :
( ( ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV573 )
= $true )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2286]) ).
thf(2412,plain,
! [SV550: $i,SV573: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 ) )
= $true )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2413,plain,
! [SV551: $i,SV574: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ SV574 ) )
= $true )
| ( ( in @ SV661 @ SV551 )
= $true )
| ( ( in @ SV574 @ ( powerset @ SV551 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2414,plain,
! [SV626: $i,SV199: $i,SV510: $i,SV383: $o] :
( ( ( ~ SV383 ) = $true )
| ( ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2632: $i] :
( ~ ( ~ SV383
| ( SY2632 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2632 != SV626 ) ) ) ) )
= $true )
| ( ( in @ SV626 @ SV199 )
= $false )
| ( ( in @ SV510 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2415,plain,
! [SV627: $i,SV199: $i,SV511: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2633: $i] :
( ~ ( ~ $true
| ( SY2633 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2633 != SV627 ) ) ) ) )
= $true )
| ( ( in @ SV627 @ SV199 )
= $false )
| ( ( in @ SV511 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2416,plain,
! [SV628: $i,SV199: $i,SV512: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2634: $i] :
( ~ ( ~ $false
| ( SY2634 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2634 != SV628 ) ) ) ) )
= $true )
| ( ( in @ SV628 @ SV199 )
= $false )
| ( ( in @ SV512 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2417,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
| ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2418,plain,
! [SV202: $i,SV386: $i] :
( ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV386 )
= $false )
| ( ( in @ ( sK4_Xx @ SV386 @ SV202 ) @ SV202 )
= $false )
| ( ( SV202 = SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2419,plain,
! [SV515: $i,SV203: $i > $o] :
( ( ( SV203 @ SV515 )
= $false )
| ( ( SV515
= ( sK22_SY84 @ SV515 @ SV203 ) )
= $false )
| ( ( SV203 @ ( sK21_Xx @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2420,plain,
! [SV204: $i,SV662: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV662 ) )
= $true )
| ( ( ~ ( in @ SV662 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2421,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2298]) ).
thf(2422,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2299]) ).
thf(2423,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV205 ) )
= $true )
| ( ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV663 )
= ( SV516 @ SV663 ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2424,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV205 )
| ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV679 )
= ( SV516 @ SV679 ) ) )
= $true )
| ( ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2425,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) ) )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2426,plain,
! [SV518: $i,SV207: $i > $o] :
( ( ( SV207 @ SV518 )
= $false )
| ( ( SV518
= ( sK18_SY55 @ SV518 @ SV207 ) )
= $false )
| ( ( SV207
@ ( descr
@ ^ [SY2127: $i] : ( SV207 @ SY2127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2427,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2428,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2429,plain,
! [SV520: $i,SV209: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ ( sK12_B @ SV209 ) ) )
= $true )
| ( ( ~ ( in @ SV664 @ SV209 ) )
= $true )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2430,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2431,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2432,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2433,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2434,plain,
! [SV210: $i,SV650: $i,SV391: $i > $o] :
( ( ( SV391 @ SV650 )
= $false )
| ( ( ~ ( in @ SV650 @ SV210 ) )
= $true )
| ( ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2435,plain,
! [SV210: $i,SV651: $i,SV391: $i > $o] :
( ( ( SV391 @ SV651 )
= $false )
| ( ( ~ ( in @ SV651 @ SV210 ) )
= $true )
| ( ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2436,plain,
! [SV211: $i] :
( ( ( in @ ( sK7_Xx @ SV211 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2313]) ).
thf(2437,plain,
! [SV211: $i] :
( ( ( in @ ( sK7_Xx @ SV211 ) @ SV211 )
= $true )
| ( ( ~ ( in @ emptyset @ SV211 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2314]) ).
thf(2438,plain,
! [SV211: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ omega )
| ( in @ SV680 @ SV211 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 )
= $false )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2439,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( ~ ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2440,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) ) )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2441,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2442,plain,
! [SV631: $i,SV522: $i,SV213: $i,SV392: $o] :
( ( SV392 = $true )
| ( ( ( dsetconstr @ SV213
@ ^ [SY2636: $i] :
( ~ ( ~ SV392
| ( SY2636 != SV522 ) )
| ~ ( ~ ~ SV392
| ( SY2636 != SV631 ) ) ) )
= ( setadjoin @ SV631 @ emptyset ) )
= $true )
| ( ( in @ SV631 @ SV213 )
= $false )
| ( ( in @ SV522 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2443,plain,
! [SV632: $i,SV523: $i,SV213: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV213
@ ^ [SY2637: $i] :
( ~ ( ~ $true
| ( SY2637 != SV523 ) )
| ~ ( ~ ~ $true
| ( SY2637 != SV632 ) ) ) )
= ( setadjoin @ SV632 @ emptyset ) )
= $true )
| ( ( in @ SV632 @ SV213 )
= $false )
| ( ( in @ SV523 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2444,plain,
! [SV633: $i,SV524: $i,SV213: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV213
@ ^ [SY2638: $i] :
( ~ ( ~ $false
| ( SY2638 != SV524 ) )
| ~ ( ~ ~ $false
| ( SY2638 != SV633 ) ) ) )
= ( setadjoin @ SV633 @ emptyset ) )
= $true )
| ( ( in @ SV633 @ SV213 )
= $false )
| ( ( in @ SV524 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2445,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $false )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2446,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( SV214 @ SV525 )
= $false )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( ~ ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2447,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2448,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2449,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2450,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2451,plain,
! [SV218: $i,SV635: $i,SV577: $i > $o] :
( ( ( ~ ( SV577 @ SV635 ) )
= $true )
| ( ( in @ SV635
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) )
= $true )
| ( ( in @ SV635 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2452,plain,
! [SV578: $i > $o,SV218: $i,SV636: $i] :
( ( ( ~ ( in @ SV636
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) ) )
= $true )
| ( ( SV578 @ SV636 )
= $true )
| ( ( in @ SV636 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2453,plain,
! [SV219: $i,SV579: $o,SV396: $i] :
( ( ( in @ SV396 @ ( sK29_B @ SV579 @ SV396 @ SV219 ) )
= $true )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2328]) ).
thf(2454,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 ) )
= $true )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2455,plain,
! [SV219: $i,SV396: $i] :
( ( ( in @ SV396 @ ( sK29_B @ $true @ SV396 @ SV219 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2456,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2331]) ).
thf(2457,plain,
! [SV219: $i,SV396: $i] :
( ( ( in @ SV396 @ ( sK29_B @ $false @ SV396 @ SV219 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2332]) ).
thf(2458,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2459,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
| ~ ( ( SV665
!= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2460,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2335]) ).
thf(2461,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
| ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2462,plain,
! [SV637: $i,SV528: $i,SV221: $i,SV398: $o] :
( ( ( ~ SV398 ) = $true )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2642: $i] :
( ~ ( ~ SV398
| ( SY2642 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2642 != SV637 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $true )
| ( ( in @ SV637 @ SV221 )
= $false )
| ( ( in @ SV528 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2463,plain,
! [SV638: $i,SV529: $i,SV221: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2643: $i] :
( ~ ( ~ $true
| ( SY2643 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2643 != SV638 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) )
= $true )
| ( ( in @ SV638 @ SV221 )
= $false )
| ( ( in @ SV529 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2464,plain,
! [SV639: $i,SV530: $i,SV221: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2644: $i] :
( ~ ( ~ $false
| ( SY2644 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2644 != SV639 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) )
= $true )
| ( ( in @ SV639 @ SV221 )
= $false )
| ( ( in @ SV530 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2465,plain,
! [SV554: $i,SV652: $i,SV580: $i] :
( ( ( in @ SV580 @ SV652 )
= $false )
| ( ( ~ ( in @ SV652 @ SV554 ) )
= $true )
| ( ( in @ SV580 @ ( setunion @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2466,plain,
! [SV555: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) ) )
= $false )
| ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2467,plain,
! [SV555: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 ) )
= $false )
| ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2468,plain,
! [SV588: $i,SV405: $i,SV6: $i,SV227: $o] :
( ( SV227 = $false )
| ( ( ( if @ SV6 @ SV227 @ SV405 @ SV588 )
= SV405 )
= $true )
| ( ( in @ SV588 @ SV6 )
= $false )
| ( ( in @ SV405 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2469,plain,
! [SV589: $i,SV406: $i,SV6: $i] :
( ( $true = $false )
| ( ( ( if @ SV6 @ $true @ SV406 @ SV589 )
= SV406 )
= $true )
| ( ( in @ SV589 @ SV6 )
= $false )
| ( ( in @ SV406 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2470,plain,
! [SV590: $i,SV407: $i,SV6: $i] :
( ( $false = $false )
| ( ( ( if @ SV6 @ $false @ SV407 @ SV590 )
= SV407 )
= $true )
| ( ( in @ SV590 @ SV6 )
= $false )
| ( ( in @ SV407 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2471,plain,
! [SV13: $i,SV415: $i,SV594: $i,SV231: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV231 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV594 @ SV666 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SV666 ) )
= $true )
| ( ( in @ SV594 @ SV13 )
= $false )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2472,plain,
! [SV14: $i,SV416: $i,SV595: $i,SV232: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV232 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV595 @ SV667 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SV667 ) )
= $true )
| ( ( in @ SV595 @ SV14 )
= $false )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2473,plain,
! [SV558: $i,SV235: $i > $o,SV17: $i,SV653: $i] :
( ( ( in @ SV653 @ SV17 )
= $false )
| ( ( ~ ( SV235 @ SV558 )
| ~ ( SV235 @ SV653 )
| ( SV558 = SV653 ) )
= $true )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2474,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i,SV642: $i,SV537: $i] :
( ( ( ~ ( in @ ( kpair @ SV537 @ SV642 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) ) )
= $true )
| ( ( SV428 @ SV537 @ SV642 )
= $true )
| ( ( in @ SV642 @ SV245 )
= $false )
| ( ( in @ SV537 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2475,plain,
! [SV248: $i,SV30: $i,SV643: $i,SV538: $i,SV431: $i > $i > $o] :
( ( ( ~ ( SV431 @ SV538 @ SV643 ) )
= $true )
| ( ( in @ ( kpair @ SV538 @ SV643 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) )
= $true )
| ( ( in @ SV643 @ SV248 )
= $false )
| ( ( in @ SV538 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2476,plain,
! [SV335: $i,SV613: $i,SV129: $i,SV568: $i] :
( ( ( in @ SV568 @ SV129 )
= $false )
| ( ( in @ SV613 @ SV335 )
= $true )
| ( ( SV568 = SV613 )
= $false )
| ( ( SV129 = SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2477,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) ) )
= $false )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2478,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) )
= $false )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2479,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) )
| ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) )
= $false )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2480,plain,
! [SV356: $i,SV165: $i,SV668: $i,SV654: $i] :
( ( ( SV654 != SV668 )
= $true )
| ( ( ~ ( in @ SV654 @ SV165 )
| ( in @ SV668 @ SV356 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2481,plain,
! [SV165: $i,SV356: $i,SV669: $i,SV655: $i] :
( ( ( SV655 != SV669 )
= $true )
| ( ( ~ ( in @ SV669 @ SV356 )
| ( in @ SV655 @ SV165 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2482,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i] :
( ( ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
| ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) )
= $false )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2483,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2484,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2485,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2486,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2487,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) ) )
= $false )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2488,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) )
= $false )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2489,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) )
| ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) )
= $false )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2490,plain,
! [SV170: $i,SV570: $i] :
( ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2491,plain,
! [SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 ) )
= $true )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2364]) ).
thf(2492,plain,
! [SV670: $i,SV170: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( sK13_B @ SV170 ) )
| ~ ( in @ SV670 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) )
| ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2493,plain,
! [SV170: $i] :
( ( ! [SY2018: $i] :
( ~ ( in @ SY2018 @ ( sK13_B @ SV170 ) )
| ! [SY2019: $i] :
( ~ ( in @ SY2019 @ SY2018 )
| ( in @ SY2019 @ SV170 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2494,plain,
! [SV170: $i] :
( ( ! [SY2020: $i,SY2021: $i] :
( ~ ( in @ SY2020 @ SV170 )
| ~ ( in @ SY2021 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ~ ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) )
| ~ ( ( in @ SY2020 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) )
| ( in @ SY2021 @ ( sK14_SY1650 @ SY2021 @ SY2020 @ SV170 ) ) ) ) )
| ( SY2020 = SY2021 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2367]) ).
thf(2495,plain,
! [SV171: $i,SV360: $i,SV494: $i,SV615: $i] :
( ( ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
| ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) )
= $false )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2496,plain,
! [SV546: $i,SV173: $i,SV362: $i > $o] :
( ( ( SV362 @ ( sK33_Xx @ SV362 @ SV173 ) )
= $false )
| ( ( SV362 @ SV546 )
= $true )
| ( ( in @ SV546 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2497,plain,
! [SV657: $i,SV174: $i,SV671: $i] :
( ( ( SV671 != SV174 )
= $true )
| ( ( in @ SV671 @ ( setadjoin @ SV174 @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2498,plain,
! [SV174: $i,SV658: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV658 ) )
= $true )
| ( ( in @ SV672 @ ( setadjoin @ SV174 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2499,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2500,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV659: $i] :
( ( ( in @ SV659 @ SV178 )
= $false )
| ( ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV659 )
= ( SV497 @ SV659 ) )
= $true )
| ( ( in @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2501,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV178 ) )
= $true )
| ( ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV673 )
= ( SV497 @ SV673 ) )
= $true )
| ( ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2502,plain,
! [SV179: $i,SV660: $i,SV367: $i > $o] :
( ( ( SV367 @ SV660 )
= $false )
| ( ( ~ ( in @ SV660 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2503,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2504,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
| ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2379]) ).
thf(2505,plain,
! [SV547: $i,SV180: $i,SV368: $i > $o] :
( ( ( SV368 @ ( sK38_Xx @ SV368 @ SV180 ) )
= $false )
| ( ( SV368 @ SV547 )
= $true )
| ( ( in @ SV547 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2506,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2507,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2508,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2509,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2384]) ).
thf(2510,plain,
! [SV498: $i,SV674: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV674 ) )
= $true )
| ( ( ! [SY2661: $i] :
( ~ ( SV184 @ SY2661 )
| ( SV674 = SY2661 ) ) )
= $true )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2511,plain,
! [SV498: $i,SV681: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV681 )
| ! [SY2667: $i] :
( ~ ( SV184 @ SY2667 )
| ( SV681 = SY2667 ) ) )
= $true )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2512,plain,
! [SV185: $i,SV645: $i,SV372: $i > $o] :
( ( ( SV372 @ SV645 )
= $false )
| ( ( in @ SV645 @ SV185 )
= $false )
| ( ( SV372 @ ( sK37_Xx @ SV372 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2513,plain,
! [SV185: $i,SV646: $i,SV372: $i > $o] :
( ( ( SV372 @ SV646 )
= $false )
| ( ( in @ SV646 @ SV185 )
= $false )
| ( ( in @ ( sK37_Xx @ SV372 @ SV185 ) @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2514,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( SV499
!= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2515,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( ~ ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 ) )
= $false )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2516,plain,
! [SV374: $i,SV682: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2668: $i] :
( ~ ( SV187 @ SY2668 @ SV682 )
| ~ ( in @ SY2668 @ SV374 ) )
| ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2517,plain,
! [SV187: $i > $i > $o,SV374: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 )
| ~ ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2518,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2519,plain,
! [SV187: $i > $i > $o,SV374: $i,SV647: $i] :
( ( ( ~ ( ( SV647
!= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2520,plain,
! [SV188: $i,SV648: $i,SV375: $i > $o] :
( ( ( SV375 @ SV648 )
= $false )
| ( ( in @ SV648 @ SV188 )
= $false )
| ( ( SV375 @ ( sK35_Xx @ SV375 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2521,plain,
! [SV188: $i,SV649: $i,SV375: $i > $o] :
( ( ( SV375 @ SV649 )
= $false )
| ( ( in @ SV649 @ SV188 )
= $false )
| ( ( in @ ( sK35_Xx @ SV375 @ SV188 ) @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2522,plain,
! [SV377: $i,SV190: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) ) )
= $true )
| ( ( ( in @ SV675 @ SV190 )
| ( in @ SV675 @ SV377 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2523,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) ) )
= $true )
| ( ( ( in @ SV676 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2524,plain,
! [SV377: $i,SV190: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) ) )
= $true )
| ( ( ! [SY2664: $o] :
( ~ SY2664
| ( in @ SV677 @ SV377 )
| SY2664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(2525,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2526,plain,
! [SV191: $i,SV378: $i,SV500: $i,SV618: $i] :
( ( ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
| ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) )
= $false )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2527,plain,
! [SV548: $i,SV192: $i,SV379: $i > $o] :
( ( ( SV379 @ ( sK36_Xx @ SV379 @ SV192 ) )
= $false )
| ( ( SV379 @ SV548 )
= $true )
| ( ( in @ SV548 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2528,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $false )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2529,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2530,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK43_SY1663 @ SV193 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2531,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2532,plain,
! [SV502: $i,SV678: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV678 ) )
= $true )
| ( ( ! [SY2665: $i] :
( ~ ( SV194 @ SY2665 )
| ( SV678 = SY2665 ) ) )
= $true )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2533,plain,
! [SV502: $i,SV685: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV685 )
| ! [SY2669: $i] :
( ~ ( SV194 @ SY2669 )
| ( SV685 = SY2669 ) ) )
= $true )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2534,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( in @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV196 )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2535,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2536,plain,
! [SV550: $i,SV573: $i] :
( ( ( in @ ( sK5_Xx @ SV573 @ SV550 ) @ SV550 )
= $false )
| ( ( in @ SV573 @ ( powerset @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2537,plain,
! [SV551: $i,SV574: $i,SV661: $i] :
( ( ( in @ SV661 @ SV574 )
= $false )
| ( ( in @ SV661 @ SV551 )
= $true )
| ( ( in @ SV574 @ ( powerset @ SV551 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2538,plain,
! [SV626: $i,SV199: $i,SV510: $i,SV383: $o] :
( ( SV383 = $false )
| ( ( in @ SV510
@ ( dsetconstr @ SV199
@ ^ [SY2632: $i] :
( ~ ( ~ SV383
| ( SY2632 != SV510 ) )
| ~ ( ~ ~ SV383
| ( SY2632 != SV626 ) ) ) ) )
= $true )
| ( ( in @ SV626 @ SV199 )
= $false )
| ( ( in @ SV510 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2539,plain,
! [SV627: $i,SV199: $i,SV511: $i] :
( ( $true = $false )
| ( ( in @ SV511
@ ( dsetconstr @ SV199
@ ^ [SY2633: $i] :
( ~ ( ~ $true
| ( SY2633 != SV511 ) )
| ~ ( ~ ~ $true
| ( SY2633 != SV627 ) ) ) ) )
= $true )
| ( ( in @ SV627 @ SV199 )
= $false )
| ( ( in @ SV511 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2540,plain,
! [SV628: $i,SV199: $i,SV512: $i] :
( ( $false = $false )
| ( ( in @ SV512
@ ( dsetconstr @ SV199
@ ^ [SY2634: $i] :
( ~ ( ~ $false
| ( SY2634 != SV512 ) )
| ~ ( ~ ~ $false
| ( SY2634 != SV628 ) ) ) ) )
= $true )
| ( ( in @ SV628 @ SV199 )
= $false )
| ( ( in @ SV512 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2541,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ~ ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2417]) ).
thf(2542,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( ~ ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2417]) ).
thf(2543,plain,
! [SV204: $i,SV662: $i,SV387: $i > $o] :
( ( ( SV387 @ SV662 )
= $false )
| ( ( ~ ( in @ SV662 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2544,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2545,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
| ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2546,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV663: $i] :
( ( ( in @ SV663 @ SV205 )
= $false )
| ( ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV663 )
= ( SV516 @ SV663 ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) @ SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2547,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV205 ) )
= $true )
| ( ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV679 )
= ( SV516 @ SV679 ) )
= $true )
| ( ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2548,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
| ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2549,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2427]) ).
thf(2550,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) ) )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2551,plain,
! [SV520: $i,SV209: $i,SV664: $i] :
( ( ( in @ SV664 @ ( sK12_B @ SV209 ) )
= $false )
| ( ( ~ ( in @ SV664 @ SV209 ) )
= $true )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2552,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2553,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
| ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2554,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2555,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
| ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2556,plain,
! [SV391: $i > $o,SV210: $i,SV650: $i] :
( ( ( in @ SV650 @ SV210 )
= $false )
| ( ( SV391 @ SV650 )
= $false )
| ( ( in @ ( sK34_Xx @ SV391 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2557,plain,
! [SV391: $i > $o,SV210: $i,SV651: $i] :
( ( ( in @ SV651 @ SV210 )
= $false )
| ( ( SV391 @ SV651 )
= $false )
| ( ( SV391 @ ( sK34_Xx @ SV391 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2558,plain,
! [SV211: $i] :
( ( ( in @ emptyset @ SV211 )
= $false )
| ( ( in @ ( sK7_Xx @ SV211 ) @ omega )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2559,plain,
! [SV211: $i] :
( ( ( in @ emptyset @ SV211 )
= $false )
| ( ( in @ ( sK7_Xx @ SV211 ) @ SV211 )
= $true )
| ( ( ! [SY2136: $i] :
( ~ ( in @ SY2136 @ omega )
| ( in @ SY2136 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2560,plain,
! [SV211: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ omega ) )
= $true )
| ( ( in @ SV680 @ SV211 )
= $true )
| ( ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 )
= $false )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2561,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) )
| ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) )
= $false )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2562,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) ) )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2563,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( SV212 @ ( sK44_SY209 @ SV212 ) )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2564,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) ) )
= $false )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2445]) ).
thf(2565,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $false )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2445]) ).
thf(2566,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) )
| ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $false )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2567,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2568,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) ) )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2569,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2570,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2449]) ).
thf(2571,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2572,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2573,plain,
! [SV218: $i,SV635: $i,SV577: $i > $o] :
( ( ( SV577 @ SV635 )
= $false )
| ( ( in @ SV635
@ ( dsetconstr @ SV218
@ ^ [SY2611: $i] : ( SV577 @ SY2611 ) ) )
= $true )
| ( ( in @ SV635 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2574,plain,
! [SV578: $i > $o,SV218: $i,SV636: $i] :
( ( ( in @ SV636
@ ( dsetconstr @ SV218
@ ^ [SY2613: $i] : ( SV578 @ SY2613 ) ) )
= $false )
| ( ( SV578 @ SV636 )
= $true )
| ( ( in @ SV636 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2575,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
| ~ ~ SV579 )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2576,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2577,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
| ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2578,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
| ~ ( ( SV665
!= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2579,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) ) )
= $true )
| ( ( ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2580,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2581,plain,
! [SV637: $i,SV528: $i,SV221: $i,SV398: $o] :
( ( SV398 = $false )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2642: $i] :
( ~ ( ~ SV398
| ( SY2642 != SV528 ) )
| ~ ( ~ ~ SV398
| ( SY2642 != SV637 ) ) ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $true )
| ( ( in @ SV637 @ SV221 )
= $false )
| ( ( in @ SV528 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2582,plain,
! [SV638: $i,SV529: $i,SV221: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2643: $i] :
( ~ ( ~ $true
| ( SY2643 != SV529 ) )
| ~ ( ~ ~ $true
| ( SY2643 != SV638 ) ) ) )
= ( setadjoin @ SV529 @ emptyset ) )
= $true )
| ( ( in @ SV638 @ SV221 )
= $false )
| ( ( in @ SV529 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2583,plain,
! [SV639: $i,SV530: $i,SV221: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV221
@ ^ [SY2644: $i] :
( ~ ( ~ $false
| ( SY2644 != SV530 ) )
| ~ ( ~ ~ $false
| ( SY2644 != SV639 ) ) ) )
= ( setadjoin @ SV530 @ emptyset ) )
= $true )
| ( ( in @ SV639 @ SV221 )
= $false )
| ( ( in @ SV530 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2584,plain,
! [SV580: $i,SV554: $i,SV652: $i] :
( ( ( in @ SV652 @ SV554 )
= $false )
| ( ( in @ SV580 @ SV652 )
= $false )
| ( ( in @ SV580 @ ( setunion @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2585,plain,
! [SV555: $i,SV581: $i] :
( ( ( in @ SV581 @ ( sK6_B @ SV581 @ SV555 ) )
= $true )
| ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2586,plain,
! [SV555: $i,SV581: $i] :
( ( ( in @ ( sK6_B @ SV581 @ SV555 ) @ SV555 )
= $true )
| ( ( in @ SV581 @ ( setunion @ SV555 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2587,plain,
! [SV13: $i,SV415: $i,SV594: $i,SV231: $i,SV666: $i] :
( ( ( in @ SV666 @ SV231 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV594 @ SV666 ) @ SV415 )
| ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SV666 ) )
= $true )
| ( ( in @ SV594 @ SV13 )
= $false )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2588,plain,
! [SV14: $i,SV416: $i,SV595: $i,SV232: $i,SV667: $i] :
( ( ( in @ SV667 @ SV232 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV595 @ SV667 ) @ SV416 )
| ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SV667 ) )
= $true )
| ( ( in @ SV595 @ SV14 )
= $false )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2589,plain,
! [SV17: $i,SV653: $i,SV558: $i,SV235: $i > $o] :
( ( ( ~ ( SV235 @ SV558 ) )
= $true )
| ( ( ~ ( SV235 @ SV653 )
| ( SV558 = SV653 ) )
= $true )
| ( ( in @ SV653 @ SV17 )
= $false )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2590,plain,
! [SV428: $i > $i > $o,SV245: $i,SV27: $i,SV642: $i,SV537: $i] :
( ( ( in @ ( kpair @ SV537 @ SV642 )
@ ( dpsetconstr @ SV27 @ SV245
@ ^ [SY2470: $i,SY2471: $i] : ( SV428 @ SY2470 @ SY2471 ) ) )
= $false )
| ( ( SV428 @ SV537 @ SV642 )
= $true )
| ( ( in @ SV642 @ SV245 )
= $false )
| ( ( in @ SV537 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2591,plain,
! [SV248: $i,SV30: $i,SV643: $i,SV538: $i,SV431: $i > $i > $o] :
( ( ( SV431 @ SV538 @ SV643 )
= $false )
| ( ( in @ ( kpair @ SV538 @ SV643 )
@ ( dpsetconstr @ SV30 @ SV248
@ ^ [SY2478: $i,SY2479: $i] : ( SV431 @ SY2478 @ SY2479 ) ) )
= $true )
| ( ( in @ SV643 @ SV248 )
= $false )
| ( ( in @ SV538 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2592,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) ) )
= $true )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2593,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( SV164 @ ( sK19_Xx @ SV164 ) )
= $true )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2478]) ).
thf(2594,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) ) )
= $false )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2595,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ ( sK19_Xx @ SV164 ) ) )
= $false )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2596,plain,
! [SV356: $i,SV165: $i,SV668: $i,SV654: $i] :
( ( ( SV654 = SV668 )
= $false )
| ( ( ~ ( in @ SV654 @ SV165 )
| ( in @ SV668 @ SV356 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2597,plain,
! [SV165: $i,SV356: $i,SV669: $i,SV655: $i] :
( ( ( SV655 = SV669 )
= $false )
| ( ( ~ ( in @ SV669 @ SV356 )
| ( in @ SV655 @ SV165 ) )
= $true )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2598,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i] :
( ( ( ~ ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 ) )
= $false )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2599,plain,
! [SV614: $i,SV490: $i,SV357: $i,SV166: $i] :
( ( ( ~ ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) ) ) )
= $false )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2600,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ( in @ SV492 @ SV168 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2601,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2602,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2603,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2604,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) ) )
= $true )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2605,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( SV169 @ ( sK39_SY196 @ SV169 ) )
= $true )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2606,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) ) )
= $false )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2607,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK39_SY196 @ SV169 ) ) )
= $false )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2608,plain,
! [SV170: $i,SV570: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2609,plain,
! [SV170: $i,SV570: $i] :
( ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( ! [SY2597: $i] :
~ ( in @ SY2597 @ SV570 ) )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2610,plain,
! [SV670: $i,SV170: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ~ ( in @ SV670 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) )
| ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2611,plain,
! [SV170: $i,SV687: $i] :
( ( ~ ( in @ SV687 @ ( sK13_B @ SV170 ) )
| ! [SY2670: $i] :
( ~ ( in @ SY2670 @ SV687 )
| ( in @ SY2670 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2612,plain,
! [SV170: $i,SV688: $i] :
( ( ! [SY2671: $i] :
( ~ ( in @ SV688 @ SV170 )
| ~ ( in @ SY2671 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SY2671 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SY2671 @ SV688 @ SV170 ) )
| ~ ( in @ SY2671 @ ( sK14_SY1650 @ SY2671 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SY2671 @ SV688 @ SV170 ) )
| ( in @ SY2671 @ ( sK14_SY1650 @ SY2671 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SY2671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2613,plain,
! [SV171: $i,SV360: $i,SV494: $i,SV615: $i] :
( ( ( ~ ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 ) )
= $false )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2614,plain,
! [SV615: $i,SV494: $i,SV360: $i,SV171: $i] :
( ( ( ~ ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) ) ) )
= $false )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2615,plain,
! [SV657: $i,SV174: $i,SV671: $i] :
( ( ( SV671 = SV174 )
= $false )
| ( ( in @ SV671 @ ( setadjoin @ SV174 @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2616,plain,
! [SV174: $i,SV658: $i,SV672: $i] :
( ( ( in @ SV672 @ SV658 )
= $false )
| ( ( in @ SV672 @ ( setadjoin @ SV174 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2617,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2618,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2499]) ).
thf(2619,plain,
! [SV497: $i > $i,SV366: $i,SV178: $i,SV673: $i] :
( ( ( in @ SV673 @ SV178 )
= $false )
| ( ( ( ap @ SV178 @ SV366
@ ( lam @ SV178 @ SV366
@ ^ [SY2517: $i] : ( SV497 @ SY2517 ) )
@ SV673 )
= ( SV497 @ SV673 ) )
= $true )
| ( ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV366 @ SV178 ) ) @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2620,plain,
! [SV367: $i > $o,SV179: $i,SV660: $i] :
( ( ( in @ SV660 @ SV179 )
= $false )
| ( ( SV367 @ SV660 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK68_Xx @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2621,plain,
! [SV179: $i,SV689: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV689 )
| ~ ( in @ SV689 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2622,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2504]) ).
thf(2623,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2504]) ).
thf(2624,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2625,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV370 )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2626,plain,
! [SV182: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 ) )
= $true )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2627,plain,
! [SV498: $i,SV674: $i,SV184: $i > $o] :
( ( ( SV184 @ SV674 )
= $false )
| ( ( ! [SY2661: $i] :
( ~ ( SV184 @ SY2661 )
| ( SV674 = SY2661 ) ) )
= $true )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2628,plain,
! [SV498: $i,SV681: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV681 ) )
= $true )
| ( ( ! [SY2667: $i] :
( ~ ( SV184 @ SY2667 )
| ( SV681 = SY2667 ) ) )
= $true )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2629,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( SV499
= ( kpair @ ( sK65_Xx @ SV499 @ SV373 @ SV186 ) @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) ) )
= $true )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2630,plain,
! [SV186: $i,SV373: $i,SV499: $i] :
( ( ( in @ ( sK66_SY1671 @ SV499 @ SV373 @ SV186 ) @ SV373 )
= $true )
| ( ( in @ SV499 @ ( cartprod @ SV186 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2631,plain,
! [SV374: $i,SV682: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2668: $i] :
( ~ ( SV187 @ SY2668 @ SV682 )
| ~ ( in @ SY2668 @ SV374 ) ) )
= $true )
| ( ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2632,plain,
! [SV187: $i > $i > $o,SV374: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 )
| ~ ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2633,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2518]) ).
thf(2634,plain,
! [SV187: $i > $i > $o,SV374: $i,SV647: $i] :
( ( ( SV647
!= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2519]) ).
thf(2635,plain,
! [SV377: $i,SV190: $i,SV675: $i] :
( ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false )
| ( ( ( in @ SV675 @ SV190 )
| ( in @ SV675 @ SV377 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2636,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false )
| ( ( ( in @ SV676 @ SV190 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2637,plain,
! [SV377: $i,SV190: $i,SV677: $i] :
( ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false )
| ( ( ! [SY2664: $o] :
( ~ SY2664
| ( in @ SV677 @ SV377 )
| SY2664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2638,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2639,plain,
! [SV191: $i,SV378: $i,SV500: $i,SV618: $i] :
( ( ( ~ ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 ) )
= $false )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2640,plain,
! [SV618: $i,SV500: $i,SV378: $i,SV191: $i] :
( ( ( ~ ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) ) ) )
= $false )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2641,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $true )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2642,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK41_SY203 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2643,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2644,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ( sK42_Xx @ SV193 )
!= ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2531]) ).
thf(2645,plain,
! [SV502: $i,SV678: $i,SV194: $i > $o] :
( ( ( SV194 @ SV678 )
= $false )
| ( ( ! [SY2665: $i] :
( ~ ( SV194 @ SY2665 )
| ( SV678 = SY2665 ) ) )
= $true )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2646,plain,
! [SV502: $i,SV685: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV685 ) )
= $true )
| ( ( ! [SY2669: $i] :
( ~ ( SV194 @ SY2669 )
| ( SV685 = SY2669 ) ) )
= $true )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2647,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
| ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2648,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( in @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) @ SV200 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2649,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( ~ ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2650,plain,
! [SV387: $i > $o,SV204: $i,SV662: $i] :
( ( ( in @ SV662 @ SV204 )
= $false )
| ( ( SV387 @ SV662 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK72_Xx @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2651,plain,
! [SV204: $i,SV690: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV690 )
| ~ ( in @ SV690 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2652,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2653,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2654,plain,
! [SV516: $i > $i,SV388: $i,SV205: $i,SV679: $i] :
( ( ( in @ SV679 @ SV205 )
= $false )
| ( ( ( ap @ SV205 @ SV388
@ ( lam @ SV205 @ SV388
@ ^ [SY2541: $i] : ( SV516 @ SY2541 ) )
@ SV679 )
= ( SV516 @ SV679 ) )
= $true )
| ( ( in @ ( SV516 @ ( sK92_Xx @ SV516 @ SV388 @ SV205 ) ) @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2655,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2548]) ).
thf(2656,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2548]) ).
thf(2657,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV519 )
| ( SV630 @ SV691 ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2658,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2659,plain,
! [SV520: $i,SV209: $i,SV664: $i] :
( ( ( in @ SV664 @ SV209 )
= $false )
| ( ( in @ SV664 @ ( sK12_B @ SV209 ) )
= $false )
| ( ( in @ SV520 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2551]) ).
thf(2660,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
| ~ ( ( SV692
!= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2661,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2662,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2663,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
| ~ ( ( SV693
!= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2664,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2665,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2666,plain,
! [SV211: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ omega )
| ( in @ SV694 @ SV211 ) )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(2667,plain,
! [SV211: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ omega )
| ( in @ SV695 @ SV211 ) )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ SV211 )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2668,plain,
! [SV211: $i,SV680: $i] :
( ( ( in @ SV680 @ omega )
= $false )
| ( ( in @ SV680 @ SV211 )
= $true )
| ( ( in @ ( setadjoin @ ( sK7_Xx @ SV211 ) @ ( sK7_Xx @ SV211 ) ) @ SV211 )
= $false )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2669,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) ) )
= $false )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2670,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ ( sK44_SY209 @ SV212 ) ) )
= $false )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2671,plain,
! [SV521: $i,SV696: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ SV696 )
| ( ( sK44_SY209 @ SV212 )
= SV696 ) )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2672,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2673,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2674,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) ) )
= $false )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2566]) ).
thf(2675,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ~ ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $false )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2566]) ).
thf(2676,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV526 )
| ( SV634 @ SV697 ) )
= $true )
| ( ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2677,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2678,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ( SV527 = SV217 )
| ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2679,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ( SV527 = SV217 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2680,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ! [SY2555: $o] :
( ~ SY2555
| ( in @ SV527 @ SV395 )
| SY2555 ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2681,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2682,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 ) )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2683,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ ~ SV579 )
= $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2684,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2685,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2686,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2687,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2688,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2689,plain,
! [SV220: $i > $o,SV397: $i > $o,SV665: $i] :
( ( ( ~ ( ( SV665
!= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2690,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2691,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2692,plain,
! [SV231: $i,SV13: $i,SV415: $i,SV666: $i,SV594: $i] :
( ( ( ~ ( in @ ( kpair @ SV594 @ SV666 ) @ SV415 ) )
= $true )
| ( ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SV666 )
= $true )
| ( ( in @ SV666 @ SV231 )
= $false )
| ( ( in @ SV594 @ SV13 )
= $false )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2693,plain,
! [SV232: $i,SV14: $i,SV416: $i,SV667: $i,SV595: $i] :
( ( ( ~ ( in @ ( kpair @ SV595 @ SV667 ) @ SV416 ) )
= $true )
| ( ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SV667 )
= $true )
| ( ( in @ SV667 @ SV232 )
= $false )
| ( ( in @ SV595 @ SV14 )
= $false )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2694,plain,
! [SV17: $i,SV653: $i,SV558: $i,SV235: $i > $o] :
( ( ( SV235 @ SV558 )
= $false )
| ( ( ~ ( SV235 @ SV653 )
| ( SV558 = SV653 ) )
= $true )
| ( ( in @ SV653 @ SV17 )
= $false )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2695,plain,
! [SV489: $i,SV698: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ SV698 )
| ( ( sK19_Xx @ SV164 )
= SV698 ) )
= $true )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2696,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( ! [SY1982: $i] :
( ~ ( SV164 @ SY1982 )
| ( ( sK19_Xx @ SV164 )
= SY1982 ) ) )
= $true )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2594]) ).
thf(2697,plain,
! [SV489: $i,SV164: $i > $o] :
( ( ( SV164 @ ( sK19_Xx @ SV164 ) )
= $true )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2698,plain,
! [SV356: $i,SV668: $i,SV165: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV165 ) )
= $true )
| ( ( in @ SV668 @ SV356 )
= $true )
| ( ( SV654 = SV668 )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2699,plain,
! [SV165: $i,SV655: $i,SV356: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV356 ) )
= $true )
| ( ( in @ SV655 @ SV165 )
= $true )
| ( ( SV655 = SV669 )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2700,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i] :
( ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2701,plain,
! [SV614: $i,SV490: $i,SV357: $i,SV166: $i] :
( ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
!= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $true )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2702,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $true )
| ( ( ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2703,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2704,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2705,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 )
| ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2706,plain,
! [SV493: $i,SV699: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV699 )
| ( ( sK39_SY196 @ SV169 )
= SV699 ) )
= $true )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2707,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( ! [SY2008: $i] :
( ~ ( SV169 @ SY2008 )
| ( ( sK39_SY196 @ SV169 )
= SY2008 ) ) )
= $true )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2708,plain,
! [SV493: $i,SV169: $i > $o] :
( ( ( SV169 @ ( sK39_SY196 @ SV169 ) )
= $true )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2709,plain,
! [SV170: $i,SV570: $i,SV686: $i] :
( ( ( in @ SV686 @ SV570 )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2710,plain,
! [SV170: $i,SV570: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(2711,plain,
! [SV670: $i,SV170: $i,SV656: $i] :
( ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( ~ ( in @ SV670 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) )
| ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2712,plain,
! [SV170: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2670: $i] :
( ~ ( in @ SY2670 @ SV687 )
| ( in @ SY2670 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2713,plain,
! [SV701: $i,SV170: $i,SV688: $i] :
( ( ~ ( in @ SV688 @ SV170 )
| ~ ( in @ SV701 @ SV170 )
| ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(2714,plain,
! [SV171: $i,SV360: $i,SV494: $i,SV615: $i] :
( ( ( in @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) @ SV171 )
= $true )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2715,plain,
! [SV615: $i,SV494: $i,SV360: $i,SV171: $i] :
( ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
!= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) )
= $true )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2716,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2717,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2718,plain,
! [SV179: $i,SV689: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV689 ) )
= $true )
| ( ( ~ ( in @ SV689 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2719,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2720,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2721,plain,
! [SV182: $i,SV370: $i] :
( ( ( in @ ( sK23_Xx @ SV370 @ SV182 ) @ SV182 )
= $false )
| ( ( SV182 = SV370 )
= $true )
| ( ( in @ ( sK24_Xx @ SV370 @ SV182 ) @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2722,plain,
! [SV498: $i,SV674: $i,SV702: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV702 )
| ( SV674 = SV702 ) )
= $true )
| ( ( SV184 @ SV674 )
= $false )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(2723,plain,
! [SV498: $i,SV681: $i,SV184: $i > $o] :
( ( ( SV184 @ SV681 )
= $false )
| ( ( ! [SY2667: $i] :
( ~ ( SV184 @ SY2667 )
| ( SV681 = SY2667 ) ) )
= $true )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2724,plain,
! [SV374: $i,SV682: $i,SV703: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV703 @ SV682 )
| ~ ( in @ SV703 @ SV374 ) )
= $true )
| ( ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(2725,plain,
! [SV187: $i > $i > $o,SV374: $i,SV683: $i] :
( ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 )
| ~ ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2632]) ).
thf(2726,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2727,plain,
! [SV187: $i > $i > $o,SV374: $i,SV647: $i] :
( ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( ~ ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 ) )
= $true )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2728,plain,
! [SV377: $i,SV190: $i,SV675: $i] :
( ( ( in @ SV675 @ SV190 )
= $true )
| ( ( ( in @ SV675 @ SV377 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2729,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( in @ SV676 @ SV190 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2730,plain,
! [SV190: $i,SV377: $i,SV677: $i,SV704: $o] :
( ( ( ~ SV704
| ( in @ SV677 @ SV377 )
| SV704 )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2637]) ).
thf(2731,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( ~ $true
| ( in @ SV677 @ SV377 )
| $true )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2637]) ).
thf(2732,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( ~ $false
| ( in @ SV677 @ SV377 )
| $false )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2637]) ).
thf(2733,plain,
! [SV377: $i,SV190: $i,SV684: $i,SV705: $o] :
( ( ( ~ SV705
| ~ SV705
| SV705 )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2638]) ).
thf(2734,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2638]) ).
thf(2735,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2638]) ).
thf(2736,plain,
! [SV191: $i,SV378: $i,SV500: $i,SV618: $i] :
( ( ( in @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) @ SV191 )
= $true )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2737,plain,
! [SV618: $i,SV500: $i,SV378: $i,SV191: $i] :
( ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
!= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) )
= $true )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2738,plain,
! [SV501: $i,SV706: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV706 )
| ( ( sK41_SY203 @ SV193 )
= SV706 ) )
= $true )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2739,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2740,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( ~ ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2741,plain,
! [SV502: $i,SV678: $i,SV707: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV707 )
| ( SV678 = SV707 ) )
= $true )
| ( ( SV194 @ SV678 )
= $false )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(2742,plain,
! [SV502: $i,SV685: $i,SV194: $i > $o] :
( ( ( SV194 @ SV685 )
= $false )
| ( ( ! [SY2669: $i] :
( ~ ( SV194 @ SY2669 )
| ( SV685 = SY2669 ) ) )
= $true )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2743,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2647]) ).
thf(2744,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2647]) ).
thf(2745,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
| ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2746,plain,
! [SV204: $i,SV690: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV690 ) )
= $true )
| ( ( ~ ( in @ SV690 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2747,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2652]) ).
thf(2748,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2653]) ).
thf(2749,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( in @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV206 )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2750,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) ) )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2751,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV519 ) )
= $true )
| ( ( SV630 @ SV691 )
= $true )
| ( ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2752,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2753,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2658]) ).
thf(2754,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
| ~ ( ( SV692
!= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) ) ) ) )
= $true )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2755,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2661]) ).
thf(2756,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
| ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2757,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
| ~ ( ( SV693
!= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) ) ) ) )
= $true )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2758,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2759,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
| ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2760,plain,
! [SV211: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ omega ) )
= $true )
| ( ( in @ SV694 @ SV211 )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2761,plain,
! [SV211: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ omega ) )
= $true )
| ( ( in @ SV695 @ SV211 )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ SV211 )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2762,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( ! [SY2138: $i] :
( ~ ( SV212 @ SY2138 )
| ( ( sK44_SY209 @ SV212 )
= SY2138 ) ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2763,plain,
! [SV521: $i,SV212: $i > $o] :
( ( ( SV212 @ ( sK44_SY209 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2764,plain,
! [SV521: $i,SV696: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ SV696 ) )
= $true )
| ( ( ( sK44_SY209 @ SV212 )
= SV696 )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2765,plain,
! [SV525: $i,SV214: $i > $o,SV708: $i] :
( ( ( ( SV708
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SV708 ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2766,plain,
! [SV525: $i,SV709: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ SV709 )
| ( SV709
= ( sK30_Xx @ SV214 ) ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(2767,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ! [SY2144: $i] :
( ( SY2144
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SY2144 ) ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2674]) ).
thf(2768,plain,
! [SV525: $i,SV214: $i > $o] :
( ( ( ! [SY2145: $i] :
( ~ ( SV214 @ SY2145 )
| ( SY2145
= ( sK30_Xx @ SV214 ) ) ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2675]) ).
thf(2769,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV526 ) )
= $true )
| ( ( SV634 @ SV697 )
= $true )
| ( ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2770,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2771,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2772,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( SV527 = SV217 )
= $true )
| ( ( ( in @ SV527 @ SV395 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2773,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( SV527 = SV217 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2774,plain,
! [SV217: $i,SV395: $i,SV527: $i,SV710: $o] :
( ( ( ~ SV710
| ( in @ SV527 @ SV395 )
| SV710 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2680]) ).
thf(2775,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ $true
| ( in @ SV527 @ SV395 )
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2680]) ).
thf(2776,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ $false
| ( in @ SV527 @ SV395 )
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2680]) ).
thf(2777,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV711: $o] :
( ( ( ~ SV711
| ~ SV711
| SV711 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2681]) ).
thf(2778,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2681]) ).
thf(2779,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2681]) ).
thf(2780,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( in @ ( sK29_B @ SV579 @ SV396 @ SV219 ) @ SV219 )
= $true )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2682]) ).
thf(2781,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( ( ~ SV579 ) = $true )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2683]) ).
thf(2782,plain,
! [SV219: $i,SV396: $i] :
( ( ( in @ ( sK29_B @ $true @ SV396 @ SV219 ) @ SV219 )
= $true )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2783,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2784,plain,
! [SV219: $i,SV396: $i] :
( ( ( in @ ( sK29_B @ $false @ SV396 @ SV219 ) @ SV219 )
= $true )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2785,plain,
! [SV219: $i,SV396: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2687]) ).
thf(2786,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2787,plain,
! [SV220: $i > $o,SV397: $i > $o,SV665: $i] :
( ( ( SV665
!= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2788,plain,
! [SV220: $i > $o,SV397: $i > $o] :
( ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) )
| ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2789,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
| ~ ( ( SV712
!= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(2790,plain,
! [SV231: $i,SV13: $i,SV415: $i,SV666: $i,SV594: $i] :
( ( ( in @ ( kpair @ SV594 @ SV666 ) @ SV415 )
= $false )
| ( ( ( ap @ SV13 @ SV231 @ SV415 @ SV594 )
= SV666 )
= $true )
| ( ( in @ SV666 @ SV231 )
= $false )
| ( ( in @ SV594 @ SV13 )
= $false )
| ( ( in @ SV415 @ ( funcSet @ SV13 @ SV231 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2791,plain,
! [SV232: $i,SV14: $i,SV416: $i,SV667: $i,SV595: $i] :
( ( ( in @ ( kpair @ SV595 @ SV667 ) @ SV416 )
= $false )
| ( ( ( ap @ SV14 @ SV232 @ SV416 @ SV595 )
= SV667 )
= $true )
| ( ( in @ SV667 @ SV232 )
= $false )
| ( ( in @ SV595 @ SV14 )
= $false )
| ( ( func @ SV14 @ SV232 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2792,plain,
! [SV17: $i,SV558: $i,SV653: $i,SV235: $i > $o] :
( ( ( ~ ( SV235 @ SV653 ) )
= $true )
| ( ( SV558 = SV653 )
= $true )
| ( ( SV235 @ SV558 )
= $false )
| ( ( in @ SV653 @ SV17 )
= $false )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2694]) ).
thf(2793,plain,
! [SV489: $i,SV698: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ SV698 ) )
= $true )
| ( ( ( sK19_Xx @ SV164 )
= SV698 )
= $true )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2794,plain,
! [SV489: $i,SV713: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ SV713 )
| ( ( sK19_Xx @ SV164 )
= SV713 ) )
= $true )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(2795,plain,
! [SV356: $i,SV668: $i,SV165: $i,SV654: $i] :
( ( ( in @ SV654 @ SV165 )
= $false )
| ( ( in @ SV668 @ SV356 )
= $true )
| ( ( SV654 = SV668 )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2796,plain,
! [SV165: $i,SV655: $i,SV356: $i,SV669: $i] :
( ( ( in @ SV669 @ SV356 )
= $false )
| ( ( in @ SV655 @ SV165 )
= $true )
| ( ( SV655 = SV669 )
= $false )
| ( ( SV165 = SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2797,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV166 )
| ! [SY2672: $i] :
( ~ ( in @ SY2672 @ SV357 )
| ~ ( in @ ( kpair @ SV714 @ SY2672 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SY2672 ) @ SV490 ) ) )
= $true )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2798,plain,
! [SV614: $i,SV490: $i,SV357: $i,SV166: $i] :
( ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( ! [SY2622: $i] :
( ~ ( in @ SY2622 @ SV166 )
| ! [SY2623: $i] :
( ~ ( in @ SY2623 @ SV357 )
| ~ ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV614 )
| ( in @ ( kpair @ SY2622 @ SY2623 ) @ SV490 ) ) ) )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2799,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV168 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2800,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(2801,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2703]) ).
thf(2802,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2704]) ).
thf(2803,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2704]) ).
thf(2804,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2805,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2705]) ).
thf(2806,plain,
! [SV493: $i,SV699: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV699 ) )
= $true )
| ( ( ( sK39_SY196 @ SV169 )
= SV699 )
= $true )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(2807,plain,
! [SV493: $i,SV715: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV715 )
| ( ( sK39_SY196 @ SV169 )
= SV715 ) )
= $true )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2808,plain,
! [SV686: $i,SV570: $i,SV170: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2809,plain,
! [SV170: $i,SV570: $i,SV700: $i] :
( ( ( in @ SV700 @ SV570 )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( ~ ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2810,plain,
! [SV656: $i,SV170: $i,SV670: $i] :
( ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) )
| ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2811,plain,
! [SV170: $i,SV687: $i] :
( ( ( in @ SV687 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( ! [SY2670: $i] :
( ~ ( in @ SY2670 @ SV687 )
| ( in @ SY2670 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2812,plain,
! [SV701: $i,SV170: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV170 )
| ~ ( in @ SV701 @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2813,plain,
! [SV615: $i,SV494: $i,SV360: $i,SV171: $i] :
( ( ( ( ap @ SV171 @ SV360 @ SV494 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) )
= ( ap @ SV171 @ SV360 @ SV615 @ ( sK89_Xx @ SV615 @ SV494 @ SV360 @ SV171 ) ) )
= $false )
| ( ( SV494 = SV615 )
= $true )
| ( ( in @ SV615 @ ( funcSet @ SV171 @ SV360 ) )
= $false )
| ( ( in @ SV494 @ ( funcSet @ SV171 @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2814,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2815,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2816,plain,
! [SV179: $i,SV689: $i,SV367: $i > $o] :
( ( ( SV367 @ SV689 )
= $false )
| ( ( ~ ( in @ SV689 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2817,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2818,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
| ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2819,plain,
! [SV498: $i,SV674: $i,SV702: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV702 ) )
= $true )
| ( ( SV674 = SV702 )
= $true )
| ( ( SV184 @ SV674 )
= $false )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2722]) ).
thf(2820,plain,
! [SV498: $i,SV681: $i,SV716: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV716 )
| ( SV681 = SV716 ) )
= $true )
| ( ( SV184 @ SV681 )
= $false )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(2821,plain,
! [SV374: $i,SV682: $i,SV703: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV703 @ SV682 ) )
= $true )
| ( ( ~ ( in @ SV703 @ SV374 ) )
= $true )
| ( ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2822,plain,
! [SV374: $i,SV683: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 )
| ~ ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2823,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2824,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( ~ ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2825,plain,
! [SV190: $i,SV377: $i,SV675: $i] :
( ( ( in @ SV675 @ SV377 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV675 @ SV190 )
= $true )
| ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2826,plain,
! [SV377: $i,SV190: $i,SV676: $i,SV717: $o] :
( ( ( ~ SV717
| SV717 )
= $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2729]) ).
thf(2827,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2729]) ).
thf(2828,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2729]) ).
thf(2829,plain,
! [SV190: $i,SV377: $i,SV677: $i,SV704: $o] :
( ( ( ~ SV704 ) = $true )
| ( ( ( in @ SV677 @ SV377 )
| SV704 )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2830,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV677 @ SV377 )
| $true )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2731]) ).
thf(2831,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV677 @ SV377 )
| $false )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(2832,plain,
! [SV377: $i,SV190: $i,SV684: $i,SV705: $o] :
( ( ( ~ SV705 ) = $true )
| ( ( ~ SV705
| SV705 )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2833,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(2834,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2835,plain,
! [SV618: $i,SV500: $i,SV378: $i,SV191: $i] :
( ( ( ( ap @ SV191 @ SV378 @ SV500 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) )
= ( ap @ SV191 @ SV378 @ SV618 @ ( sK88_Xx @ SV618 @ SV500 @ SV378 @ SV191 ) ) )
= $false )
| ( ( SV500 = SV618 )
= $true )
| ( ( func @ SV191 @ SV378 @ SV618 )
= $false )
| ( ( func @ SV191 @ SV378 @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2836,plain,
! [SV501: $i,SV706: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV706 ) )
= $true )
| ( ( ( sK41_SY203 @ SV193 )
= SV706 )
= $true )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2837,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $false )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2838,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2839,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) )
| ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2840,plain,
! [SV502: $i,SV678: $i,SV707: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV707 ) )
= $true )
| ( ( SV678 = SV707 )
= $true )
| ( ( SV194 @ SV678 )
= $false )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(2841,plain,
! [SV502: $i,SV685: $i,SV718: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV718 )
| ( SV685 = SV718 ) )
= $true )
| ( ( SV194 @ SV685 )
= $false )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2842,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( in @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) @ SV381 )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(2843,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ~ ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2844,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( ~ ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2845,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ~ ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2846,plain,
! [SV204: $i,SV690: $i,SV387: $i > $o] :
( ( ( SV387 @ SV690 )
= $false )
| ( ( ~ ( in @ SV690 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2847,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2848,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
| ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(2849,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2850,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV691: $i] :
( ( ( in @ SV691 @ SV519 )
= $false )
| ( ( SV630 @ SV691 )
= $true )
| ( ( in @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV208 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2851,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2852,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) ) )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2753]) ).
thf(2853,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
| ~ ( ( SV692
!= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2854,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) ) )
= $true )
| ( ( ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2855,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2856,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
| ~ ( ( SV693
!= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2857,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) ) )
= $true )
| ( ( ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(2858,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(2859,plain,
! [SV211: $i,SV694: $i] :
( ( ( in @ SV694 @ omega )
= $false )
| ( ( in @ SV694 @ SV211 )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2860,plain,
! [SV211: $i,SV695: $i] :
( ( ( in @ SV695 @ omega )
= $false )
| ( ( in @ SV695 @ SV211 )
= $true )
| ( ( in @ ( sK7_Xx @ SV211 ) @ SV211 )
= $true )
| ( ( in @ emptyset @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2861,plain,
! [SV521: $i,SV719: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ SV719 )
| ( ( sK44_SY209 @ SV212 )
= SV719 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(2862,plain,
! [SV521: $i,SV696: $i,SV212: $i > $o] :
( ( ( SV212 @ SV696 )
= $false )
| ( ( ( sK44_SY209 @ SV212 )
= SV696 )
= $true )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2863,plain,
! [SV525: $i,SV214: $i > $o,SV708: $i] :
( ( ( SV708
!= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV214 @ SV708 )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2864,plain,
! [SV525: $i,SV709: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ SV709 ) )
= $true )
| ( ( SV709
= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(2865,plain,
! [SV525: $i,SV214: $i > $o,SV720: $i] :
( ( ( ( SV720
!= ( sK30_Xx @ SV214 ) )
| ( SV214 @ SV720 ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(2866,plain,
! [SV525: $i,SV721: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ SV721 )
| ( SV721
= ( sK30_Xx @ SV214 ) ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(2867,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV697: $i] :
( ( ( in @ SV697 @ SV526 )
= $false )
| ( ( SV634 @ SV697 )
= $true )
| ( ( in @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV216 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2868,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2869,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) ) )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2771]) ).
thf(2870,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( in @ SV527 @ SV395 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2871,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV722: $o] :
( ( ( ~ SV722
| SV722 )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2773]) ).
thf(2872,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2773]) ).
thf(2873,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2773]) ).
thf(2874,plain,
! [SV217: $i,SV395: $i,SV527: $i,SV710: $o] :
( ( ( ~ SV710 ) = $true )
| ( ( ( in @ SV527 @ SV395 )
| SV710 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(2875,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV527 @ SV395 )
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(2876,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV527 @ SV395 )
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2877,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV711: $o] :
( ( ( ~ SV711 ) = $true )
| ( ( ~ SV711
| SV711 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2878,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(2879,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2880,plain,
! [SV219: $i,SV396: $i,SV579: $o] :
( ( SV579 = $false )
| ( SV579 = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2881,plain,
! [SV219: $i,SV396: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2882,plain,
! [SV219: $i,SV396: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV396 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2883,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( SV220 @ SV665 )
= $false )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2884,plain,
! [SV220: $i > $o,SV397: $i > $o,SV665: $i] :
( ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV220 @ SV665 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2885,plain,
! [SV397: $i > $o,SV220: $i > $o] :
( ( ( ! [SY2421: $i] :
( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) )
| ~ ( ( SY2421
!= ( sK57_SY255 @ SY2421 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SY2421 ) ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2886,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
| ~ ( ( SV712
!= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(2887,plain,
! [SV17: $i,SV558: $i,SV653: $i,SV235: $i > $o] :
( ( ( SV235 @ SV653 )
= $false )
| ( ( SV558 = SV653 )
= $true )
| ( ( SV235 @ SV558 )
= $false )
| ( ( in @ SV653 @ SV17 )
= $false )
| ( ( in @ SV558 @ SV17 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV17
@ ^ [SY2198: $i] : ( SV235 @ SY2198 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2888,plain,
! [SV489: $i,SV698: $i,SV164: $i > $o] :
( ( ( SV164 @ SV698 )
= $false )
| ( ( ( sK19_Xx @ SV164 )
= SV698 )
= $true )
| ( ( SV164 @ ( sK20_SY72 @ SV489 @ SV164 ) )
= $true )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2889,plain,
! [SV489: $i,SV713: $i,SV164: $i > $o] :
( ( ( ~ ( SV164 @ SV713 ) )
= $true )
| ( ( ( sK19_Xx @ SV164 )
= SV713 )
= $true )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2890,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV166 ) )
= $true )
| ( ( ! [SY2672: $i] :
( ~ ( in @ SY2672 @ SV357 )
| ~ ( in @ ( kpair @ SV714 @ SY2672 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SY2672 ) @ SV490 ) ) )
= $true )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2891,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV166 )
| ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV357 )
| ~ ( in @ ( kpair @ SV723 @ SY2673 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SY2673 ) @ SV490 ) ) )
= $true )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(2892,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(2893,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ( in @ SV492 @ SV168 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2894,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ( in @ SV492 @ SV168 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2801]) ).
thf(2895,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 )
| ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(2896,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2897,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ! [SY2509: $o] :
( ~ SY2509
| ~ ( in @ SV492 @ SV168 )
| SY2509 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2898,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2899,plain,
! [SV493: $i,SV699: $i,SV169: $i > $o] :
( ( ( SV169 @ SV699 )
= $false )
| ( ( ( sK39_SY196 @ SV169 )
= SV699 )
= $true )
| ( ( SV169 @ ( sK40_Xy @ SV493 @ SV169 ) )
= $true )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2900,plain,
! [SV493: $i,SV715: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV715 ) )
= $true )
| ( ( ( sK39_SY196 @ SV169 )
= SV715 )
= $true )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(2901,plain,
! [SV686: $i,SV570: $i,SV170: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2902,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2903,plain,
! [SV700: $i,SV570: $i,SV170: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2904,plain,
! [SV170: $i,SV670: $i,SV656: $i] :
( ( ( ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV656 )
| ( in @ SY2658 @ SV670 ) ) )
= $true )
| ( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2905,plain,
! [SV170: $i,SV687: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV687 )
| ( in @ SV724 @ SV170 ) )
= $true )
| ( ( in @ SV687 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(2906,plain,
! [SV701: $i,SV170: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV170 ) )
= $true )
| ( ( ~ ( in @ SV701 @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2907,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2908,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(2909,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(2910,plain,
! [SV367: $i > $o,SV179: $i,SV689: $i] :
( ( ( in @ SV689 @ SV179 )
= $false )
| ( ( SV367 @ SV689 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( in @ ( sK69_SY1672 @ SV367 @ SV179 ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(2911,plain,
! [SV179: $i,SV725: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV725 )
| ~ ( in @ SV725 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(2912,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2913,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ~ ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) ) ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2914,plain,
! [SV498: $i,SV674: $i,SV702: $i,SV184: $i > $o] :
( ( ( SV184 @ SV702 )
= $false )
| ( ( SV674 = SV702 )
= $true )
| ( ( SV184 @ SV674 )
= $false )
| ( ( SV184 @ ( sK46_SY222 @ SV498 @ SV184 ) )
= $true )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2915,plain,
! [SV498: $i,SV681: $i,SV716: $i,SV184: $i > $o] :
( ( ( ~ ( SV184 @ SV716 ) )
= $true )
| ( ( SV681 = SV716 )
= $true )
| ( ( SV184 @ SV681 )
= $false )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2916,plain,
! [SV374: $i,SV682: $i,SV703: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ SV703 @ SV682 )
= $false )
| ( ( ~ ( in @ SV703 @ SV374 ) )
= $true )
| ( ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(2917,plain,
! [SV374: $i,SV683: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 ) )
= $false )
| ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2822]) ).
thf(2918,plain,
! [SV187: $i > $i > $o,SV374: $i,SV683: $i] :
( ( ( ~ ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2822]) ).
thf(2919,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2823]) ).
thf(2920,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2823]) ).
thf(2921,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) )
| ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2922,plain,
! [SV190: $i,SV377: $i,SV675: $i,SV726: $o] :
( ( SV726 = $true )
| ( ( in @ SV675 @ SV377 )
= $true )
| ( ( in @ SV675 @ SV190 )
= $true )
| ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2825]) ).
thf(2923,plain,
! [SV190: $i,SV377: $i,SV675: $i] :
( ( $true = $true )
| ( ( in @ SV675 @ SV377 )
= $true )
| ( ( in @ SV675 @ SV190 )
= $true )
| ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2825]) ).
thf(2924,plain,
! [SV190: $i,SV377: $i,SV675: $i] :
( ( $false = $true )
| ( ( in @ SV675 @ SV377 )
= $true )
| ( ( in @ SV675 @ SV190 )
= $true )
| ( ( in @ SV675 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2825]) ).
thf(2925,plain,
! [SV377: $i,SV190: $i,SV676: $i,SV717: $o] :
( ( ( ~ SV717 ) = $true )
| ( SV717 = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(2926,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2927,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2928,plain,
! [SV190: $i,SV377: $i,SV677: $i,SV704: $o] :
( ( SV704 = $false )
| ( ( ( in @ SV677 @ SV377 )
| SV704 )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2929,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( $true = $false )
| ( ( ( in @ SV677 @ SV377 )
| $true )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2930,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( $false = $false )
| ( ( ( in @ SV677 @ SV377 )
| $false )
= $true )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2931,plain,
! [SV377: $i,SV190: $i,SV684: $i,SV705: $o] :
( ( SV705 = $false )
| ( ( ~ SV705
| SV705 )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2932,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2933,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2934,plain,
! [SV501: $i,SV706: $i,SV193: $i > $o] :
( ( ( SV193 @ SV706 )
= $false )
| ( ( ( sK41_SY203 @ SV193 )
= SV706 )
= $true )
| ( ( SV193 @ ( sK42_Xx @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2935,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $true )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2837]) ).
thf(2936,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK41_SY203 @ SV193 ) )
= $true )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2838]) ).
thf(2937,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $false )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2938,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK41_SY203 @ SV193 ) ) )
= $false )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2939,plain,
! [SV502: $i,SV678: $i,SV707: $i,SV194: $i > $o] :
( ( ( SV194 @ SV707 )
= $false )
| ( ( SV678 = SV707 )
= $true )
| ( ( SV194 @ SV678 )
= $false )
| ( ( SV194 @ ( sK55_SY246 @ SV502 @ SV194 ) )
= $true )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2940,plain,
! [SV502: $i,SV685: $i,SV718: $i,SV194: $i > $o] :
( ( ( ~ ( SV194 @ SV718 ) )
= $true )
| ( ( SV685 = SV718 )
= $true )
| ( ( SV194 @ SV685 )
= $false )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(2941,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2942,plain,
! [SV200: $i,SV513: $i,SV384: $i > $o] :
( ( ( SV384 @ ( sK71_Xy @ SV513 @ SV384 @ SV200 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2844]) ).
thf(2943,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
!= SV513 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2845]) ).
thf(2944,plain,
! [SV387: $i > $o,SV204: $i,SV690: $i] :
( ( ( in @ SV690 @ SV204 )
= $false )
| ( ( SV387 @ SV690 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( in @ ( sK73_SY1673 @ SV387 @ SV204 ) @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2945,plain,
! [SV204: $i,SV727: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV727 )
| ~ ( in @ SV727 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(2946,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2947,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ~ ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2848]) ).
thf(2948,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2949,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2950,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV519 )
| ( SV630 @ SV728 ) )
= $true )
| ( ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(2951,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
| ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2952,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) ) )
= $false )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2853]) ).
thf(2953,plain,
! [SV552: $i > $o,SV575: $i > $o,SV692: $i] :
( ( ( ~ ( ( SV692
!= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2853]) ).
thf(2954,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) ) )
= $true )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(2955,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2956,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) ) )
= $false )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2957,plain,
! [SV553: $i > $o,SV576: $i > $o,SV693: $i] :
( ( ( ~ ( ( SV693
!= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(2958,plain,
! [SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) ) )
= $true )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2959,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2960,plain,
! [SV521: $i,SV719: $i,SV212: $i > $o] :
( ( ( ~ ( SV212 @ SV719 ) )
= $true )
| ( ( ( sK44_SY209 @ SV212 )
= SV719 )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2961,plain,
! [SV525: $i,SV214: $i > $o,SV708: $i] :
( ( ( SV708
= ( sK30_Xx @ SV214 ) )
= $false )
| ( ( SV214 @ SV708 )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2962,plain,
! [SV525: $i,SV709: $i,SV214: $i > $o] :
( ( ( SV214 @ SV709 )
= $false )
| ( ( SV709
= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV214 @ ( sK31_SY140 @ SV525 @ SV214 ) )
= $true )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2963,plain,
! [SV525: $i,SV214: $i > $o,SV720: $i] :
( ( ( SV720
!= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV214 @ SV720 )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(2964,plain,
! [SV525: $i,SV721: $i,SV214: $i > $o] :
( ( ( ~ ( SV214 @ SV721 ) )
= $true )
| ( ( SV721
= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2965,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV526 )
| ( SV634 @ SV729 ) )
= $true )
| ( ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(2966,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
| ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(2967,plain,
! [SV217: $i,SV395: $i,SV527: $i,SV730: $o] :
( ( SV730 = $true )
| ( ( in @ SV527 @ SV395 )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2870]) ).
thf(2968,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( $true = $true )
| ( ( in @ SV527 @ SV395 )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2870]) ).
thf(2969,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( $false = $true )
| ( ( in @ SV527 @ SV395 )
= $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2870]) ).
thf(2970,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV722: $o] :
( ( ( ~ SV722 ) = $true )
| ( SV722 = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(2971,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(2972,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(2973,plain,
! [SV217: $i,SV395: $i,SV527: $i,SV710: $o] :
( ( SV710 = $false )
| ( ( ( in @ SV527 @ SV395 )
| SV710 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2974,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( $true = $false )
| ( ( ( in @ SV527 @ SV395 )
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2975,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( $false = $false )
| ( ( ( in @ SV527 @ SV395 )
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2976,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV711: $o] :
( ( SV711 = $false )
| ( ( ~ SV711
| SV711 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2977,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2978,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(2979,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(2980,plain,
! [SV397: $i > $o,SV665: $i,SV220: $i > $o] :
( ( ( SV220 @ SV665 )
= $false )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2981,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
| ~ ( ( SV731
!= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) ) ) )
| ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(2982,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
| ~ ( ( SV712
!= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(2983,plain,
! [SV489: $i,SV713: $i,SV164: $i > $o] :
( ( ( SV164 @ SV713 )
= $false )
| ( ( ( sK19_Xx @ SV164 )
= SV713 )
= $true )
| ( ( SV489
= ( sK20_SY72 @ SV489 @ SV164 ) )
= $false )
| ( ( SV164 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2984,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV714: $i] :
( ( ( in @ SV714 @ SV166 )
= $false )
| ( ( ! [SY2672: $i] :
( ~ ( in @ SY2672 @ SV357 )
| ~ ( in @ ( kpair @ SV714 @ SY2672 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SY2672 ) @ SV490 ) ) )
= $true )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2985,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV166 ) )
= $true )
| ( ( ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV357 )
| ~ ( in @ ( kpair @ SV723 @ SY2673 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SY2673 ) @ SV490 ) ) )
= $true )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(2986,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV732: $o] :
( ( SV732 = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2892]) ).
thf(2987,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2892]) ).
thf(2988,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2892]) ).
thf(2989,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $true )
| ( ( ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(2990,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(2991,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 ) )
= $true )
| ( ( ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2992,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2993,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV733: $o] :
( ( ( ~ SV733
| ~ ( in @ SV492 @ SV168 )
| SV733 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2897]) ).
thf(2994,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true
| ~ ( in @ SV492 @ SV168 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2897]) ).
thf(2995,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false
| ~ ( in @ SV492 @ SV168 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2897]) ).
thf(2996,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2997,plain,
! [SV493: $i,SV715: $i,SV169: $i > $o] :
( ( ( SV169 @ SV715 )
= $false )
| ( ( ( sK39_SY196 @ SV169 )
= SV715 )
= $true )
| ( ( SV493
= ( sK40_Xy @ SV493 @ SV169 ) )
= $false )
| ( ( SV169 @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2998,plain,
! [SV686: $i,SV570: $i,SV170: $i] :
( ( ( ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(2999,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(3000,plain,
! [SV700: $i,SV570: $i,SV170: $i] :
( ( ( ~ ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2903]) ).
thf(3001,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2903]) ).
thf(3002,plain,
! [SV170: $i,SV670: $i,SV656: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV656 )
| ( in @ SV734 @ SV670 ) )
= $true )
| ( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3003,plain,
! [SV170: $i,SV687: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV687 ) )
= $true )
| ( ( in @ SV724 @ SV170 )
= $true )
| ( ( in @ SV687 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(3004,plain,
! [SV701: $i,SV170: $i,SV688: $i] :
( ( ( in @ SV688 @ SV170 )
= $false )
| ( ( ~ ( in @ SV701 @ SV170 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3005,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(3006,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2907]) ).
thf(3007,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2908]) ).
thf(3008,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2909]) ).
thf(3009,plain,
! [SV179: $i,SV725: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV725 ) )
= $true )
| ( ( ~ ( in @ SV725 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3010,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(3011,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ( sK68_Xx @ SV367 @ SV179 )
!= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2913]) ).
thf(3012,plain,
! [SV498: $i,SV681: $i,SV716: $i,SV184: $i > $o] :
( ( ( SV184 @ SV716 )
= $false )
| ( ( SV681 = SV716 )
= $true )
| ( ( SV184 @ SV681 )
= $false )
| ( ( SV498
= ( sK46_SY222 @ SV498 @ SV184 ) )
= $false )
| ( ( SV184 @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(3013,plain,
! [SV682: $i,SV187: $i > $i > $o,SV374: $i,SV703: $i] :
( ( ( in @ SV703 @ SV374 )
= $false )
| ( ( SV187 @ SV703 @ SV682 )
= $false )
| ( ( in @ SV682 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3014,plain,
! [SV374: $i,SV683: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV683 )
= $true )
| ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(3015,plain,
! [SV187: $i > $i > $o,SV374: $i,SV683: $i] :
( ( ( in @ ( sK9_Xy @ SV683 @ SV374 @ SV187 ) @ SV374 )
= $true )
| ( ( in @ SV683 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( in @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV374 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(3016,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(3017,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i] :
( ( ( ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(3018,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ~ ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3019,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i] :
( ( ( ~ ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3020,plain,
! [SV377: $i,SV190: $i,SV676: $i,SV717: $o] :
( ( SV717 = $false )
| ( SV717 = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3021,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3022,plain,
! [SV377: $i,SV190: $i,SV676: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV676 @ SV190 )
= $true )
| ( ( in @ SV676 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3023,plain,
! [SV190: $i,SV704: $o,SV377: $i,SV677: $i] :
( ( ( in @ SV677 @ SV377 )
= $true )
| ( SV704 = $true )
| ( SV704 = $false )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3024,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( in @ SV677 @ SV377 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3025,plain,
! [SV190: $i,SV377: $i,SV677: $i] :
( ( ( in @ SV677 @ SV377 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV677 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3026,plain,
! [SV377: $i,SV190: $i,SV684: $i,SV705: $o] :
( ( ( ~ SV705 ) = $true )
| ( SV705 = $true )
| ( SV705 = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3027,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3028,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(3029,plain,
! [SV501: $i,SV735: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV735 )
| ( ( sK41_SY203 @ SV193 )
= SV735 ) )
= $true )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3030,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( ! [SY2085: $i] :
( ~ ( SV193 @ SY2085 )
| ( ( sK41_SY203 @ SV193 )
= SY2085 ) ) )
= $true )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(3031,plain,
! [SV501: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK41_SY203 @ SV193 ) )
= $true )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3032,plain,
! [SV502: $i,SV685: $i,SV718: $i,SV194: $i > $o] :
( ( ( SV194 @ SV718 )
= $false )
| ( ( SV685 = SV718 )
= $true )
| ( ( SV194 @ SV685 )
= $false )
| ( ( SV502
= ( sK55_SY246 @ SV502 @ SV194 ) )
= $false )
| ( ( SV194 @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3033,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
!= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2941]) ).
thf(3034,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2941]) ).
thf(3035,plain,
! [SV200: $i,SV384: $i > $o,SV513: $i] :
( ( ( ( sK71_Xy @ SV513 @ SV384 @ SV200 )
= SV513 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV200
@ ^ [SY2395: $i] : ( SV384 @ SY2395 ) ) )
= $true )
| ( ( SV384 @ SV513 )
= $false )
| ( ( in @ SV513 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3036,plain,
! [SV204: $i,SV727: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV727 ) )
= $true )
| ( ( ~ ( in @ SV727 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3037,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(3038,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ( sK72_Xx @ SV387 @ SV204 )
!= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(3039,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( in @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) @ SV389 )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2948]) ).
thf(3040,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) ) )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2949]) ).
thf(3041,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV519 ) )
= $true )
| ( ( SV630 @ SV728 )
= $true )
| ( ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3042,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3043,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2951]) ).
thf(3044,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3045,plain,
! [SV552: $i > $o,SV575: $i > $o,SV692: $i] :
( ( ( SV692
!= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3046,plain,
! [SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) )
| ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3047,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
| ~ ( ( SV736
!= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3048,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3049,plain,
! [SV553: $i > $o,SV576: $i > $o,SV693: $i] :
( ( ( SV693
!= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2957]) ).
thf(3050,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) )
| ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3051,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
| ~ ( ( SV737
!= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3052,plain,
! [SV521: $i,SV719: $i,SV212: $i > $o] :
( ( ( SV212 @ SV719 )
= $false )
| ( ( ( sK44_SY209 @ SV212 )
= SV719 )
= $true )
| ( ( ( sK45_Xy @ SV521 @ SV212 )
= SV521 )
= $false )
| ( ( SV212 @ ( sK45_Xy @ SV521 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3053,plain,
! [SV525: $i,SV214: $i > $o,SV720: $i] :
( ( ( SV720
= ( sK30_Xx @ SV214 ) )
= $false )
| ( ( SV214 @ SV720 )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3054,plain,
! [SV525: $i,SV721: $i,SV214: $i > $o] :
( ( ( SV214 @ SV721 )
= $false )
| ( ( SV721
= ( sK30_Xx @ SV214 ) )
= $true )
| ( ( SV525
= ( sK31_SY140 @ SV525 @ SV214 ) )
= $false )
| ( ( SV214 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3055,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV526 ) )
= $true )
| ( ( SV634 @ SV729 )
= $true )
| ( ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3056,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3057,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3058,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV722: $o] :
( ( SV722 = $false )
| ( SV722 = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3059,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3060,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV527 = SV217 )
= $true )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3061,plain,
! [SV217: $i,SV710: $o,SV395: $i,SV527: $i] :
( ( ( in @ SV527 @ SV395 )
= $true )
| ( SV710 = $true )
| ( SV710 = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3062,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( in @ SV527 @ SV395 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3063,plain,
! [SV217: $i,SV395: $i,SV527: $i] :
( ( ( in @ SV527 @ SV395 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3064,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV711: $o] :
( ( ( ~ SV711 ) = $true )
| ( SV711 = $true )
| ( SV711 = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3065,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3066,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3067,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
| ~ ( ( SV738
!= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3068,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3069,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( ~ ( ~ ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
| ~ ( ( SV731
!= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3070,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2982]) ).
thf(3071,plain,
! [SV220: $i > $o,SV397: $i > $o,SV712: $i] :
( ( ( ~ ( ( SV712
!= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2982]) ).
thf(3072,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV714: $i,SV357: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ SV357 )
| ~ ( in @ ( kpair @ SV714 @ SV739 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SV739 ) @ SV490 ) )
= $true )
| ( ( in @ SV714 @ SV166 )
= $false )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3073,plain,
! [SV490: $i,SV614: $i,SV357: $i,SV166: $i,SV723: $i] :
( ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ! [SY2673: $i] :
( ~ ( in @ SY2673 @ SV357 )
| ~ ( in @ ( kpair @ SV723 @ SY2673 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SY2673 ) @ SV490 ) ) )
= $true )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3074,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3075,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV740: $o] :
( ( ( ~ SV740
| SV740 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2990]) ).
thf(3076,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2990]) ).
thf(3077,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2990]) ).
thf(3078,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $false )
| ( ( ~ ( in @ SV492 @ SV168 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3079,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2992]) ).
thf(3080,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2992]) ).
thf(3081,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV733: $o] :
( ( ( ~ SV733 ) = $true )
| ( ( ~ ( in @ SV492 @ SV168 )
| SV733 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3082,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ ( in @ SV492 @ SV168 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3083,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ ( in @ SV492 @ SV168 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3084,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3085,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3086,plain,
! [SV686: $i,SV570: $i,SV170: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( sK13_B @ SV170 ) )
| ! [SY2674: $i] :
( ~ ( in @ SY2674 @ SV741 )
| ( in @ SY2674 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3087,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3088,plain,
! [SV700: $i,SV570: $i,SV170: $i] :
( ( ( ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( sK13_B @ SV170 ) )
| ! [SY2599: $i] :
( ~ ( in @ SY2599 @ SY2598 )
| ( in @ SY2599 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SY2598 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3089,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3001]) ).
thf(3090,plain,
! [SV170: $i,SV670: $i,SV656: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV656 ) )
= $true )
| ( ( in @ SV734 @ SV670 )
= $true )
| ( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3091,plain,
! [SV170: $i,SV687: $i,SV724: $i] :
( ( ( in @ SV724 @ SV687 )
= $false )
| ( ( in @ SV724 @ SV170 )
= $true )
| ( ( in @ SV687 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3092,plain,
! [SV688: $i,SV170: $i,SV701: $i] :
( ( ( in @ SV701 @ SV170 )
= $false )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
| ( SV688 = SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3093,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3094,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3006]) ).
thf(3095,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3096,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
| ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3097,plain,
! [SV179: $i,SV725: $i,SV367: $i > $o] :
( ( ( SV367 @ SV725 )
= $false )
| ( ( ~ ( in @ SV725 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3098,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3099,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false )
| ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) )
| ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3100,plain,
! [SV647: $i,SV374: $i,SV742: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2675: $i] :
( ~ ( SV187 @ SY2675 @ SV742 )
| ~ ( in @ SY2675 @ SV374 ) )
| ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3101,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 )
| ~ ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3102,plain,
! [SV647: $i,SV374: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2366: $i] :
( ! [SY2367: $i] :
( ~ ( SV187 @ SY2367 @ SY2366 )
| ~ ( in @ SY2367 @ SV374 ) )
| ( in @ SY2366 @ ( sK8_B @ SV374 @ SV187 ) ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3018]) ).
thf(3103,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i] :
( ( ( ! [SY2368: $i] :
( ~ ( in @ SY2368 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SY2368 )
| ~ ( in @ ( sK9_Xy @ SY2368 @ SV374 @ SV187 ) @ SV374 ) ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3104,plain,
! [SV377: $i,SV190: $i,SV684: $i,SV705: $o] :
( ( SV705 = $false )
| ( SV705 = $true )
| ( SV705 = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3105,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3106,plain,
! [SV377: $i,SV190: $i,SV684: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV684 @ ( binunion @ SV190 @ SV377 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3107,plain,
! [SV501: $i,SV735: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV735 ) )
= $true )
| ( ( ( sK41_SY203 @ SV193 )
= SV735 )
= $true )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3108,plain,
! [SV501: $i,SV744: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV744 )
| ( ( sK41_SY203 @ SV193 )
= SV744 ) )
= $true )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3109,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 )
= ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3110,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3111,plain,
! [SV204: $i,SV727: $i,SV387: $i > $o] :
( ( ( SV387 @ SV727 )
= $false )
| ( ( ~ ( in @ SV727 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3112,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3113,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) )
| ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3114,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
| ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3115,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV728: $i] :
( ( ( in @ SV728 @ SV519 )
= $false )
| ( ( SV630 @ SV728 )
= $true )
| ( ( in @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) @ SV390 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3116,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3042]) ).
thf(3117,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( ~ ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) ) )
= $true )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3043]) ).
thf(3118,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( SV552 @ SV692 )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3119,plain,
! [SV552: $i > $o,SV575: $i > $o,SV692: $i] :
( ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( SV552 @ SV692 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3120,plain,
! [SV575: $i > $o,SV552: $i > $o] :
( ( ( ! [SY2606: $i] :
( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) )
| ~ ( ( SY2606
!= ( sK52_SY231 @ SY2606 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SY2606 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3046]) ).
thf(3121,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
| ~ ( ( SV736
!= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) ) ) ) )
= $true )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3122,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( SV576 @ SV693 )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3123,plain,
! [SV553: $i > $o,SV576: $i > $o,SV693: $i] :
( ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( SV576 @ SV693 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3124,plain,
! [SV553: $i > $o,SV576: $i > $o] :
( ( ( ! [SY2608: $i] :
( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) )
| ~ ( ( SY2608
!= ( sK48_SY234 @ SY2608 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SY2608 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3125,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
| ~ ( ( SV737
!= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) ) ) ) )
= $true )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3126,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV729: $i] :
( ( ( in @ SV729 @ SV526 )
= $false )
| ( ( SV634 @ SV729 )
= $true )
| ( ( in @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) @ SV394 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3127,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3128,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( ~ ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) ) )
= $true )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3057]) ).
thf(3129,plain,
! [SV395: $i,SV217: $i,SV527: $i,SV711: $o] :
( ( SV711 = $false )
| ( SV711 = $true )
| ( SV711 = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3130,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3131,plain,
! [SV395: $i,SV217: $i,SV527: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV527 @ ( setadjoin @ SV217 @ SV395 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3132,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
| ~ ( ( SV738
!= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3133,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
| ~ ( ( SV745
!= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3134,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
| ~ ( ( SV731
!= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3135,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3070]) ).
thf(3136,plain,
! [SV220: $i > $o,SV397: $i > $o,SV712: $i] :
( ( ( SV712
!= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3137,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV714: $i,SV357: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ SV357 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV714 @ SV739 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SV739 ) @ SV490 ) )
= $true )
| ( ( in @ SV714 @ SV166 )
= $false )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3138,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV723: $i,SV357: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV357 )
| ~ ( in @ ( kpair @ SV723 @ SV746 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SV746 ) @ SV490 ) )
= $true )
| ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3139,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV747: $o] :
( ( SV747 = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3074]) ).
thf(3140,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $true = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3074]) ).
thf(3141,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $false = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3074]) ).
thf(3142,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV740: $o] :
( ( ( ~ SV740 ) = $true )
| ( SV740 = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3143,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3144,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3145,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV168 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3146,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 )
| ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3147,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3080]) ).
thf(3148,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV733: $o] :
( ( SV733 = $false )
| ( ( ~ ( in @ SV492 @ SV168 )
| SV733 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3149,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $false )
| ( ( ~ ( in @ SV492 @ SV168 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3082]) ).
thf(3150,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $false )
| ( ( ~ ( in @ SV492 @ SV168 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3151,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ! [SY2510: $o] :
( ~ SY2510
| ( in @ SV492 @ SV359 )
| SY2510 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3152,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3085]) ).
thf(3153,plain,
! [SV686: $i,SV570: $i,SV170: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2674: $i] :
( ~ ( in @ SY2674 @ SV741 )
| ( in @ SY2674 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3154,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3155,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3156,plain,
! [SV700: $i,SV570: $i,SV170: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( sK13_B @ SV170 ) )
| ! [SY2676: $i] :
( ~ ( in @ SY2676 @ SV748 )
| ( in @ SY2676 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3157,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
| ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3158,plain,
! [SV170: $i,SV670: $i,SV656: $i,SV734: $i] :
( ( ( in @ SV734 @ SV656 )
= $false )
| ( ( in @ SV734 @ SV670 )
= $true )
| ( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ SV670 )
| ( in @ SY2659 @ SV656 ) ) )
= $true )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3159,plain,
! [SV170: $i,SV688: $i,SV701: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3160,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3161,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3162,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3163,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3164,plain,
! [SV367: $i > $o,SV179: $i,SV725: $i] :
( ( ( in @ SV725 @ SV179 )
= $false )
| ( ( SV367 @ SV725 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK68_Xx @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3165,plain,
! [SV179: $i,SV749: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV749 )
| ~ ( in @ SV749 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3166,plain,
! [SV179: $i,SV367: $i > $o] :
( ( ( ! [SY2360: $i] :
( ~ ( SV367 @ SY2360 )
| ~ ( in @ SY2360 @ SV179 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3167,plain,
! [SV647: $i,SV374: $i,SV742: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2675: $i] :
( ~ ( SV187 @ SY2675 @ SV742 )
| ~ ( in @ SY2675 @ SV374 ) ) )
= $true )
| ( ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3168,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 )
| ~ ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3169,plain,
! [SV647: $i,SV374: $i,SV750: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2677: $i] :
( ~ ( SV187 @ SY2677 @ SV750 )
| ~ ( in @ SY2677 @ SV374 ) )
| ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3170,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
| ~ ( ~ ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 )
| ~ ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3171,plain,
! [SV501: $i,SV735: $i,SV193: $i > $o] :
( ( ( SV193 @ SV735 )
= $false )
| ( ( ( sK41_SY203 @ SV193 )
= SV735 )
= $true )
| ( ( SV193 @ ( sK43_SY1663 @ SV193 ) )
= $true )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3172,plain,
! [SV501: $i,SV744: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ SV744 ) )
= $true )
| ( ( ( sK41_SY203 @ SV193 )
= SV744 )
= $true )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3173,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
| ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3174,plain,
! [SV387: $i > $o,SV204: $i,SV727: $i] :
( ( ( in @ SV727 @ SV204 )
= $false )
| ( ( SV387 @ SV727 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK72_Xx @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3175,plain,
! [SV204: $i,SV752: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV752 )
| ~ ( in @ SV752 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3176,plain,
! [SV204: $i,SV387: $i > $o] :
( ( ( ! [SY2398: $i] :
( ~ ( SV387 @ SY2398 )
| ~ ( in @ SY2398 @ SV204 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3177,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3178,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3179,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV519 )
| ( SV630 @ SV753 ) )
= $true )
| ( ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3180,plain,
! [SV208: $i,SV390: $i,SV519: $i,SV630: $i > $o] :
( ( ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) )
= $false )
| ( ( ! [SY2635: $i] :
( ~ ( in @ SY2635 @ SV519 )
| ( SV630 @ SY2635 ) ) )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3181,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3182,plain,
! [SV575: $i > $o,SV692: $i,SV552: $i > $o] :
( ( ( SV552 @ SV692 )
= $false )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3183,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
| ~ ( ( SV754
!= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) ) ) )
| ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3184,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
| ~ ( ( SV736
!= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3185,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3186,plain,
! [SV553: $i > $o,SV693: $i,SV576: $i > $o] :
( ( ( SV576 @ SV693 )
= $false )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3187,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
| ~ ( ( SV755
!= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) ) ) )
| ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3188,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
| ~ ( ( SV737
!= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3189,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV526 )
| ( SV634 @ SV756 ) )
= $true )
| ( ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3190,plain,
! [SV216: $i,SV394: $i,SV526: $i,SV634: $i > $o] :
( ( ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) )
= $false )
| ( ( ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV526 )
| ( SV634 @ SY2639 ) ) )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3191,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
| ~ ( ( SV738
!= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3192,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
| ~ ( ( SV745
!= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3193,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3134]) ).
thf(3194,plain,
! [SV220: $i > $o,SV397: $i > $o,SV731: $i] :
( ( ( ~ ( ( SV731
!= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3134]) ).
thf(3195,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( SV220 @ SV712 )
= $false )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3196,plain,
! [SV220: $i > $o,SV397: $i > $o,SV712: $i] :
( ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV220 @ SV712 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3197,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV714: $i,SV357: $i,SV739: $i] :
( ( ( in @ SV739 @ SV357 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV714 @ SV739 ) @ SV614 )
| ( in @ ( kpair @ SV714 @ SV739 ) @ SV490 ) )
= $true )
| ( ( in @ SV714 @ SV166 )
= $false )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3198,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV723: $i,SV357: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV357 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV723 @ SV746 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SV746 ) @ SV490 ) )
= $true )
| ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3199,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV740: $o] :
( ( SV740 = $false )
| ( SV740 = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3200,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3201,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV492 @ SV168 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3202,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3203,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 ) )
= $true )
| ( ( ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3204,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV359 ) )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3205,plain,
! [SV359: $i,SV733: $o,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV168 ) )
= $true )
| ( SV733 = $true )
| ( SV733 = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3206,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV168 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3207,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV168 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3208,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV757: $o] :
( ( ( ~ SV757
| ( in @ SV492 @ SV359 )
| SV757 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3151]) ).
thf(3209,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $true
| ( in @ SV492 @ SV359 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3151]) ).
thf(3210,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $false
| ( in @ SV492 @ SV359 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3151]) ).
thf(3211,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV758: $o] :
( ( ( ~ SV758
| ~ SV758
| SV758 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3152]) ).
thf(3212,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3152]) ).
thf(3213,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3152]) ).
thf(3214,plain,
! [SV686: $i,SV570: $i,SV170: $i,SV741: $i] :
( ( ( in @ SV741 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( ! [SY2674: $i] :
( ~ ( in @ SY2674 @ SV741 )
| ( in @ SY2674 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3215,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3216,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3217,plain,
! [SV700: $i,SV570: $i,SV170: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( sK13_B @ SV170 ) ) )
= $true )
| ( ( ! [SY2676: $i] :
( ~ ( in @ SY2676 @ SV748 )
| ( in @ SY2676 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3218,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3219,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3220,plain,
! [SV170: $i,SV734: $i,SV656: $i,SV670: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV670 )
| ( in @ SV759 @ SV656 ) )
= $true )
| ( ( in @ SV734 @ SV670 )
= $true )
| ( ( in @ SV734 @ SV656 )
= $false )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3221,plain,
! [SV170: $i,SV688: $i,SV701: $i] :
( ( ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3222,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3160]) ).
thf(3223,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3160]) ).
thf(3224,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3225,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3226,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3227,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3228,plain,
! [SV179: $i,SV749: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV749 ) )
= $true )
| ( ( ~ ( in @ SV749 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3229,plain,
! [SV179: $i,SV760: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV760 )
| ~ ( in @ SV760 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3230,plain,
! [SV647: $i,SV374: $i,SV742: $i,SV761: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV761 @ SV742 )
| ~ ( in @ SV761 @ SV374 ) )
= $true )
| ( ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3231,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV743: $i] :
( ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 )
| ~ ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3232,plain,
! [SV647: $i,SV374: $i,SV750: $i,SV187: $i > $i > $o] :
( ( ( ! [SY2677: $i] :
( ~ ( SV187 @ SY2677 @ SV750 )
| ~ ( in @ SY2677 @ SV374 ) ) )
= $true )
| ( ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3233,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) ) )
= $true )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 )
| ~ ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3234,plain,
! [SV501: $i,SV744: $i,SV193: $i > $o] :
( ( ( SV193 @ SV744 )
= $false )
| ( ( ( sK41_SY203 @ SV193 )
= SV744 )
= $true )
| ( ( ( sK42_Xx @ SV193 )
= ( sK43_SY1663 @ SV193 ) )
= $false )
| ( ( SV193 @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3235,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3236,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3237,plain,
! [SV204: $i,SV752: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV752 ) )
= $true )
| ( ( ~ ( in @ SV752 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3238,plain,
! [SV204: $i,SV762: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV762 )
| ~ ( in @ SV762 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3239,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV517 )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3240,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 ) )
= $true )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3241,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ SV519 ) )
= $true )
| ( ( SV630 @ SV753 )
= $true )
| ( ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3242,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV519 )
| ( SV630 @ SV763 ) )
= $true )
| ( ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) )
= $false )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3243,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3244,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3245,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3246,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( ~ ( ~ ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
| ~ ( ( SV754
!= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) ) ) ) )
= $true )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3247,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) ) )
= $false )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3248,plain,
! [SV552: $i > $o,SV575: $i > $o,SV736: $i] :
( ( ( ~ ( ( SV736
!= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3184]) ).
thf(3249,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3250,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3251,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3252,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( ~ ( ~ ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
| ~ ( ( SV755
!= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) ) ) ) )
= $true )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3253,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) ) )
= $false )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3254,plain,
! [SV553: $i > $o,SV576: $i > $o,SV737: $i] :
( ( ( ~ ( ( SV737
!= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3255,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV526 ) )
= $true )
| ( ( SV634 @ SV756 )
= $true )
| ( ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3256,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV526 )
| ( SV634 @ SV764 ) )
= $true )
| ( ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) )
= $false )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3257,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3258,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV738: $i] :
( ( ( ~ ( ( SV738
!= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3191]) ).
thf(3259,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
| ~ ( ( SV745
!= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3260,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3193]) ).
thf(3261,plain,
! [SV220: $i > $o,SV397: $i > $o,SV731: $i] :
( ( ( SV731
!= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3262,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3263,plain,
! [SV397: $i > $o,SV712: $i,SV220: $i > $o] :
( ( ( SV220 @ SV712 )
= $false )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3264,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i,SV739: $i,SV714: $i] :
( ( ( ~ ( in @ ( kpair @ SV714 @ SV739 ) @ SV614 ) )
= $true )
| ( ( in @ ( kpair @ SV714 @ SV739 ) @ SV490 )
= $true )
| ( ( in @ SV739 @ SV357 )
= $false )
| ( ( in @ SV714 @ SV166 )
= $false )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3265,plain,
! [SV166: $i,SV490: $i,SV614: $i,SV723: $i,SV357: $i,SV746: $i] :
( ( ( in @ SV746 @ SV357 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV723 @ SV746 ) @ SV614 )
| ( in @ ( kpair @ SV723 @ SV746 ) @ SV490 ) )
= $true )
| ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3266,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV765: $o] :
( ( SV765 = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3202]) ).
thf(3267,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3202]) ).
thf(3268,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $true )
| ( ( in @ SV492 @ SV168 )
= $false )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3202]) ).
thf(3269,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $false )
| ( ( ( in @ SV492 @ SV359 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3270,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $false )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3271,plain,
! [SV359: $i,SV733: $o,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $false )
| ( SV733 = $true )
| ( SV733 = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3272,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3273,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( in @ SV492 @ SV168 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3274,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV757: $o] :
( ( ( ~ SV757 ) = $true )
| ( ( ( in @ SV492 @ SV359 )
| SV757 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3275,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV492 @ SV359 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3276,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV492 @ SV359 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3277,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV758: $o] :
( ( ( ~ SV758 ) = $true )
| ( ( ~ SV758
| SV758 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3278,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3279,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3280,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV741: $i] :
( ( ( ! [SY2674: $i] :
( ~ ( in @ SY2674 @ SV741 )
| ( in @ SY2674 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 )
= $true )
| ( ( in @ SV741 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3281,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3282,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SV766 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3283,plain,
! [SV700: $i,SV570: $i,SV170: $i,SV748: $i] :
( ( ( in @ SV748 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( ! [SY2676: $i] :
( ~ ( in @ SY2676 @ SV748 )
| ( in @ SY2676 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
| ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3284,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3218]) ).
thf(3285,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ! [SY2600: $i] :
( ~ ( in @ SY2600 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SY2600 @ SV570 ) ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3219]) ).
thf(3286,plain,
! [SV170: $i,SV734: $i,SV656: $i,SV670: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV670 ) )
= $true )
| ( ( in @ SV759 @ SV656 )
= $true )
| ( ( in @ SV734 @ SV670 )
= $true )
| ( ( in @ SV734 @ SV656 )
= $false )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3287,plain,
! [SV170: $i,SV688: $i,SV701: $i] :
( ( ( ~ ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3221]) ).
thf(3288,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3221]) ).
thf(3289,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3222]) ).
thf(3290,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3223]) ).
thf(3291,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3224]) ).
thf(3292,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3225]) ).
thf(3293,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3294,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
| ( SV495 = SV617 ) )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3295,plain,
! [SV179: $i,SV749: $i,SV367: $i > $o] :
( ( ( SV367 @ SV749 )
= $false )
| ( ( ~ ( in @ SV749 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3296,plain,
! [SV179: $i,SV760: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ SV760 ) )
= $true )
| ( ( ~ ( in @ SV760 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3297,plain,
! [SV647: $i,SV374: $i,SV742: $i,SV761: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV761 @ SV742 ) )
= $true )
| ( ( ~ ( in @ SV761 @ SV374 ) )
= $true )
| ( ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3298,plain,
! [SV647: $i,SV374: $i,SV743: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 )
| ~ ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3299,plain,
! [SV647: $i,SV374: $i,SV750: $i,SV767: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV767 @ SV750 )
| ~ ( in @ SV767 @ SV374 ) )
= $true )
| ( ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3300,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV751: $i] :
( ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( ~ ( ~ ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 )
| ~ ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 ) ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3301,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3302,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
| ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3236]) ).
thf(3303,plain,
! [SV204: $i,SV752: $i,SV387: $i > $o] :
( ( ( SV387 @ SV752 )
= $false )
| ( ( ~ ( in @ SV752 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3304,plain,
! [SV204: $i,SV762: $i,SV387: $i > $o] :
( ( ( ~ ( SV387 @ SV762 ) )
= $true )
| ( ( ~ ( in @ SV762 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3305,plain,
! [SV206: $i,SV389: $i,SV517: $i,SV629: $i] :
( ( ( in @ ( kpair @ ( sK82_Xx @ SV629 @ SV517 @ SV389 @ SV206 ) @ ( sK83_SY1676 @ SV629 @ SV517 @ SV389 @ SV206 ) ) @ SV629 )
= $false )
| ( ( subset @ SV517 @ SV629 )
= $true )
| ( ( subset @ SV629 @ ( cartprod @ SV206 @ SV389 ) )
= $false )
| ( ( subset @ SV517 @ ( cartprod @ SV206 @ SV389 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3306,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV753: $i] :
( ( ( in @ SV753 @ SV519 )
= $false )
| ( ( SV630 @ SV753 )
= $true )
| ( ( in @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) @ SV519 )
= $true )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3307,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV519 ) )
= $true )
| ( ( SV630 @ SV763 )
= $true )
| ( ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) )
= $false )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3308,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3309,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3244]) ).
thf(3310,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3245]) ).
thf(3311,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3245]) ).
thf(3312,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
| ~ ( ( SV754
!= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3313,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3247]) ).
thf(3314,plain,
! [SV552: $i > $o,SV575: $i > $o,SV736: $i] :
( ( ( SV736
!= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3315,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3316,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3317,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3318,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3319,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
| ~ ( ( SV755
!= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3320,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3253]) ).
thf(3321,plain,
! [SV553: $i > $o,SV576: $i > $o,SV737: $i] :
( ( ( SV737
!= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3254]) ).
thf(3322,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV756: $i] :
( ( ( in @ SV756 @ SV526 )
= $false )
| ( ( SV634 @ SV756 )
= $true )
| ( ( in @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) @ SV526 )
= $true )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3323,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV526 ) )
= $true )
| ( ( SV634 @ SV764 )
= $true )
| ( ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) )
= $false )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3324,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3257]) ).
thf(3325,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV738: $i] :
( ( ( SV738
!= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3258]) ).
thf(3326,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3327,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV745: $i] :
( ( ( ~ ( ( SV745
!= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3328,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3329,plain,
! [SV220: $i > $o,SV397: $i > $o,SV731: $i] :
( ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV220 @ SV731 ) )
= $true )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3330,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
| ~ ( ( SV768
!= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3331,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3332,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i,SV739: $i,SV714: $i] :
( ( ( in @ ( kpair @ SV714 @ SV739 ) @ SV614 )
= $false )
| ( ( in @ ( kpair @ SV714 @ SV739 ) @ SV490 )
= $true )
| ( ( in @ SV739 @ SV357 )
= $false )
| ( ( in @ SV714 @ SV166 )
= $false )
| ( ( in @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) @ SV166 )
= $true )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3333,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i,SV746: $i,SV723: $i] :
( ( ( ~ ( in @ ( kpair @ SV723 @ SV746 ) @ SV614 ) )
= $true )
| ( ( in @ ( kpair @ SV723 @ SV746 ) @ SV490 )
= $true )
| ( ( in @ SV746 @ SV357 )
= $false )
| ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3334,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3335,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV769: $o] :
( ( ( ~ SV769
| SV769 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3270]) ).
thf(3336,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3270]) ).
thf(3337,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3270]) ).
thf(3338,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV757: $o] :
( ( SV757 = $false )
| ( ( ( in @ SV492 @ SV359 )
| SV757 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3274]) ).
thf(3339,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $true = $false )
| ( ( ( in @ SV492 @ SV359 )
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3340,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $false = $false )
| ( ( ( in @ SV492 @ SV359 )
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3341,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV758: $o] :
( ( SV758 = $false )
| ( ( ~ SV758
| SV758 )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3342,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3343,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3344,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV741: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV741 )
| ( in @ SV770 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 )
= $true )
| ( ( in @ SV741 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3345,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3346,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3347,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
= $true )
| ( ( ~ ( in @ SV766 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3348,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV748: $i] :
( ( ( ! [SY2676: $i] :
( ~ ( in @ SY2676 @ SV748 )
| ( in @ SY2676 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 )
= $true )
| ( ( in @ SV748 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3349,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
| ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3350,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
| ~ ( in @ SV771 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(3351,plain,
! [SV170: $i,SV734: $i,SV656: $i,SV670: $i,SV759: $i] :
( ( ( in @ SV759 @ SV670 )
= $false )
| ( ( in @ SV759 @ SV656 )
= $true )
| ( ( in @ SV734 @ SV670 )
= $true )
| ( ( in @ SV734 @ SV656 )
= $false )
| ( ( in @ SV656 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ SV670 @ ( sK13_B @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3352,plain,
! [SV170: $i,SV688: $i,SV701: $i] :
( ( ( in @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) @ ( sK13_B @ SV170 ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3287]) ).
thf(3353,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3354,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3355,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3356,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3357,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3358,plain,
! [SV367: $i > $o,SV179: $i,SV749: $i] :
( ( ( in @ SV749 @ SV179 )
= $false )
| ( ( SV367 @ SV749 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( SV367 @ ( sK69_SY1672 @ SV367 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3359,plain,
! [SV179: $i,SV760: $i,SV367: $i > $o] :
( ( ( SV367 @ SV760 )
= $false )
| ( ( ~ ( in @ SV760 @ SV179 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3360,plain,
! [SV647: $i,SV374: $i,SV742: $i,SV761: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ SV761 @ SV742 )
= $false )
| ( ( ~ ( in @ SV761 @ SV374 ) )
= $true )
| ( ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3361,plain,
! [SV647: $i,SV374: $i,SV743: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 ) )
= $false )
| ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3298]) ).
thf(3362,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV743: $i] :
( ( ( ~ ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3298]) ).
thf(3363,plain,
! [SV647: $i,SV374: $i,SV750: $i,SV767: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ SV767 @ SV750 ) )
= $true )
| ( ( ~ ( in @ SV767 @ SV374 ) )
= $true )
| ( ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3299]) ).
thf(3364,plain,
! [SV647: $i,SV374: $i,SV751: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 )
| ~ ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3365,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( ~ ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
= $true )
| ( ( ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3366,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $true )
| ( ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3367,plain,
! [SV387: $i > $o,SV204: $i,SV752: $i] :
( ( ( in @ SV752 @ SV204 )
= $false )
| ( ( SV387 @ SV752 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( SV387 @ ( sK73_SY1673 @ SV387 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3368,plain,
! [SV204: $i,SV762: $i,SV387: $i > $o] :
( ( ( SV387 @ SV762 )
= $false )
| ( ( ~ ( in @ SV762 @ SV204 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3369,plain,
! [SV208: $i,SV390: $i,SV630: $i > $o,SV519: $i,SV763: $i] :
( ( ( in @ SV763 @ SV519 )
= $false )
| ( ( SV630 @ SV763 )
= $true )
| ( ( SV630 @ ( kpair @ ( sK77_Xx @ SV630 @ SV519 @ SV390 @ SV208 ) @ ( sK78_SY1674 @ SV630 @ SV519 @ SV390 @ SV208 ) ) )
= $false )
| ( ( subset @ SV519 @ ( cartprod @ SV208 @ SV390 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3370,plain,
! [SV692: $i,SV552: $i > $o,SV772: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV772 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV772 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3371,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3310]) ).
thf(3372,plain,
! [SV692: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3311]) ).
thf(3373,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( ~ ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) ) )
= $false )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3374,plain,
! [SV552: $i > $o,SV575: $i > $o,SV754: $i] :
( ( ( ~ ( ( SV754
!= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) ) ) )
= $false )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3375,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( SV552 @ SV736 )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3376,plain,
! [SV552: $i > $o,SV575: $i > $o,SV736: $i] :
( ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( SV552 @ SV736 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3377,plain,
! [SV693: $i,SV576: $i > $o,SV773: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV773 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV773 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3378,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3379,plain,
! [SV693: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3318]) ).
thf(3380,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( ~ ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) ) )
= $false )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3381,plain,
! [SV553: $i > $o,SV576: $i > $o,SV755: $i] :
( ( ( ~ ( ( SV755
!= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) ) ) )
= $false )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3382,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3383,plain,
! [SV553: $i > $o,SV576: $i > $o,SV737: $i] :
( ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( SV576 @ SV737 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3384,plain,
! [SV216: $i,SV394: $i,SV634: $i > $o,SV526: $i,SV764: $i] :
( ( ( in @ SV764 @ SV526 )
= $false )
| ( ( SV634 @ SV764 )
= $true )
| ( ( SV634 @ ( kpair @ ( sK79_Xx @ SV634 @ SV526 @ SV394 @ SV216 ) @ ( sK80_SY1675 @ SV634 @ SV526 @ SV394 @ SV216 ) ) )
= $false )
| ( ( subset @ SV526 @ ( cartprod @ SV216 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3385,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( SV397 @ SV738 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3386,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV738: $i] :
( ( ( SV738
= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV738 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3387,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3326]) ).
thf(3388,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV745: $i] :
( ( ( SV745
!= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3389,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3390,plain,
! [SV397: $i > $o,SV731: $i,SV220: $i > $o] :
( ( ( SV220 @ SV731 )
= $false )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) )
| ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3391,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
| ~ ( ( SV768
!= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3330]) ).
thf(3392,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
| ~ ( ( SV774
!= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3393,plain,
! [SV166: $i,SV357: $i,SV490: $i,SV614: $i,SV746: $i,SV723: $i] :
( ( ( in @ ( kpair @ SV723 @ SV746 ) @ SV614 )
= $false )
| ( ( in @ ( kpair @ SV723 @ SV746 ) @ SV490 )
= $true )
| ( ( in @ SV746 @ SV357 )
= $false )
| ( ( in @ SV723 @ SV166 )
= $false )
| ( ( ( ap @ SV166 @ SV357 @ SV490 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) )
= ( ap @ SV166 @ SV357 @ SV614 @ ( sK81_Xx @ SV614 @ SV490 @ SV357 @ SV166 ) ) )
= $false )
| ( ( func @ SV166 @ SV357 @ SV614 )
= $false )
| ( ( func @ SV166 @ SV357 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3394,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV775: $o] :
( ( SV775 = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3334]) ).
thf(3395,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $true = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3334]) ).
thf(3396,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $false = $true )
| ( ( in @ SV492 @ SV359 )
= $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3334]) ).
thf(3397,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV769: $o] :
( ( ( ~ SV769 ) = $true )
| ( SV769 = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3398,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3399,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3400,plain,
! [SV168: $i,SV757: $o,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $true )
| ( SV757 = $true )
| ( SV757 = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3401,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3402,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( ( in @ SV492 @ SV359 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3403,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV758: $o] :
( ( ( ~ SV758 ) = $true )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3404,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3405,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3406,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV741: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV741 ) )
= $true )
| ( ( in @ SV770 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 )
= $true )
| ( ( in @ SV741 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3407,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3345]) ).
thf(3408,plain,
! [SV686: $i,SV170: $i,SV570: $i] :
( ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3346]) ).
thf(3409,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV766: $i] :
( ( ( in @ SV766 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $false )
| ( ( ~ ( in @ SV766 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3410,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV748: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV748 )
| ( in @ SV776 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 )
= $true )
| ( ( in @ SV748 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3411,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3349]) ).
thf(3412,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( ~ ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3349]) ).
thf(3413,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( sK15_SY1637 @ SV570 @ SV170 ) ) )
= $true )
| ( ( ~ ( in @ SV771 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3350]) ).
thf(3414,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
| ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3415,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3354]) ).
thf(3416,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3354]) ).
thf(3417,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3355]) ).
thf(3418,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3355]) ).
thf(3419,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3356]) ).
thf(3420,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3356]) ).
thf(3421,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
| ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3422,plain,
! [SV367: $i > $o,SV179: $i,SV760: $i] :
( ( ( in @ SV760 @ SV179 )
= $false )
| ( ( SV367 @ SV760 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV179
@ ^ [SY2361: $i] : ( SV367 @ SY2361 ) ) )
= $true )
| ( ( ( sK68_Xx @ SV367 @ SV179 )
= ( sK69_SY1672 @ SV367 @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3423,plain,
! [SV647: $i,SV742: $i,SV187: $i > $i > $o,SV374: $i,SV761: $i] :
( ( ( in @ SV761 @ SV374 )
= $false )
| ( ( SV187 @ SV761 @ SV742 )
= $false )
| ( ( in @ SV742 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3424,plain,
! [SV647: $i,SV374: $i,SV743: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV743 )
= $true )
| ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3361]) ).
thf(3425,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV743: $i] :
( ( ( in @ ( sK9_Xy @ SV743 @ SV374 @ SV187 ) @ SV374 )
= $true )
| ( ( in @ SV743 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3426,plain,
! [SV647: $i,SV374: $i,SV750: $i,SV767: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ SV767 @ SV750 )
= $false )
| ( ( ~ ( in @ SV767 @ SV374 ) )
= $true )
| ( ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3363]) ).
thf(3427,plain,
! [SV647: $i,SV374: $i,SV751: $i,SV187: $i > $i > $o] :
( ( ( ~ ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 ) )
= $false )
| ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3428,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV751: $i] :
( ( ( ~ ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 ) )
= $false )
| ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3429,plain,
! [SV196: $i,SV381: $i,SV622: $i > $o,SV572: $i > $o] :
( ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $false )
| ( ( ~ ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) ) )
= $true )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3430,plain,
! [SV387: $i > $o,SV204: $i,SV762: $i] :
( ( ( in @ SV762 @ SV204 )
= $false )
| ( ( SV387 @ SV762 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV204
@ ^ [SY2399: $i] : ( SV387 @ SY2399 ) ) )
= $true )
| ( ( ( sK72_Xx @ SV387 @ SV204 )
= ( sK73_SY1673 @ SV387 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3431,plain,
! [SV692: $i,SV552: $i > $o,SV772: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV772 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV772 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3370]) ).
thf(3432,plain,
! [SV692: $i,SV552: $i > $o,SV777: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV777 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV777 ) )
= $true )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3433,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3373]) ).
thf(3434,plain,
! [SV552: $i > $o,SV575: $i > $o,SV754: $i] :
( ( ( SV754
!= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3374]) ).
thf(3435,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3375]) ).
thf(3436,plain,
! [SV575: $i > $o,SV736: $i,SV552: $i > $o] :
( ( ( SV552 @ SV736 )
= $false )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3437,plain,
! [SV693: $i,SV576: $i > $o,SV773: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV773 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV773 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3438,plain,
! [SV693: $i,SV576: $i > $o,SV778: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV778 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV778 ) )
= $true )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3439,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3380]) ).
thf(3440,plain,
! [SV553: $i > $o,SV576: $i > $o,SV755: $i] :
( ( ( SV755
!= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3381]) ).
thf(3441,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3442,plain,
! [SV553: $i > $o,SV737: $i,SV576: $i > $o] :
( ( ( SV576 @ SV737 )
= $false )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3443,plain,
! [SV665: $i,SV220: $i > $o,SV738: $i,SV397: $i > $o] :
( ( ( SV397 @ SV738 )
= $false )
| ( ( SV738
= ( sK56_SY258 @ SV738 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3444,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( SV397 @ SV745 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3445,plain,
! [SV665: $i,SV220: $i > $o,SV397: $i > $o,SV745: $i] :
( ( ( SV745
= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV745 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3388]) ).
thf(3446,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
| ~ ( ( SV779
!= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3447,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o] :
( ( ( ! [SY2422: $i] :
( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) )
| ~ ( ( SY2422
!= ( sK56_SY258 @ SY2422 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SY2422 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3448,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
| ~ ( ( SV768
!= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3449,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
| ~ ( ( SV774
!= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3450,plain,
! [SV168: $i,SV359: $i,SV492: $i,SV769: $o] :
( ( SV769 = $false )
| ( SV769 = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3451,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3452,plain,
! [SV168: $i,SV359: $i,SV492: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV492 @ SV359 )
= $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3453,plain,
! [SV359: $i,SV168: $i,SV492: $i,SV758: $o] :
( ( SV758 = $false )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3454,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3455,plain,
! [SV359: $i,SV168: $i,SV492: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV492 @ ( symdiff @ SV168 @ SV359 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3456,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV741: $i,SV770: $i] :
( ( ( in @ SV770 @ SV741 )
= $false )
| ( ( in @ SV770 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV741 )
= $true )
| ( ( in @ SV741 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(3457,plain,
! [SV686: $i,SV170: $i,SV570: $i,SV766: $i] :
( ( ( in @ SV766 @ SV570 )
= $false )
| ( ( in @ SV766 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ SV686 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3458,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV748: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV748 ) )
= $true )
| ( ( in @ SV776 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 )
= $true )
| ( ( in @ SV748 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3410]) ).
thf(3459,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( in @ ( sK15_SY1637 @ SV570 @ SV170 ) @ ( sK13_B @ SV170 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3411]) ).
thf(3460,plain,
! [SV700: $i,SV170: $i,SV570: $i] :
( ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV570 )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3412]) ).
thf(3461,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV771: $i] :
( ( ( in @ SV771 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $false )
| ( ( ~ ( in @ SV771 @ SV570 ) )
= $true )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3462,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3463,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3414]) ).
thf(3464,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3415]) ).
thf(3465,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3416]) ).
thf(3466,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3417]) ).
thf(3467,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3418]) ).
thf(3468,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3469,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3420]) ).
thf(3470,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3421]) ).
thf(3471,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3421]) ).
thf(3472,plain,
! [SV647: $i,SV750: $i,SV187: $i > $i > $o,SV374: $i,SV767: $i] :
( ( ( in @ SV767 @ SV374 )
= $false )
| ( ( SV187 @ SV767 @ SV750 )
= $false )
| ( ( in @ SV750 @ ( sK8_B @ SV374 @ SV187 ) )
= $true )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3473,plain,
! [SV647: $i,SV374: $i,SV751: $i,SV187: $i > $i > $o] :
( ( ( SV187 @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV751 )
= $true )
| ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3427]) ).
thf(3474,plain,
! [SV647: $i,SV187: $i > $i > $o,SV374: $i,SV751: $i] :
( ( ( in @ ( sK9_Xy @ SV751 @ SV374 @ SV187 ) @ SV374 )
= $true )
| ( ( in @ SV751 @ ( sK8_B @ SV374 @ SV187 ) )
= $false )
| ( ( SV647
= ( sK11_SY1632 @ SV647 @ SV374 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK10_SY22 @ SV374 @ SV187 ) @ SV647 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3475,plain,
! [SV196: $i,SV381: $i,SV572: $i > $o,SV622: $i > $o] :
( ( ( SV622 @ ( sK61_SY1670 @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $false )
| ( ( SV572 @ ( sK60_Xx @ SV622 @ SV572 @ SV381 @ SV196 ) )
= $false )
| ( ( ( dsetconstr @ SV196
@ ^ [SY2603: $i] : ( SV572 @ SY2603 ) )
= ( dsetconstr @ SV381
@ ^ [SY2628: $i] : ( SV622 @ SY2628 ) ) )
= $true )
| ( ( SV196 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3476,plain,
! [SV692: $i,SV552: $i > $o,SV772: $i,SV575: $i > $o] :
( ( ( SV575 @ SV772 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV772 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3477,plain,
! [SV692: $i,SV552: $i > $o,SV777: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV777 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV777 )
= $true )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3478,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3479,plain,
! [SV552: $i > $o,SV575: $i > $o,SV754: $i] :
( ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( SV552 @ SV754 ) )
= $true )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3480,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3435]) ).
thf(3481,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3435]) ).
thf(3482,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3483,plain,
! [SV693: $i,SV576: $i > $o,SV773: $i,SV553: $i > $o] :
( ( ( SV553 @ SV773 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV773 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3484,plain,
! [SV693: $i,SV576: $i > $o,SV778: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV778 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV778 )
= $true )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3438]) ).
thf(3485,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( SV576 @ SV755 )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3486,plain,
! [SV553: $i > $o,SV576: $i > $o,SV755: $i] :
( ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( SV576 @ SV755 ) )
= $true )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3487,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3488,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3489,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3490,plain,
! [SV665: $i,SV220: $i > $o,SV745: $i,SV397: $i > $o] :
( ( ( SV397 @ SV745 )
= $false )
| ( ( SV745
= ( sK56_SY258 @ SV745 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV665
= ( sK57_SY255 @ SV665 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV665 )
= $false )
| ( ( ( sK58_Xx @ SV397 @ SV220 )
= ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3491,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
| ~ ( ( SV779
!= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3492,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
| ~ ( ( SV780
!= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) ) ) )
| ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(3493,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3448]) ).
thf(3494,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV768: $i] :
( ( ( ~ ( ( SV768
!= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3448]) ).
thf(3495,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
| ~ ( ( SV774
!= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(3496,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV748: $i,SV776: $i] :
( ( ( in @ SV776 @ SV748 )
= $false )
| ( ( in @ SV776 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $true )
| ( ( in @ ( sK16_SY1651 @ SV570 @ SV170 ) @ SV748 )
= $true )
| ( ( in @ SV748 @ ( sK13_B @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3497,plain,
! [SV700: $i,SV170: $i,SV570: $i,SV771: $i] :
( ( ( in @ SV771 @ SV570 )
= $false )
| ( ( in @ SV771 @ ( sK15_SY1637 @ SV570 @ SV170 ) )
= $false )
| ( ( in @ ( sK17_Xx @ SV570 @ SV170 ) @ SV170 )
= $false )
| ( ( in @ SV700 @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3498,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3462]) ).
thf(3499,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
| ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3463]) ).
thf(3500,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3501,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3467]) ).
thf(3502,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3503,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV176 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3470]) ).
thf(3504,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3471]) ).
thf(3505,plain,
! [SV692: $i,SV552: $i > $o,SV777: $i,SV575: $i > $o] :
( ( ( SV575 @ SV777 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV777 )
= $true )
| ( ( SV692
= ( sK52_SY231 @ SV692 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV692 )
= $false )
| ( ( ( sK53_Xx @ SV575 @ SV552 )
= ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3506,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3507,plain,
! [SV575: $i > $o,SV754: $i,SV552: $i > $o] :
( ( ( SV552 @ SV754 )
= $false )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( ~ ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3508,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3480]) ).
thf(3509,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3481]) ).
thf(3510,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3482]) ).
thf(3511,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3482]) ).
thf(3512,plain,
! [SV693: $i,SV576: $i > $o,SV778: $i,SV553: $i > $o] :
( ( ( SV553 @ SV778 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV778 )
= $true )
| ( ( SV693
= ( sK48_SY234 @ SV693 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV693 )
= $false )
| ( ( ( sK49_Xx @ SV576 @ SV553 )
= ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3513,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3514,plain,
! [SV553: $i > $o,SV755: $i,SV576: $i > $o] :
( ( ( SV576 @ SV755 )
= $false )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( ~ ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3515,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3516,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3517,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3518,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3519,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
| ~ ( ( SV779
!= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3520,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( ~ ( ~ ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
| ~ ( ( SV780
!= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) ) ) ) )
= $true )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3521,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3493]) ).
thf(3522,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV768: $i] :
( ( ( SV768
!= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3494]) ).
thf(3523,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3495]) ).
thf(3524,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV774: $i] :
( ( ( ~ ( ( SV774
!= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3495]) ).
thf(3525,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
= $true )
| ( ( ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3498]) ).
thf(3526,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
= $true )
| ( ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(3527,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3501]) ).
thf(3528,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3501]) ).
thf(3529,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3530,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3531,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3532,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3533,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3534,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) )
| ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3535,plain,
! [SV736: $i,SV552: $i > $o,SV781: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV781 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV781 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3536,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3510]) ).
thf(3537,plain,
! [SV736: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3511]) ).
thf(3538,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3513]) ).
thf(3539,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3513]) ).
thf(3540,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) )
| ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3541,plain,
! [SV737: $i,SV576: $i > $o,SV782: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV782 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV782 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(3542,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3517]) ).
thf(3543,plain,
! [SV737: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3518]) ).
thf(3544,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3519]) ).
thf(3545,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV779: $i] :
( ( ( ~ ( ( SV779
!= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3519]) ).
thf(3546,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
| ~ ( ( SV780
!= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3547,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( SV397 @ SV768 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3548,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV768: $i] :
( ( ( SV768
= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV768 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3549,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3523]) ).
thf(3550,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV774: $i] :
( ( ( SV774
!= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3524]) ).
thf(3551,plain,
! [SV170: $i,SV701: $i,SV688: $i] :
( ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
= $false )
| ( ( ~ ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) ) )
= $true )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3525]) ).
thf(3552,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3527]) ).
thf(3553,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3554,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3529]) ).
thf(3555,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3530]) ).
thf(3556,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3531]) ).
thf(3557,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3531]) ).
thf(3558,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3559,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3533]) ).
thf(3560,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $false )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3534]) ).
thf(3561,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ~ ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) ) )
= $false )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3534]) ).
thf(3562,plain,
! [SV736: $i,SV552: $i > $o,SV781: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV781 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV781 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(3563,plain,
! [SV736: $i,SV552: $i > $o,SV783: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV783 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV783 ) )
= $true )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(3564,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3538]) ).
thf(3565,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3539]) ).
thf(3566,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $false )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3567,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ~ ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) ) )
= $false )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3568,plain,
! [SV737: $i,SV576: $i > $o,SV782: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV782 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV782 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3569,plain,
! [SV737: $i,SV576: $i > $o,SV784: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV784 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV784 ) )
= $true )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(3570,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3544]) ).
thf(3571,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV779: $i] :
( ( ( SV779
!= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3545]) ).
thf(3572,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( ~ ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) ) )
= $false )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3573,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV780: $i] :
( ( ( ~ ( ( SV780
!= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) ) ) )
= $false )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3574,plain,
! [SV712: $i,SV220: $i > $o,SV768: $i,SV397: $i > $o] :
( ( ( SV397 @ SV768 )
= $false )
| ( ( SV768
= ( sK56_SY258 @ SV768 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3575,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( SV397 @ SV774 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3576,plain,
! [SV712: $i,SV220: $i > $o,SV397: $i > $o,SV774: $i] :
( ( ( SV774
= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV774 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3577,plain,
! [SV170: $i,SV688: $i,SV701: $i] :
( ( ( in @ SV701 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
= $false )
| ( ( in @ SV688 @ ( sK14_SY1650 @ SV701 @ SV688 @ SV170 ) )
= $false )
| ( ( SV688 = SV701 )
= $true )
| ( ( in @ SV688 @ SV170 )
= $false )
| ( ( in @ SV701 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3578,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3553]) ).
thf(3579,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3580,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) @ SV364 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3556]) ).
thf(3581,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3557]) ).
thf(3582,plain,
! [SV754: $i,SV552: $i > $o,SV785: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV785 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV785 ) )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(3583,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( ! [SY2607: $i] :
( ~ ( SV575 @ SY2607 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SY2607 ) ) )
= $true )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3560]) ).
thf(3584,plain,
! [SV754: $i,SV552: $i > $o,SV575: $i > $o] :
( ( ( SV575 @ ( sK51_SY233 @ SV575 @ SV552 ) )
= $true )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(3585,plain,
! [SV736: $i,SV552: $i > $o,SV781: $i,SV575: $i > $o] :
( ( ( SV575 @ SV781 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV781 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3586,plain,
! [SV736: $i,SV552: $i > $o,SV783: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV783 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV783 )
= $true )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3563]) ).
thf(3587,plain,
! [SV755: $i,SV576: $i > $o,SV786: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV786 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV786 ) )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(3588,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( ! [SY2609: $i] :
( ~ ( SV553 @ SY2609 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SY2609 ) ) )
= $true )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3566]) ).
thf(3589,plain,
! [SV755: $i,SV576: $i > $o,SV553: $i > $o] :
( ( ( SV553 @ ( sK47_SY230 @ SV576 @ SV553 ) )
= $true )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3590,plain,
! [SV737: $i,SV576: $i > $o,SV782: $i,SV553: $i > $o] :
( ( ( SV553 @ SV782 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV782 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3568]) ).
thf(3591,plain,
! [SV737: $i,SV576: $i > $o,SV784: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV784 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV784 )
= $true )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(3592,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( SV397 @ SV779 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3593,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV779: $i] :
( ( ( SV779
= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV779 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3571]) ).
thf(3594,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3572]) ).
thf(3595,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV780: $i] :
( ( ( SV780
!= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
= $true )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3573]) ).
thf(3596,plain,
! [SV712: $i,SV220: $i > $o,SV774: $i,SV397: $i > $o] :
( ( ( SV397 @ SV774 )
= $false )
| ( ( SV774
= ( sK56_SY258 @ SV774 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV712
= ( sK57_SY255 @ SV712 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV712 )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3597,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3598,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3599,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
| ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3581]) ).
thf(3600,plain,
! [SV754: $i,SV552: $i > $o,SV785: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV785 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV785 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3601,plain,
! [SV754: $i,SV552: $i > $o,SV787: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV787 )
| ( ( sK51_SY233 @ SV575 @ SV552 )
= SV787 ) )
= $true )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(3602,plain,
! [SV736: $i,SV552: $i > $o,SV783: $i,SV575: $i > $o] :
( ( ( SV575 @ SV783 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV783 )
= $true )
| ( ( SV736
= ( sK52_SY231 @ SV736 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV736 )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3603,plain,
! [SV755: $i,SV576: $i > $o,SV786: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV786 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV786 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3604,plain,
! [SV755: $i,SV576: $i > $o,SV788: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV788 )
| ( ( sK47_SY230 @ SV576 @ SV553 )
= SV788 ) )
= $true )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(3605,plain,
! [SV737: $i,SV576: $i > $o,SV784: $i,SV553: $i > $o] :
( ( ( SV553 @ SV784 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV784 )
= $true )
| ( ( SV737
= ( sK48_SY234 @ SV737 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV737 )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $true )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3606,plain,
! [SV731: $i,SV220: $i > $o,SV779: $i,SV397: $i > $o] :
( ( ( SV397 @ SV779 )
= $false )
| ( ( SV779
= ( sK56_SY258 @ SV779 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV220 @ ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $true )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3607,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( SV397 @ SV780 )
= $false )
| ( ( SV397 @ ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3608,plain,
! [SV731: $i,SV220: $i > $o,SV397: $i > $o,SV780: $i] :
( ( ( SV780
= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
= $false )
| ( ( ~ ( SV397 @ SV780 ) )
= $true )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3595]) ).
thf(3609,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3610,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3598]) ).
thf(3611,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3599]) ).
thf(3612,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3599]) ).
thf(3613,plain,
! [SV754: $i,SV552: $i > $o,SV785: $i,SV575: $i > $o] :
( ( ( SV575 @ SV785 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV785 )
= $true )
| ( ( SV552 @ ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $true )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3600]) ).
thf(3614,plain,
! [SV754: $i,SV552: $i > $o,SV787: $i,SV575: $i > $o] :
( ( ( ~ ( SV575 @ SV787 ) )
= $true )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV787 )
= $true )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(3615,plain,
! [SV755: $i,SV576: $i > $o,SV786: $i,SV553: $i > $o] :
( ( ( SV553 @ SV786 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV786 )
= $true )
| ( ( SV576 @ ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $true )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(3616,plain,
! [SV755: $i,SV576: $i > $o,SV788: $i,SV553: $i > $o] :
( ( ( ~ ( SV553 @ SV788 ) )
= $true )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV788 )
= $true )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(3617,plain,
! [SV731: $i,SV220: $i > $o,SV780: $i,SV397: $i > $o] :
( ( ( SV397 @ SV780 )
= $false )
| ( ( SV780
= ( sK56_SY258 @ SV780 @ SV397 @ SV220 ) )
= $false )
| ( ( ( descr
@ ^ [SY2168: $i] : ( SV220 @ SY2168 ) )
= ( descr
@ ^ [SY2424: $i] : ( SV397 @ SY2424 ) ) )
= $true )
| ( ( SV731
= ( sK57_SY255 @ SV731 @ SV397 @ SV220 ) )
= $false )
| ( ( SV220 @ SV731 )
= $false )
| ( ( SV220 @ ( sK58_Xx @ SV397 @ SV220 ) )
= $false )
| ( ( SV397 @ ( sK59_SY1669 @ SV397 @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3618,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $true )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3619,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(3620,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 ) )
= $true )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3612]) ).
thf(3621,plain,
! [SV754: $i,SV552: $i > $o,SV787: $i,SV575: $i > $o] :
( ( ( SV575 @ SV787 )
= $false )
| ( ( ( sK51_SY233 @ SV575 @ SV552 )
= SV787 )
= $true )
| ( ( SV754
= ( sK52_SY231 @ SV754 @ SV575 @ SV552 ) )
= $false )
| ( ( SV552 @ SV754 )
= $false )
| ( ( SV552 @ ( sK53_Xx @ SV575 @ SV552 ) )
= $false )
| ( ( SV575 @ ( sK54_SY1668 @ SV575 @ SV552 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3622,plain,
! [SV755: $i,SV576: $i > $o,SV788: $i,SV553: $i > $o] :
( ( ( SV553 @ SV788 )
= $false )
| ( ( ( sK47_SY230 @ SV576 @ SV553 )
= SV788 )
= $true )
| ( ( SV755
= ( sK48_SY234 @ SV755 @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ SV755 )
= $false )
| ( ( SV553 @ ( sK49_Xx @ SV576 @ SV553 ) )
= $false )
| ( ( SV576 @ ( sK50_SY1666 @ SV576 @ SV553 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(3623,plain,
! [SV176: $i,SV364: $i,SV495: $i,SV617: $i] :
( ( ( in @ ( kpair @ ( sK84_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK85_SY1677 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV495 )
= $false )
| ( ( SV495 = SV617 )
= $true )
| ( ( in @ ( kpair @ ( sK86_Xx @ SV617 @ SV495 @ SV364 @ SV176 ) @ ( sK87_SY1678 @ SV617 @ SV495 @ SV364 @ SV176 ) ) @ SV617 )
= $false )
| ( ( subset @ SV617 @ ( cartprod @ SV176 @ SV364 ) )
= $false )
| ( ( subset @ SV495 @ ( cartprod @ SV176 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3620]) ).
thf(3624,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[587,3623,3622,3621,3619,3618,3617,3615,3613,3609,3607,3606,3605,3602,3596,3592,3590,3589,3585,3584,3580,3578,3577,3575,3574,3565,3559,3554,3552,3547,3543,3537,3526,3516,3512,3509,3505,3503,3500,3497,3496,3490,3483,3476,3475,3474,3473,3472,3468,3466,3464,3460,3459,3457,3456,3455,3454,3453,3452,3451,3450,3444,3443,3430,3425,3424,3423,3422,3408,3407,3402,3401,3400,3396,3395,3394,3393,3385,3384,3379,3372,3369,3367,3366,3358,3352,3351,3332,3322,3316,3309,3306,3305,3291,3289,3273,3272,3271,3268,3267,3266,3239,3234,3201,3200,3199,3174,3171,3164,3141,3140,3139,3131,3130,3129,3126,3115,3109,3106,3105,3104,3093,3091,3063,3062,3061,3060,3059,3058,3054,3053,3052,3039,3035,3032,3031,3025,3024,3023,3022,3021,3020,3015,3014,3013,3012,2997,2988,2987,2986,2983,2969,2968,2967,2962,2961,2944,2942,2939,2936,2934,2924,2923,2922,2914,2910,2899,2888,2887,2882,2881,2880,2867,2862,2860,2859,2850,2842,2835,2813,2796,2795,2791,2790,2784,2782,2780,2763,2749,2736,2721,2714,2708,2697,2668,2659,2654,2650,2648,2642,2630,2629,2625,2624,2620,2619,2616,2615,2605,2593,2591,2590,2586,2585,2584,2583,2582,2581,2574,2573,2563,2557,2556,2546,2540,2539,2538,2537,2536,2534,2527,2521,2520,2513,2512,2506,2505,2500,2496,2476,2470,2469,2468,2457,2455,2453,2444,2443,2442,2426,2419,2418,2411,2408,2407,2406,2400,2380,2371,2369,2344,2343,2342,2303,2295,2293,2285,2284,2283,2282,2261,2246,2231,2225,2224,2222,2221,2220,2219,2218,2217,2216,2215,2214,2213,2212,2211,2208,2207,2206,2205,2203,2202,2199,2198,2197,2196,2195,2188,2187,2186,2170,2155,2144,2141,2133,2115,2104,2101,2100,2093,2091,2090,2079,2075,2069,2067,2066,2062,2061,2060,2059,2058,2057,2056,2042,2041,2040,2016,2015,1999,1946,1935,1916,1915,1907,1896,1893,1884,1883,1880,1879,1878,1877,1876,1875,1874,1872,1871,1864,1863,1861,1860,1859,1858,1835,1725,1724,1722,1721,1708,1706,1705,1701,1700,1698,1694,1688,1680,1679,1678,1674,1671,1665,1656,1654,1646,1645,1547,1546,1545,1544,1543,1542,1535,1534,1533,1532,1531,1528,1525,1524,1523,1522,1518,1514,1512,1511,1510,1503,1502,1500,1499,1495,1490,1485,1484,1474,1469,1468,1421,1347,1341,1319,1318,1317,1316,1315,1314,1298,1283,1256,1255,1245,1244,1235,1234,1122,1113,1112,1111,1110,1109,1106,1100,1094,1093,1072,1064,1063,1061,1058,1057,1053,1049,1037,1031,1030,1029,1028,1027,1011,1000,872,871,870,844,838,829,778,777,776,653,629,591]) ).
thf(3625,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU713^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.18 % Computer : n019.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 15:33:01 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.03/12.09 .
% 71.03/12.09
% 71.03/12.09 No.of.Axioms: 0
% 71.03/12.09
% 71.03/12.09 Length.of.Defs: 51724
% 71.03/12.09
% 71.03/12.09 Contains.Choice.Funs: true
% 71.03/12.09 ..........................................................................................................................................................
% 71.03/12.09
% 71.03/12.09 ********************************
% 71.03/12.09 * All subproblems solved! *
% 71.03/12.09 ********************************
% 71.03/12.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:229,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3624,loop_count:0,foatp_calls:1,translation:fof_full)
% 71.03/12.09
% 71.03/12.09 %**** Beginning of derivation protocol ****
% 71.03/12.09 % SZS output start CNFRefutation
% See solution above
% 71.03/12.10
% 71.03/12.10 %**** End of derivation protocol ****
% 71.03/12.10 %**** no. of clauses in derivation: 3625 ****
% 71.03/12.10 %**** clause counter: 3624 ****
% 71.03/12.10
% 71.03/12.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:229,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3624,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------