%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU682^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:46:13 AM UTC 2026
% Result : Theorem 94.57s 19.33s
% Output : CNFRefutation 94.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 207
% Syntax : Number of formulae : 3378 (1389 unt; 0 typ; 206 def)
% Number of atoms : 26770 (10606 equ; 0 cnn)
% Maximal formula atoms : 203 ( 7 avg)
% Number of connectives : 65928 (9598 ~;9741 |; 426 &;44604 @)
% ( 42 <=>;1517 =>; 0 <=; 0 <~>)
% Maximal formula depth : 214 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1963 (1963 >; 0 *; 0 +; 0 <<)
% Number of symbols : 333 ( 330 usr; 206 con; 0-4 aty)
% Number of variables : 13711 (1877 ^;11672 !; 162 ?;13711 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
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_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_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_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $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_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $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_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcinfuncset,type,
funcinfuncset: $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_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_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_B,type,
sK10_B: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_Xy,type,
sK11_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK12_SY29,type,
sK12_SY29: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK13_SY1613,type,
sK13_SY1613: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_B,type,
sK15_B: $i > $i ).
thf(tp_sK16_SY1631,type,
sK16_SY1631: $i > $i > $i > $i ).
thf(tp_sK17_SY1618,type,
sK17_SY1618: $i > $i > $i ).
thf(tp_sK18_SY1632,type,
sK18_SY1632: $i > $i > $i ).
thf(tp_sK19_Xx,type,
sK19_Xx: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK20_SY62,type,
sK20_SY62: $i > ( $i > $o ) > $i ).
thf(tp_sK21_Xx,type,
sK21_Xx: ( $i > $o ) > $i ).
thf(tp_sK22_SY79,type,
sK22_SY79: $i > ( $i > $o ) > $i ).
thf(tp_sK23_Xx,type,
sK23_Xx: ( $i > $o ) > $i ).
thf(tp_sK24_SY91,type,
sK24_SY91: $i > ( $i > $o ) > $i ).
thf(tp_sK25_Xx,type,
sK25_Xx: $i > $i > $i ).
thf(tp_sK26_Xx,type,
sK26_Xx: $i > $i > $i ).
thf(tp_sK27_Xx,type,
sK27_Xx: $i > $i ).
thf(tp_sK28_Xx,type,
sK28_Xx: $i > $i ).
thf(tp_sK29_Xx,type,
sK29_Xx: $i > $i ).
thf(tp_sK2_SY1590,type,
sK2_SY1590: $i ).
thf(tp_sK30_Xx,type,
sK30_Xx: $i > $i > $i ).
thf(tp_sK31_B,type,
sK31_B: $o > $i > $i > $i ).
thf(tp_sK32_Xx,type,
sK32_Xx: ( $i > $o ) > $i ).
thf(tp_sK33_SY147,type,
sK33_SY147: $i > ( $i > $o ) > $i ).
thf(tp_sK34_Xx,type,
sK34_Xx: $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_Xx,type,
sK39_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK3_SY1596,type,
sK3_SY1596: $i ).
thf(tp_sK40_Xx,type,
sK40_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK41_SY203,type,
sK41_SY203: ( $i > $o ) > $i ).
thf(tp_sK42_Xy,type,
sK42_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY210,type,
sK43_SY210: ( $i > $o ) > $i ).
thf(tp_sK44_Xx,type,
sK44_Xx: ( $i > $o ) > $i ).
thf(tp_sK45_SY1644,type,
sK45_SY1644: ( $i > $o ) > $i ).
thf(tp_sK46_SY216,type,
sK46_SY216: ( $i > $o ) > $i ).
thf(tp_sK47_Xy,type,
sK47_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY229,type,
sK48_SY229: $i > ( $i > $o ) > $i ).
thf(tp_sK49_SY237,type,
sK49_SY237: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK4_SY1601,type,
sK4_SY1601: $i > $o ).
thf(tp_sK50_SY241,type,
sK50_SY241: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK51_Xx,type,
sK51_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK52_SY1647,type,
sK52_SY1647: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK53_SY240,type,
sK53_SY240: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK54_SY238,type,
sK54_SY238: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK55_Xx,type,
sK55_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK56_SY1649,type,
sK56_SY1649: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK57_SY253,type,
sK57_SY253: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY265,type,
sK58_SY265: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK59_SY262,type,
sK59_SY262: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK5_SY1607,type,
sK5_SY1607: $i ).
thf(tp_sK60_Xx,type,
sK60_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK61_SY1650,type,
sK61_SY1650: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK62_Xx,type,
sK62_Xx: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK63_SY1651,type,
sK63_SY1651: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK64_Xx,type,
sK64_Xx: $i > $i > $i ).
thf(tp_sK65_Xx,type,
sK65_Xx: $i > $i > $i ).
thf(tp_sK66_Xx,type,
sK66_Xx: $i > $i > $i ).
thf(tp_sK67_Xx,type,
sK67_Xx: $i > $i > $i > $i ).
thf(tp_sK68_SY1652,type,
sK68_SY1652: $i > $i > $i > $i ).
thf(tp_sK69_X,type,
sK69_X: $i > $i > $i ).
thf(tp_sK6_Xx,type,
sK6_Xx: $i > $i > $i ).
thf(tp_sK70_SY484,type,
sK70_SY484: ( $i > $o ) > $i > $i ).
thf(tp_sK71_Xx,type,
sK71_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK72_SY1655,type,
sK72_SY1655: ( $i > $o ) > $i > $i ).
thf(tp_sK73_Xx,type,
sK73_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK74_SY503,type,
sK74_SY503: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK75_Xy,type,
sK75_Xy: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK76_SY515,type,
sK76_SY515: ( $i > $o ) > $i > $i ).
thf(tp_sK77_Xx,type,
sK77_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK78_SY1660,type,
sK78_SY1660: ( $i > $o ) > $i > $i ).
thf(tp_sK79_SY525,type,
sK79_SY525: $i > $i ).
thf(tp_sK7_Xx,type,
sK7_Xx: $i > $i > $i ).
thf(tp_sK80_SY562,type,
sK80_SY562: $i > $i ).
thf(tp_sK81_SY667,type,
sK81_SY667: $i > $i > $i > $i > $i ).
thf(tp_sK82_SY661,type,
sK82_SY661: $i > $i > $i > $i ).
thf(tp_sK83_SY689,type,
sK83_SY689: $i > $i > $i > $i ).
thf(tp_sK84_SY716,type,
sK84_SY716: $i > $i > $i > $i ).
thf(tp_sK85_SY753,type,
sK85_SY753: $i > $i > $i > $i > $i ).
thf(tp_sK86_SY791,type,
sK86_SY791: $i > $i > $i > $i ).
thf(tp_sK87_Xx,type,
sK87_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK88_SY820,type,
sK88_SY820: $i > ( $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 ).
thf(tp_sK90_Xx,type,
sK90_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK91_SY856,type,
sK91_SY856: $i > ( $i > $i ) > $i > $i > $i ).
thf(tp_sK92_Xx,type,
sK92_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK93_Xx,type,
sK93_Xx: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK94_Xx,type,
sK94_Xx: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK95_SY1693,type,
sK95_SY1693: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK9_Xx,type,
sK9_Xx: $i > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $o ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_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_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_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(ap,definition,
( ap
= ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap) ).
thf(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairsurjEq,definition,
( cartprodpairsurjEq
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dpsetconstrEL1,definition,
( dpsetconstrEL1
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,definition,
( dpsetconstrEL2
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrERa,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,definition,
( dpsetconstrSub
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(func,definition,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam,definition,
( lam
= ( ^ [A: $i,B: $i,Xf: $i > $i] :
( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY27: $i > $i > $o,SY28: $i] :
( ! [SY29: $i] :
( ( in @ SY29 @ SY28 )
=> ? [SY31: $i] :
( ( SY27 @ SY29 @ SY31 )
& ! [SY32: $i] :
( ( SY27 @ SY29 @ SY32 )
=> ( SY31 = SY32 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY28 )
& ( SY27 @ 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 ) ) ) ) ) )
=> ( ! [SY59: $i > $o] :
( ? [SY61: $i] :
( ( SY59 @ SY61 )
& ! [SY62: $i] :
( ( SY59 @ SY62 )
=> ( SY61 = SY62 ) ) )
=> ( SY59
@ ( descr
@ ^ [Xx: $i] : ( SY59 @ 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 ) )
=> ( ! [SY76: $i > $o] :
( ? [SY78: $i] :
( ( SY76 @ SY78 )
& ! [SY79: $i] :
( ( SY76 @ SY79 )
=> ( SY78 = SY79 ) ) )
=> ? [Xx: $i] :
( ( SY76 @ Xx )
& ! [Xy: $i] :
( ( SY76 @ 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 )
=> ( ! [SY88: $i > $o] :
( ? [SY90: $i] :
( ( SY88 @ SY90 )
& ! [SY91: $i] :
( ( SY88 @ SY91 )
=> ( SY90 = SY91 ) ) )
=> ? [Xx: $i] : ( SY88 @ 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 ) ) )
=> ( ! [SY105: $i] :
( ( SY105 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY105 ) )
=> ( ! [SY107: $i,SY108: $i > $o,SY109: $i] :
( ( in @ SY109 @ SY107 )
=> ( ( SY108 @ SY109 )
=> ( ( dsetconstr @ SY107
@ ^ [Xy: $i] : ( SY108 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY111: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY111 )
=> ( SY111 != 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 ) ) ) )
=> ( ! [SY144: $i > $o] :
( ? [SY146: $i] :
( ( SY144 @ SY146 )
& ! [SY147: $i] :
( ( SY144 @ SY147 )
=> ( SY146 = SY147 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY144 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY150: $i] :
( ( SY150 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY150 )
& $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 ) ) )
=> ( ! [SY199: $i > $o] :
( ? [Xx: $i] :
( ( SY199 @ Xx )
& ! [Xy: $i] :
( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY199 @ SY203 )
& ! [SY204: $i] :
( ( SY199 @ SY204 )
=> ( SY203 = SY204 ) ) ) )
=> ( ! [SY205: $i > $o] :
( ? [Xx: $i] : ( SY205 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY205 @ Xx )
=> ( ( SY205 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY210: $i] :
( ( SY205 @ SY210 )
& ! [SY211: $i] :
( ( SY205 @ SY211 )
=> ( SY210 = SY211 ) ) ) ) )
=> ( ! [SY212: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY212 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY216: $i] :
( ( SY212 @ SY216 )
& ! [SY217: $i] :
( ( SY212 @ SY217 )
=> ( SY216 = SY217 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [SY226: $i > $o] :
( ? [SY228: $i] :
( ( SY226 @ SY228 )
& ! [SY229: $i] :
( ( SY226 @ SY229 )
=> ( SY228 = SY229 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY226 @ Xx )
=> ( ( SY226 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY232: $i > $o,SY233: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY232 @ Xx )
<=> ( SY233 @ Xy ) ) )
=> ( ? [SY237: $i] :
( ( SY232 @ SY237 )
& ! [SY238: $i] :
( ( SY232 @ SY238 )
=> ( SY237 = SY238 ) ) )
<=> ? [SY240: $i] :
( ( SY233 @ SY240 )
& ! [SY241: $i] :
( ( SY233 @ SY241 )
=> ( SY240 = SY241 ) ) ) ) )
=> ( ( 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 )
=> ( ! [SY250: $i > $o] :
( ? [SY252: $i] :
( ( SY250 @ SY252 )
& ! [SY253: $i] :
( ( SY250 @ SY253 )
=> ( SY252 = SY253 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY250 @ Xx )
=> ( ( SY250 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY256: $i > $o,SY257: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY256 @ Xx )
<=> ( SY257 @ Xy ) ) )
=> ( ? [SY261: $i] :
( ( SY256 @ SY261 )
& ! [SY262: $i] :
( ( SY256 @ SY262 )
=> ( SY261 = SY262 ) ) )
=> ( ? [SY264: $i] :
( ( SY257 @ SY264 )
& ! [SY265: $i] :
( ( SY257 @ SY265 )
=> ( SY264 = SY265 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY256 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY257 @ 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 )
=> ( ! [SY478: $i,SY479: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY478 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY478 )
=> ( ( SY479 @ Xx )
=> ( ( SY479 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY478 )
& ( SY479 @ Xx ) )
=> ? [SY484: $i] :
( ( in @ SY484
@ ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) ) )
& ( ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) )
= ( setadjoin @ SY484 @ emptyset ) ) ) ) )
=> ( ! [SY485: $i,SY486: $i > $o] :
( ? [SY491: $i] :
( ( in @ SY491
@ ( dsetconstr @ SY485
@ ^ [SY492: $i] : ( SY486 @ SY492 ) ) )
& ( ( dsetconstr @ SY485
@ ^ [SY493: $i] : ( SY486 @ SY493 ) )
= ( setadjoin @ SY491 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY485 )
& ( SY486 @ Xx ) ) )
=> ( ! [SY495: $i,SY496: $i > $o,SY497: $i] :
( ( in @ SY497 @ SY495 )
=> ( ( SY496 @ SY497 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY495 )
=> ( ( SY496 @ Xy )
=> ( Xy = SY497 ) ) )
=> ? [SY503: $i] :
( ( in @ SY503
@ ( dsetconstr @ SY495
@ ^ [SY504: $i] : ( SY496 @ SY504 ) ) )
& ( ( dsetconstr @ SY495
@ ^ [SY505: $i] : ( SY496 @ SY505 ) )
= ( setadjoin @ SY503 @ emptyset ) ) ) ) ) )
=> ( ! [SY506: $i,SY507: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY506 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY506 )
=> ( ( SY507 @ Xx )
=> ( ( SY507 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY506 )
& ( SY507 @ Xx ) )
=> ? [SY515: $i] :
( ( in @ SY515
@ ( dsetconstr @ SY506
@ ^ [SY516: $i] : ( SY507 @ SY516 ) ) )
& ( ( dsetconstr @ SY506
@ ^ [SY517: $i] : ( SY507 @ SY517 ) )
= ( setadjoin @ SY515 @ emptyset ) ) ) ) )
=> ( ! [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 ) )
=> ( ! [SY523: $i] :
( ( iskpair @ SY523 )
=> ? [SY525: $i] :
( ( in @ SY525
@ ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) ) )
& ( ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) )
= ( setadjoin @ SY525 @ emptyset ) ) ) )
=> ( ! [SY526: $i] :
( ? [SY527: $i] :
( ( in @ SY527 @ SY526 )
& ( SY526
= ( setadjoin @ SY527 @ emptyset ) ) )
=> ( in @ ( setunion @ SY526 ) @ SY526 ) )
=> ( ! [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 ) )
=> ( ! [SY560: $i] :
( ( iskpair @ SY560 )
=> ? [SY562: $i] :
( ( in @ SY562
@ ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) ) )
& ( ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) )
= ( setadjoin @ SY562 @ emptyset ) ) ) )
=> ( ! [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 ) )
=> ( ! [SY604: $i,SY605: $i,SY606: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY604 @ SY605
@ ^ [Xx: $i,Xy: $i] : ( SY606 @ Xx @ Xy ) )
@ ( cartprod @ SY604 @ SY605 ) )
=> ( ! [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 ) )
=> ( ! [SY640: $i,SY641: $i,SY642: $i] :
( ( ( subset @ SY642 @ ( cartprod @ SY640 @ SY641 ) )
& ! [SY661: $i] :
( ( in @ SY661 @ SY640 )
=> ? [SY662: $i] :
( ( in @ SY662
@ ( dsetconstr @ SY641
@ ^ [SY663: $i] : ( in @ ( kpair @ SY661 @ SY663 ) @ SY642 ) ) )
& ( ( dsetconstr @ SY641
@ ^ [SY664: $i] : ( in @ ( kpair @ SY661 @ SY664 ) @ SY642 ) )
= ( setadjoin @ SY662 @ emptyset ) ) ) ) )
=> ! [SY665: $i] :
( ( in @ SY665 @ SY640 )
=> ? [SY667: $i] :
( ( in @ SY667
@ ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) ) )
& ( ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) )
= ( setadjoin @ SY667 @ emptyset ) ) ) ) )
=> ( ! [SY668: $i,SY669: $i,SY670: $i] :
( ( ( subset @ SY670 @ ( cartprod @ SY668 @ SY669 ) )
& ! [SY689: $i] :
( ( in @ SY689 @ SY668 )
=> ? [SY690: $i] :
( ( in @ SY690
@ ( dsetconstr @ SY669
@ ^ [SY691: $i] : ( in @ ( kpair @ SY689 @ SY691 ) @ SY670 ) ) )
& ( ( dsetconstr @ SY669
@ ^ [SY692: $i] : ( in @ ( kpair @ SY689 @ SY692 ) @ SY670 ) )
= ( setadjoin @ SY690 @ emptyset ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY668 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY669
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ SY670 ) ) )
@ SY669 ) ) )
=> ( ! [SY695: $i,SY696: $i,SY697: $i] :
( ( ( subset @ SY697 @ ( cartprod @ SY695 @ SY696 ) )
& ! [SY716: $i] :
( ( in @ SY716 @ SY695 )
=> ? [SY717: $i] :
( ( in @ SY717
@ ( dsetconstr @ SY696
@ ^ [SY718: $i] : ( in @ ( kpair @ SY716 @ SY718 ) @ SY697 ) ) )
& ( ( dsetconstr @ SY696
@ ^ [SY719: $i] : ( in @ ( kpair @ SY716 @ SY719 ) @ SY697 ) )
= ( setadjoin @ SY717 @ emptyset ) ) ) ) )
=> ! [SY720: $i] :
( ( in @ SY720 @ SY695 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY696
@ ^ [SY730: $i] : ( in @ ( kpair @ SY720 @ SY730 ) @ SY697 ) ) )
@ SY696 ) ) )
=> ( ! [SY731: $i,SY732: $i,SY733: $i] :
( ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
=> ( ( subset @ SY733 @ ( cartprod @ SY731 @ SY732 ) )
& ! [SY752: $i] :
( ( in @ SY752 @ SY731 )
=> ? [SY753: $i] :
( ( in @ SY753
@ ( dsetconstr @ SY732
@ ^ [SY754: $i] : ( in @ ( kpair @ SY752 @ SY754 ) @ SY733 ) ) )
& ( ( dsetconstr @ SY732
@ ^ [SY755: $i] : ( in @ ( kpair @ SY752 @ SY755 ) @ SY733 ) )
= ( setadjoin @ SY753 @ emptyset ) ) ) ) ) )
=> ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ( in @ SY758 @ ( funcSet @ SY756 @ SY757 ) )
=> ! [SY759: $i] :
( ( in @ SY759 @ SY756 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY757
@ ^ [SY769: $i] : ( in @ ( kpair @ SY759 @ SY769 ) @ SY758 ) ) )
@ SY757 ) ) )
=> ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ( ( subset @ SY772 @ ( cartprod @ SY770 @ SY771 ) )
& ! [SY791: $i] :
( ( in @ SY791 @ SY770 )
=> ? [SY792: $i] :
( ( in @ SY792
@ ( dsetconstr @ SY771
@ ^ [SY793: $i] : ( in @ ( kpair @ SY791 @ SY793 ) @ SY772 ) ) )
& ( ( dsetconstr @ SY771
@ ^ [SY794: $i] : ( in @ ( kpair @ SY791 @ SY794 ) @ SY772 ) )
= ( setadjoin @ SY792 @ emptyset ) ) ) ) )
=> ( in @ SY772 @ ( funcSet @ SY770 @ SY771 ) ) )
=> ( ! [SY795: $i,SY796: $i,SY797: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY795 )
=> ( in @ ( SY797 @ Xx ) @ SY796 ) )
=> ( ( subset
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) )
@ ( cartprod @ SY795 @ SY796 ) )
& ! [SY819: $i] :
( ( in @ SY819 @ SY795 )
=> ? [SY820: $i] :
( ( in @ SY820
@ ( dsetconstr @ SY796
@ ^ [SY821: $i] :
( in @ ( kpair @ SY819 @ SY821 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) ) )
& ( ( dsetconstr @ SY796
@ ^ [SY822: $i] :
( in @ ( kpair @ SY819 @ SY822 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) )
= ( setadjoin @ SY820 @ emptyset ) ) ) ) ) )
=> ( ! [SY823: $i,SY824: $i,SY825: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY823 )
=> ( in @ ( SY825 @ Xx ) @ SY824 ) )
=> ( ( subset
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) )
@ ( cartprod @ SY823 @ SY824 ) )
& ! [SY855: $i] :
( ( in @ SY855 @ SY823 )
=> ? [SY856: $i] :
( ( in @ SY856
@ ( dsetconstr @ SY824
@ ^ [SY857: $i] :
( in @ ( kpair @ SY855 @ SY857 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) ) )
& ( ( dsetconstr @ SY824
@ ^ [SY858: $i] :
( in @ ( kpair @ SY855 @ SY858 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) )
= ( setadjoin @ SY856 @ emptyset ) ) ) ) ) )
=> ( ! [SY859: $i,SY860: $i,SY861: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY859 )
=> ( in @ ( SY861 @ Xx ) @ SY860 ) )
=> ( in
@ ( dpsetconstr @ SY859 @ SY860
@ ^ [SY871: $i,SY872: $i] :
( ( SY861 @ SY871 )
= SY872 ) )
@ ( funcSet @ SY859 @ SY860 ) ) )
=> ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ( subset @ SY875 @ ( cartprod @ SY873 @ SY874 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY873 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY874 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY875 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY875 )
=> ( Xphi @ Xx ) ) ) )
=> ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,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,
( ( ! [SY27: $i > $i > $o,SY28: $i] :
( ! [SY29: $i] :
( ( in @ SY29 @ SY28 )
=> ? [SY31: $i] :
( ( SY27 @ SY29 @ SY31 )
& ! [SY32: $i] :
( ( SY27 @ SY29 @ SY32 )
=> ( SY31 = SY32 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY28 )
& ( SY27 @ 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,
( ( ! [SY59: $i > $o] :
( ? [SY61: $i] :
( ( SY59 @ SY61 )
& ! [SY62: $i] :
( ( SY59 @ SY62 )
=> ( SY61 = SY62 ) ) )
=> ( SY59
@ ( descr
@ ^ [Xx: $i] : ( SY59 @ 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,
( ( ! [SY76: $i > $o] :
( ? [SY78: $i] :
( ( SY76 @ SY78 )
& ! [SY79: $i] :
( ( SY76 @ SY79 )
=> ( SY78 = SY79 ) ) )
=> ? [Xx: $i] :
( ( SY76 @ Xx )
& ! [Xy: $i] :
( ( SY76 @ 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,
( ( ! [SY88: $i > $o] :
( ? [SY90: $i] :
( ( SY88 @ SY90 )
& ! [SY91: $i] :
( ( SY88 @ SY91 )
=> ( SY90 = SY91 ) ) )
=> ? [Xx: $i] : ( SY88 @ 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,
( ( ! [SY105: $i] :
( ( SY105 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY105 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY107: $i,SY108: $i > $o,SY109: $i] :
( ( in @ SY109 @ SY107 )
=> ( ( SY108 @ SY109 )
=> ( ( dsetconstr @ SY107
@ ^ [Xy: $i] : ( SY108 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY111: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY111 )
=> ( SY111 != 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,
( ( ! [SY144: $i > $o] :
( ? [SY146: $i] :
( ( SY144 @ SY146 )
& ! [SY147: $i] :
( ( SY144 @ SY147 )
=> ( SY146 = SY147 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY144 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY150: $i] :
( ( SY150 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY150 )
& $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,
( ( ! [SY199: $i > $o] :
( ? [Xx: $i] :
( ( SY199 @ Xx )
& ! [Xy: $i] :
( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY203: $i] :
( ( SY199 @ SY203 )
& ! [SY204: $i] :
( ( SY199 @ SY204 )
=> ( SY203 = SY204 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY205: $i > $o] :
( ? [Xx: $i] : ( SY205 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY205 @ Xx )
=> ( ( SY205 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY210: $i] :
( ( SY205 @ SY210 )
& ! [SY211: $i] :
( ( SY205 @ SY211 )
=> ( SY210 = SY211 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY212: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY212 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY216: $i] :
( ( SY212 @ SY216 )
& ! [SY217: $i] :
( ( SY212 @ SY217 )
=> ( SY216 = SY217 ) ) ) ) )
= $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,
( ( ! [SY226: $i > $o] :
( ? [SY228: $i] :
( ( SY226 @ SY228 )
& ! [SY229: $i] :
( ( SY226 @ SY229 )
=> ( SY228 = SY229 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY226 @ Xx )
=> ( ( SY226 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY232: $i > $o,SY233: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY232 @ Xx )
<=> ( SY233 @ Xy ) ) )
=> ( ? [SY237: $i] :
( ( SY232 @ SY237 )
& ! [SY238: $i] :
( ( SY232 @ SY238 )
=> ( SY237 = SY238 ) ) )
<=> ? [SY240: $i] :
( ( SY233 @ SY240 )
& ! [SY241: $i] :
( ( SY233 @ SY241 )
=> ( SY240 = SY241 ) ) ) ) ) )
= $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,
( ( ! [SY250: $i > $o] :
( ? [SY252: $i] :
( ( SY250 @ SY252 )
& ! [SY253: $i] :
( ( SY250 @ SY253 )
=> ( SY252 = SY253 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY250 @ Xx )
=> ( ( SY250 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY256: $i > $o,SY257: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY256 @ Xx )
<=> ( SY257 @ Xy ) ) )
=> ( ? [SY261: $i] :
( ( SY256 @ SY261 )
& ! [SY262: $i] :
( ( SY256 @ SY262 )
=> ( SY261 = SY262 ) ) )
=> ( ? [SY264: $i] :
( ( SY257 @ SY264 )
& ! [SY265: $i] :
( ( SY257 @ SY265 )
=> ( SY264 = SY265 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY256 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY257 @ 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,
( ( ! [SY478: $i,SY479: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY478 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY478 )
=> ( ( SY479 @ Xx )
=> ( ( SY479 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY478 )
& ( SY479 @ Xx ) )
=> ? [SY484: $i] :
( ( in @ SY484
@ ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) ) )
& ( ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) )
= ( setadjoin @ SY484 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [SY485: $i,SY486: $i > $o] :
( ? [SY491: $i] :
( ( in @ SY491
@ ( dsetconstr @ SY485
@ ^ [SY492: $i] : ( SY486 @ SY492 ) ) )
& ( ( dsetconstr @ SY485
@ ^ [SY493: $i] : ( SY486 @ SY493 ) )
= ( setadjoin @ SY491 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY485 )
& ( SY486 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY495: $i,SY496: $i > $o,SY497: $i] :
( ( in @ SY497 @ SY495 )
=> ( ( SY496 @ SY497 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY495 )
=> ( ( SY496 @ Xy )
=> ( Xy = SY497 ) ) )
=> ? [SY503: $i] :
( ( in @ SY503
@ ( dsetconstr @ SY495
@ ^ [SY504: $i] : ( SY496 @ SY504 ) ) )
& ( ( dsetconstr @ SY495
@ ^ [SY505: $i] : ( SY496 @ SY505 ) )
= ( setadjoin @ SY503 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY506: $i,SY507: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY506 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY506 )
=> ( ( SY507 @ Xx )
=> ( ( SY507 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY506 )
& ( SY507 @ Xx ) )
=> ? [SY515: $i] :
( ( in @ SY515
@ ( dsetconstr @ SY506
@ ^ [SY516: $i] : ( SY507 @ SY516 ) ) )
& ( ( dsetconstr @ SY506
@ ^ [SY517: $i] : ( SY507 @ SY517 ) )
= ( setadjoin @ SY515 @ emptyset ) ) ) ) ) )
= $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,
( ( ! [SY523: $i] :
( ( iskpair @ SY523 )
=> ? [SY525: $i] :
( ( in @ SY525
@ ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) ) )
& ( ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) )
= ( setadjoin @ SY525 @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [SY526: $i] :
( ? [SY527: $i] :
( ( in @ SY527 @ SY526 )
& ( SY526
= ( setadjoin @ SY527 @ emptyset ) ) )
=> ( in @ ( setunion @ SY526 ) @ SY526 ) ) )
= $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,
( ( ! [SY560: $i] :
( ( iskpair @ SY560 )
=> ? [SY562: $i] :
( ( in @ SY562
@ ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) ) )
& ( ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) )
= ( setadjoin @ SY562 @ emptyset ) ) ) ) )
= $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,
( ( ! [SY604: $i,SY605: $i,SY606: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY604 @ SY605
@ ^ [Xx: $i,Xy: $i] : ( SY606 @ Xx @ Xy ) )
@ ( cartprod @ SY604 @ SY605 ) ) )
= $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,
( ( ! [SY640: $i,SY641: $i,SY642: $i] :
( ( ( subset @ SY642 @ ( cartprod @ SY640 @ SY641 ) )
& ! [SY661: $i] :
( ( in @ SY661 @ SY640 )
=> ? [SY662: $i] :
( ( in @ SY662
@ ( dsetconstr @ SY641
@ ^ [SY663: $i] : ( in @ ( kpair @ SY661 @ SY663 ) @ SY642 ) ) )
& ( ( dsetconstr @ SY641
@ ^ [SY664: $i] : ( in @ ( kpair @ SY661 @ SY664 ) @ SY642 ) )
= ( setadjoin @ SY662 @ emptyset ) ) ) ) )
=> ! [SY665: $i] :
( ( in @ SY665 @ SY640 )
=> ? [SY667: $i] :
( ( in @ SY667
@ ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) ) )
& ( ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) )
= ( setadjoin @ SY667 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(193,plain,
( ( ! [SY668: $i,SY669: $i,SY670: $i] :
( ( ( subset @ SY670 @ ( cartprod @ SY668 @ SY669 ) )
& ! [SY689: $i] :
( ( in @ SY689 @ SY668 )
=> ? [SY690: $i] :
( ( in @ SY690
@ ( dsetconstr @ SY669
@ ^ [SY691: $i] : ( in @ ( kpair @ SY689 @ SY691 ) @ SY670 ) ) )
& ( ( dsetconstr @ SY669
@ ^ [SY692: $i] : ( in @ ( kpair @ SY689 @ SY692 ) @ SY670 ) )
= ( setadjoin @ SY690 @ emptyset ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY668 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY669
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ SY670 ) ) )
@ SY669 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(194,plain,
( ( ! [SY695: $i,SY696: $i,SY697: $i] :
( ( ( subset @ SY697 @ ( cartprod @ SY695 @ SY696 ) )
& ! [SY716: $i] :
( ( in @ SY716 @ SY695 )
=> ? [SY717: $i] :
( ( in @ SY717
@ ( dsetconstr @ SY696
@ ^ [SY718: $i] : ( in @ ( kpair @ SY716 @ SY718 ) @ SY697 ) ) )
& ( ( dsetconstr @ SY696
@ ^ [SY719: $i] : ( in @ ( kpair @ SY716 @ SY719 ) @ SY697 ) )
= ( setadjoin @ SY717 @ emptyset ) ) ) ) )
=> ! [SY720: $i] :
( ( in @ SY720 @ SY695 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY696
@ ^ [SY730: $i] : ( in @ ( kpair @ SY720 @ SY730 ) @ SY697 ) ) )
@ SY696 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(195,plain,
( ( ! [SY731: $i,SY732: $i,SY733: $i] :
( ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
=> ( ( subset @ SY733 @ ( cartprod @ SY731 @ SY732 ) )
& ! [SY752: $i] :
( ( in @ SY752 @ SY731 )
=> ? [SY753: $i] :
( ( in @ SY753
@ ( dsetconstr @ SY732
@ ^ [SY754: $i] : ( in @ ( kpair @ SY752 @ SY754 ) @ SY733 ) ) )
& ( ( dsetconstr @ SY732
@ ^ [SY755: $i] : ( in @ ( kpair @ SY752 @ SY755 ) @ SY733 ) )
= ( setadjoin @ SY753 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(196,plain,
( ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ( in @ SY758 @ ( funcSet @ SY756 @ SY757 ) )
=> ! [SY759: $i] :
( ( in @ SY759 @ SY756 )
=> ( in
@ ( setunion
@ ( dsetconstr @ SY757
@ ^ [SY769: $i] : ( in @ ( kpair @ SY759 @ SY769 ) @ SY758 ) ) )
@ SY757 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(197,plain,
( ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ( ( subset @ SY772 @ ( cartprod @ SY770 @ SY771 ) )
& ! [SY791: $i] :
( ( in @ SY791 @ SY770 )
=> ? [SY792: $i] :
( ( in @ SY792
@ ( dsetconstr @ SY771
@ ^ [SY793: $i] : ( in @ ( kpair @ SY791 @ SY793 ) @ SY772 ) ) )
& ( ( dsetconstr @ SY771
@ ^ [SY794: $i] : ( in @ ( kpair @ SY791 @ SY794 ) @ SY772 ) )
= ( setadjoin @ SY792 @ emptyset ) ) ) ) )
=> ( in @ SY772 @ ( funcSet @ SY770 @ SY771 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(198,plain,
( ( ! [SY795: $i,SY796: $i,SY797: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY795 )
=> ( in @ ( SY797 @ Xx ) @ SY796 ) )
=> ( ( subset
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) )
@ ( cartprod @ SY795 @ SY796 ) )
& ! [SY819: $i] :
( ( in @ SY819 @ SY795 )
=> ? [SY820: $i] :
( ( in @ SY820
@ ( dsetconstr @ SY796
@ ^ [SY821: $i] :
( in @ ( kpair @ SY819 @ SY821 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) ) )
& ( ( dsetconstr @ SY796
@ ^ [SY822: $i] :
( in @ ( kpair @ SY819 @ SY822 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) )
= ( setadjoin @ SY820 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(199,plain,
( ( ! [SY823: $i,SY824: $i,SY825: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY823 )
=> ( in @ ( SY825 @ Xx ) @ SY824 ) )
=> ( ( subset
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) )
@ ( cartprod @ SY823 @ SY824 ) )
& ! [SY855: $i] :
( ( in @ SY855 @ SY823 )
=> ? [SY856: $i] :
( ( in @ SY856
@ ( dsetconstr @ SY824
@ ^ [SY857: $i] :
( in @ ( kpair @ SY855 @ SY857 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) ) )
& ( ( dsetconstr @ SY824
@ ^ [SY858: $i] :
( in @ ( kpair @ SY855 @ SY858 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) )
= ( setadjoin @ SY856 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(200,plain,
( ( ! [SY859: $i,SY860: $i,SY861: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ SY859 )
=> ( in @ ( SY861 @ Xx ) @ SY860 ) )
=> ( in
@ ( dpsetconstr @ SY859 @ SY860
@ ^ [SY871: $i,SY872: $i] :
( ( SY861 @ SY871 )
= SY872 ) )
@ ( funcSet @ SY859 @ SY860 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(201,plain,
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ( subset @ SY875 @ ( cartprod @ SY873 @ SY874 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY873 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY874 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY875 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY875 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(202,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(203,plain,
( ( ~ ! [SY0: $i,SY1: $i,SY2: $i] :
( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY1 )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ SY2 )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY2 )
=> ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[202]) ).
thf(204,plain,
( ( ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) )
& ! [SY1605: $i] :
( ~ ( in @ SY1605 @ sK1_SY0 )
| ! [SY1606: $i] :
( ~ ( in @ SY1606 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SY1605 @ SY1606 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SY1605 @ SY1606 ) ) ) )
& ( in @ sK5_SY1607 @ sK3_SY1596 )
& ~ ( sK4_SY1601 @ sK5_SY1607 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK6_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK6_Xx @ B @ A ) @ A )
| ( in @ ( sK6_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(206,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(207,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK7_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK7_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(208,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 @ ( sK8_B @ Xx @ A ) )
& ( in @ ( sK8_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(209,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(210,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK9_Xx @ A ) @ omega )
& ( in @ ( sK9_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK9_Xx @ A ) @ ( sK9_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(211,plain,
( ( ! [SY27: $i > $i > $o,SY28: $i] :
( ( ( in @ ( sK12_SY29 @ SY28 @ SY27 ) @ SY28 )
& ! [SY1612: $i] :
( ( ( SY27 @ ( sK12_SY29 @ SY28 @ SY27 ) @ ( sK13_SY1613 @ SY1612 @ SY28 @ SY27 ) )
& ( SY1612
!= ( sK13_SY1613 @ SY1612 @ SY28 @ SY27 ) ) )
| ~ ( SY27 @ ( sK12_SY29 @ SY28 @ SY27 ) @ SY1612 ) ) )
| ( ! [SY1608: $i] :
( ! [Xy: $i] :
( ~ ( SY27 @ Xy @ SY1608 )
| ~ ( in @ Xy @ SY28 ) )
| ( in @ SY1608 @ ( sK10_B @ SY28 @ SY27 ) ) )
& ! [SY1610: $i] :
( ~ ( in @ SY1610 @ ( sK10_B @ SY28 @ SY27 ) )
| ( ( SY27 @ ( sK11_Xy @ SY1610 @ SY28 @ SY27 ) @ SY1610 )
& ( in @ ( sK11_Xy @ SY1610 @ SY28 @ SY27 ) @ SY28 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(212,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK14_B @ A ) @ A )
& ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK14_B @ A ) )
| ~ ( in @ SY1614 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(213,plain,
( ( ! [A: $i] :
( ! [SY1615: $i] :
( ( ( in @ ( sK19_Xx @ SY1615 @ A ) @ SY1615 )
& ~ ( in @ ( sK19_Xx @ SY1615 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1615 )
| ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK15_B @ A ) )
| ! [SY1634: $i] :
( ~ ( in @ SY1634 @ SY1636 )
| ( in @ SY1634 @ ( sK17_SY1618 @ SY1615 @ A ) ) )
| ( in @ ( sK18_SY1632 @ SY1615 @ A ) @ SY1636 ) )
& ( in @ ( sK17_SY1618 @ SY1615 @ A ) @ ( sK15_B @ A ) )
& ( in @ ( sK18_SY1632 @ SY1615 @ A ) @ SY1615 )
& ! [SY1635: $i] :
( ~ ( in @ SY1635 @ ( sK17_SY1618 @ SY1615 @ A ) )
| ~ ( in @ SY1635 @ SY1615 ) ) ) )
& ! [SY1623: $i,SY1624: $i] :
( ~ ( in @ SY1623 @ ( sK15_B @ A ) )
| ~ ( in @ SY1624 @ ( sK15_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1623 )
| ( in @ Xx @ SY1624 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1624 )
| ( in @ Xx @ SY1623 ) ) )
& ! [SY1627: $i] :
( ~ ( in @ SY1627 @ ( sK15_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1627 )
| ( in @ Xx @ A ) ) )
& ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ SY1629 @ A )
| ~ ( in @ SY1630 @ A )
| ( ( in @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) @ ( sK15_B @ A ) )
& ( ~ ( in @ SY1629 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) )
| ~ ( in @ SY1630 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) ) )
& ( ( in @ SY1629 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) )
| ( in @ SY1630 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) ) ) )
| ( SY1629 = SY1630 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(214,plain,
( ( ! [SY59: $i > $o] :
( ! [SY61: $i] :
( ( ( SY59 @ ( sK20_SY62 @ SY61 @ SY59 ) )
& ( SY61
!= ( sK20_SY62 @ SY61 @ SY59 ) ) )
| ~ ( SY59 @ SY61 ) )
| ( SY59
@ ( descr
@ ^ [Xx: $i] : ( SY59 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(215,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(216,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(217,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(218,plain,
( ( ! [SY76: $i > $o] :
( ! [SY78: $i] :
( ( ( SY76 @ ( sK22_SY79 @ SY78 @ SY76 ) )
& ( SY78
!= ( sK22_SY79 @ SY78 @ SY76 ) ) )
| ~ ( SY76 @ SY78 ) )
| ( ! [SY1639: $i] :
( ~ ( SY76 @ SY1639 )
| ( ( sK21_Xx @ SY76 )
= SY1639 ) )
& ( SY76 @ ( sK21_Xx @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(219,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(220,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(221,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(222,plain,
( ( ! [SY88: $i > $o] :
( ! [SY90: $i] :
( ( ( SY88 @ ( sK24_SY91 @ SY90 @ SY88 ) )
& ( SY90
!= ( sK24_SY91 @ SY90 @ SY88 ) ) )
| ~ ( SY88 @ SY90 ) )
| ( SY88 @ ( sK23_Xx @ SY88 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK26_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK26_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK25_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK25_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(224,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( in @ ( sK28_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(226,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(227,plain,
( ( ! [SY105: $i] :
( ( SY105 = emptyset )
| ( in @ ( sK29_Xx @ SY105 ) @ SY105 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(228,plain,
( ( ! [SY107: $i,SY108: $i > $o,SY109: $i] :
( ~ ( in @ SY109 @ SY107 )
| ~ ( SY108 @ SY109 )
| ( ( dsetconstr @ SY107
@ ^ [Xy: $i] : ( SY108 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(229,plain,
( ( ! [SY111: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY111 )
| ( SY111 != emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(230,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(231,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(232,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(233,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK30_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK30_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(234,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(235,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(236,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK31_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK31_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(237,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(238,plain,
( ( ! [SY144: $i > $o] :
( ! [SY146: $i] :
( ( ( SY144 @ ( sK33_SY147 @ SY146 @ SY144 ) )
& ( SY146
!= ( sK33_SY147 @ SY146 @ SY144 ) ) )
| ~ ( SY144 @ SY146 ) )
| ( ! [SY1640: $i] :
( ( SY1640
!= ( sK32_Xx @ SY144 ) )
| ( SY144 @ SY1640 ) )
& ! [SY1641: $i] :
( ~ ( SY144 @ SY1641 )
| ( SY1641
= ( sK32_Xx @ SY144 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(239,plain,
( ( ! [SY150: $i] :
( ( SY150 = emptyset )
| ( in @ ( sK34_Xx @ SY150 ) @ SY150 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(240,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(241,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(242,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(243,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(244,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(245,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(246,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(247,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(248,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(249,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)],[58]) ).
thf(250,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)],[59]) ).
thf(251,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(252,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(253,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK39_Xx @ Xphi @ A ) )
& ( in @ ( sK39_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(254,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK40_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK40_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(255,plain,
( ( ! [SY199: $i > $o] :
( ! [Xx: $i] :
( ( ( SY199 @ ( sK42_Xy @ Xx @ SY199 ) )
& ( Xx
!= ( sK42_Xy @ Xx @ SY199 ) ) )
| ~ ( SY199 @ Xx ) )
| ( ! [SY1642: $i] :
( ~ ( SY199 @ SY1642 )
| ( ( sK41_SY203 @ SY199 )
= SY1642 ) )
& ( SY199 @ ( sK41_SY203 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(256,plain,
( ( ! [SY205: $i > $o] :
( ! [Xx: $i] :
~ ( SY205 @ Xx )
| ( ( SY205 @ ( sK44_Xx @ SY205 ) )
& ( SY205 @ ( sK45_SY1644 @ SY205 ) )
& ( ( sK44_Xx @ SY205 )
!= ( sK45_SY1644 @ SY205 ) ) )
| ( ! [SY1643: $i] :
( ~ ( SY205 @ SY1643 )
| ( ( sK43_SY210 @ SY205 )
= SY1643 ) )
& ( SY205 @ ( sK43_SY210 @ SY205 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(257,plain,
( ( ! [SY212: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK47_Xy @ Xx @ SY212 )
!= Xx )
| ~ ( SY212 @ ( sK47_Xy @ Xx @ SY212 ) ) )
& ( ( ( sK47_Xy @ Xx @ SY212 )
= Xx )
| ( SY212 @ ( sK47_Xy @ Xx @ SY212 ) ) ) )
| ( ! [SY1645: $i] :
( ~ ( SY212 @ SY1645 )
| ( ( sK46_SY216 @ SY212 )
= SY1645 ) )
& ( SY212 @ ( sK46_SY216 @ SY212 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(258,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(259,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(260,plain,
( ( ! [SY226: $i > $o] :
( ! [SY228: $i] :
( ( ( SY226 @ ( sK48_SY229 @ SY228 @ SY226 ) )
& ( SY228
!= ( sK48_SY229 @ SY228 @ SY226 ) ) )
| ~ ( SY226 @ SY228 ) )
| ! [Xx: $i] :
( ~ ( SY226 @ Xx )
| ! [Xy: $i] :
( ~ ( SY226 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(261,plain,
( ( ! [SY232: $i > $o,SY233: $i > $o] :
( ( ( ( sK55_Xx @ SY233 @ SY232 )
= ( sK56_SY1649 @ SY233 @ SY232 ) )
& ( ~ ( SY232 @ ( sK55_Xx @ SY233 @ SY232 ) )
| ~ ( SY233 @ ( sK56_SY1649 @ SY233 @ SY232 ) ) )
& ( ( SY232 @ ( sK55_Xx @ SY233 @ SY232 ) )
| ( SY233 @ ( sK56_SY1649 @ SY233 @ SY232 ) ) ) )
| ! [SY237: $i] :
( ( ( SY232 @ ( sK54_SY238 @ SY237 @ SY233 @ SY232 ) )
& ( SY237
!= ( sK54_SY238 @ SY237 @ SY233 @ SY232 ) ) )
| ~ ( SY232 @ SY237 ) )
| ( ! [SY1648: $i] :
( ~ ( SY233 @ SY1648 )
| ( ( sK53_SY240 @ SY233 @ SY232 )
= SY1648 ) )
& ( SY233 @ ( sK53_SY240 @ SY233 @ SY232 ) ) ) )
& ! [SY232: $i > $o,SY233: $i > $o] :
( ( ( ( sK51_Xx @ SY233 @ SY232 )
= ( sK52_SY1647 @ SY233 @ SY232 ) )
& ( ~ ( SY232 @ ( sK51_Xx @ SY233 @ SY232 ) )
| ~ ( SY233 @ ( sK52_SY1647 @ SY233 @ SY232 ) ) )
& ( ( SY232 @ ( sK51_Xx @ SY233 @ SY232 ) )
| ( SY233 @ ( sK52_SY1647 @ SY233 @ SY232 ) ) ) )
| ! [SY240: $i] :
( ( ( SY233 @ ( sK50_SY241 @ SY240 @ SY233 @ SY232 ) )
& ( SY240
!= ( sK50_SY241 @ SY240 @ SY233 @ SY232 ) ) )
| ~ ( SY233 @ SY240 ) )
| ( ! [SY1646: $i] :
( ~ ( SY232 @ SY1646 )
| ( ( sK49_SY237 @ SY233 @ SY232 )
= SY1646 ) )
& ( SY232 @ ( sK49_SY237 @ SY233 @ SY232 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(262,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[71]) ).
thf(263,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(264,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(266,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[75]) ).
thf(267,plain,
( ( ! [SY250: $i > $o] :
( ! [SY252: $i] :
( ( ( SY250 @ ( sK57_SY253 @ SY252 @ SY250 ) )
& ( SY252
!= ( sK57_SY253 @ SY252 @ SY250 ) ) )
| ~ ( SY250 @ SY252 ) )
| ! [Xx: $i] :
( ~ ( SY250 @ Xx )
| ! [Xy: $i] :
( ~ ( SY250 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(268,plain,
( ( ! [SY256: $i > $o,SY257: $i > $o] :
( ( ( ( sK60_Xx @ SY257 @ SY256 )
= ( sK61_SY1650 @ SY257 @ SY256 ) )
& ( ~ ( SY256 @ ( sK60_Xx @ SY257 @ SY256 ) )
| ~ ( SY257 @ ( sK61_SY1650 @ SY257 @ SY256 ) ) )
& ( ( SY256 @ ( sK60_Xx @ SY257 @ SY256 ) )
| ( SY257 @ ( sK61_SY1650 @ SY257 @ SY256 ) ) ) )
| ! [SY261: $i] :
( ( ( SY256 @ ( sK59_SY262 @ SY261 @ SY257 @ SY256 ) )
& ( SY261
!= ( sK59_SY262 @ SY261 @ SY257 @ SY256 ) ) )
| ~ ( SY256 @ SY261 ) )
| ! [SY264: $i] :
( ( ( SY257 @ ( sK58_SY265 @ SY264 @ SY257 @ SY256 ) )
& ( SY264
!= ( sK58_SY265 @ SY264 @ SY257 @ SY256 ) ) )
| ~ ( SY257 @ SY264 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY256 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY257 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK62_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK65_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(276,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(278,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(279,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(280,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(283,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(284,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(287,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(288,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(289,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(290,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(291,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(292,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(293,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(296,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK66_Xx @ B @ A ) @ A )
& ( in @ ( sK66_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(300,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(301,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(302,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(304,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(305,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(306,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(307,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(309,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(310,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(311,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(312,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(313,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(314,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(315,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(316,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(317,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(318,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(319,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(320,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(321,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(322,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(323,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(324,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK67_Xx @ Xu @ B @ A ) @ ( sK68_SY1652 @ Xu @ B @ A ) ) )
& ( in @ ( sK68_SY1652 @ Xu @ B @ A ) @ B )
& ( in @ ( sK67_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(325,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( iskpair @ Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(326,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK69_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK69_X @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(327,plain,
( ( ! [SY478: $i,SY479: $i > $o] :
( ( ( in @ ( sK71_Xx @ SY479 @ SY478 ) @ SY478 )
& ( in @ ( sK72_SY1655 @ SY479 @ SY478 ) @ SY478 )
& ( SY479 @ ( sK71_Xx @ SY479 @ SY478 ) )
& ( SY479 @ ( sK72_SY1655 @ SY479 @ SY478 ) )
& ( ( sK71_Xx @ SY479 @ SY478 )
!= ( sK72_SY1655 @ SY479 @ SY478 ) ) )
| ! [Xx: $i] :
( ~ ( SY479 @ Xx )
| ~ ( in @ Xx @ SY478 ) )
| ( ( ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) )
= ( setadjoin @ ( sK70_SY484 @ SY479 @ SY478 ) @ emptyset ) )
& ( in @ ( sK70_SY484 @ SY479 @ SY478 )
@ ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(328,plain,
( ( ! [SY485: $i,SY486: $i > $o] :
( ! [SY491: $i] :
( ( ( dsetconstr @ SY485
@ ^ [SY493: $i] : ( SY486 @ SY493 ) )
!= ( setadjoin @ SY491 @ emptyset ) )
| ~ ( in @ SY491
@ ( dsetconstr @ SY485
@ ^ [SY492: $i] : ( SY486 @ SY492 ) ) ) )
| ( ( SY486 @ ( sK73_Xx @ SY486 @ SY485 ) )
& ( in @ ( sK73_Xx @ SY486 @ SY485 ) @ SY485 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(329,plain,
( ( ! [SY495: $i,SY496: $i > $o,SY497: $i] :
( ~ ( in @ SY497 @ SY495 )
| ~ ( SY496 @ SY497 )
| ( ( in @ ( sK75_Xy @ SY497 @ SY496 @ SY495 ) @ SY495 )
& ( SY496 @ ( sK75_Xy @ SY497 @ SY496 @ SY495 ) )
& ( ( sK75_Xy @ SY497 @ SY496 @ SY495 )
!= SY497 ) )
| ( ( ( dsetconstr @ SY495
@ ^ [SY505: $i] : ( SY496 @ SY505 ) )
= ( setadjoin @ ( sK74_SY503 @ SY497 @ SY496 @ SY495 ) @ emptyset ) )
& ( in @ ( sK74_SY503 @ SY497 @ SY496 @ SY495 )
@ ( dsetconstr @ SY495
@ ^ [SY504: $i] : ( SY496 @ SY504 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(330,plain,
( ( ! [SY506: $i,SY507: $i > $o] :
( ( ( in @ ( sK77_Xx @ SY507 @ SY506 ) @ SY506 )
& ( in @ ( sK78_SY1660 @ SY507 @ SY506 ) @ SY506 )
& ( SY507 @ ( sK77_Xx @ SY507 @ SY506 ) )
& ( SY507 @ ( sK78_SY1660 @ SY507 @ SY506 ) )
& ( ( sK77_Xx @ SY507 @ SY506 )
!= ( sK78_SY1660 @ SY507 @ SY506 ) ) )
| ! [Xx: $i] :
( ~ ( SY507 @ Xx )
| ~ ( in @ Xx @ SY506 ) )
| ( ( ( dsetconstr @ SY506
@ ^ [SY517: $i] : ( SY507 @ SY517 ) )
= ( setadjoin @ ( sK76_SY515 @ SY507 @ SY506 ) @ emptyset ) )
& ( in @ ( sK76_SY515 @ SY507 @ SY506 )
@ ( dsetconstr @ SY506
@ ^ [SY516: $i] : ( SY507 @ SY516 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(331,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(332,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(333,plain,
( ( ! [SY523: $i] :
( ~ ( iskpair @ SY523 )
| ( ( ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) )
= ( setadjoin @ ( sK79_SY525 @ SY523 ) @ emptyset ) )
& ( in @ ( sK79_SY525 @ SY523 )
@ ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(334,plain,
( ( ! [SY526: $i] :
( ! [SY527: $i] :
( ( SY526
!= ( setadjoin @ SY527 @ emptyset ) )
| ~ ( in @ SY527 @ SY526 ) )
| ( in @ ( setunion @ SY526 ) @ SY526 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(336,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(337,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(338,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(339,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(340,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(341,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(342,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(343,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(344,plain,
( ( ! [SY560: $i] :
( ~ ( iskpair @ SY560 )
| ( ( ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) )
= ( setadjoin @ ( sK80_SY562 @ SY560 ) @ emptyset ) )
& ( in @ ( sK80_SY562 @ SY560 )
@ ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(345,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(346,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(347,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(348,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(349,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(350,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(351,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(352,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(353,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(354,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(355,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(356,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(357,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(358,plain,
( ( ! [SY640: $i,SY641: $i,SY642: $i] :
( ( ( in @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY640 )
& ! [SY1667: $i] :
( ( ( dsetconstr @ SY641
@ ^ [SY1668: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY1668 ) @ SY642 ) )
!= ( setadjoin @ SY1667 @ emptyset ) )
| ~ ( in @ SY1667
@ ( dsetconstr @ SY641
@ ^ [SY1669: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY1669 ) @ SY642 ) ) ) ) )
| ~ ( subset @ SY642 @ ( cartprod @ SY640 @ SY641 ) )
| ! [SY665: $i] :
( ~ ( in @ SY665 @ SY640 )
| ( ( ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) )
= ( setadjoin @ ( sK81_SY667 @ SY665 @ SY642 @ SY641 @ SY640 ) @ emptyset ) )
& ( in @ ( sK81_SY667 @ SY665 @ SY642 @ SY641 @ SY640 )
@ ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[192]) ).
thf(359,plain,
( ( ! [SY668: $i,SY669: $i,SY670: $i] :
( ( ( in @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY668 )
& ! [SY1670: $i] :
( ( ( dsetconstr @ SY669
@ ^ [SY1671: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY1671 ) @ SY670 ) )
!= ( setadjoin @ SY1670 @ emptyset ) )
| ~ ( in @ SY1670
@ ( dsetconstr @ SY669
@ ^ [SY1672: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY1672 ) @ SY670 ) ) ) ) )
| ~ ( subset @ SY670 @ ( cartprod @ SY668 @ SY669 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY668 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY669
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ SY670 ) ) )
@ SY669 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[193]) ).
thf(360,plain,
( ( ! [SY695: $i,SY696: $i,SY697: $i] :
( ( ( in @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY695 )
& ! [SY1673: $i] :
( ( ( dsetconstr @ SY696
@ ^ [SY1674: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY1674 ) @ SY697 ) )
!= ( setadjoin @ SY1673 @ emptyset ) )
| ~ ( in @ SY1673
@ ( dsetconstr @ SY696
@ ^ [SY1675: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY1675 ) @ SY697 ) ) ) ) )
| ~ ( subset @ SY697 @ ( cartprod @ SY695 @ SY696 ) )
| ! [SY720: $i] :
( ~ ( in @ SY720 @ SY695 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY696
@ ^ [SY730: $i] : ( in @ ( kpair @ SY720 @ SY730 ) @ SY697 ) ) )
@ SY696 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(361,plain,
( ( ! [SY731: $i] :
( ! [SY732: $i,SY733: $i] :
( ~ ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
| ! [SY752: $i] :
( ~ ( in @ SY752 @ SY731 )
| ( ( ( dsetconstr @ SY732
@ ^ [SY755: $i] : ( in @ ( kpair @ SY752 @ SY755 ) @ SY733 ) )
= ( setadjoin @ ( sK85_SY753 @ SY752 @ SY733 @ SY732 @ SY731 ) @ emptyset ) )
& ( in @ ( sK85_SY753 @ SY752 @ SY733 @ SY732 @ SY731 )
@ ( dsetconstr @ SY732
@ ^ [SY754: $i] : ( in @ ( kpair @ SY752 @ SY754 ) @ SY733 ) ) ) ) ) )
& ! [SY732: $i,SY733: $i] :
( ~ ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
| ( subset @ SY733 @ ( cartprod @ SY731 @ SY732 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[195]) ).
thf(362,plain,
( ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ~ ( in @ SY758 @ ( funcSet @ SY756 @ SY757 ) )
| ! [SY759: $i] :
( ~ ( in @ SY759 @ SY756 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY757
@ ^ [SY769: $i] : ( in @ ( kpair @ SY759 @ SY769 ) @ SY758 ) ) )
@ SY757 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(363,plain,
( ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ( ( in @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY770 )
& ! [SY1678: $i] :
( ( ( dsetconstr @ SY771
@ ^ [SY1679: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY1679 ) @ SY772 ) )
!= ( setadjoin @ SY1678 @ emptyset ) )
| ~ ( in @ SY1678
@ ( dsetconstr @ SY771
@ ^ [SY1680: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY1680 ) @ SY772 ) ) ) ) )
| ~ ( subset @ SY772 @ ( cartprod @ SY770 @ SY771 ) )
| ( in @ SY772 @ ( funcSet @ SY770 @ SY771 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(364,plain,
( ( ! [SY795: $i] :
( ! [SY796: $i,SY797: $i > $i] :
( ( ( in @ ( sK89_Xx @ SY797 @ SY796 @ SY795 ) @ SY795 )
& ~ ( in @ ( SY797 @ ( sK89_Xx @ SY797 @ SY796 @ SY795 ) ) @ SY796 ) )
| ! [SY819: $i] :
( ~ ( in @ SY819 @ SY795 )
| ( ( ( dsetconstr @ SY796
@ ^ [SY822: $i] :
( in @ ( kpair @ SY819 @ SY822 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) )
= ( setadjoin @ ( sK88_SY820 @ SY819 @ SY797 @ SY796 @ SY795 ) @ emptyset ) )
& ( in @ ( sK88_SY820 @ SY819 @ SY797 @ SY796 @ SY795 )
@ ( dsetconstr @ SY796
@ ^ [SY821: $i] :
( in @ ( kpair @ SY819 @ SY821 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) ) ) ) ) )
& ! [SY796: $i,SY797: $i > $i] :
( ( ( in @ ( sK87_Xx @ SY797 @ SY796 @ SY795 ) @ SY795 )
& ~ ( in @ ( SY797 @ ( sK87_Xx @ SY797 @ SY796 @ SY795 ) ) @ SY796 ) )
| ( subset
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) )
@ ( cartprod @ SY795 @ SY796 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(365,plain,
( ( ! [SY823: $i] :
( ! [SY824: $i,SY825: $i > $i] :
( ( ( in @ ( sK92_Xx @ SY825 @ SY824 @ SY823 ) @ SY823 )
& ~ ( in @ ( SY825 @ ( sK92_Xx @ SY825 @ SY824 @ SY823 ) ) @ SY824 ) )
| ! [SY855: $i] :
( ~ ( in @ SY855 @ SY823 )
| ( ( ( dsetconstr @ SY824
@ ^ [SY858: $i] :
( in @ ( kpair @ SY855 @ SY858 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) )
= ( setadjoin @ ( sK91_SY856 @ SY855 @ SY825 @ SY824 @ SY823 ) @ emptyset ) )
& ( in @ ( sK91_SY856 @ SY855 @ SY825 @ SY824 @ SY823 )
@ ( dsetconstr @ SY824
@ ^ [SY857: $i] :
( in @ ( kpair @ SY855 @ SY857 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) ) ) ) ) )
& ! [SY824: $i,SY825: $i > $i] :
( ( ( in @ ( sK90_Xx @ SY825 @ SY824 @ SY823 ) @ SY823 )
& ~ ( in @ ( SY825 @ ( sK90_Xx @ SY825 @ SY824 @ SY823 ) ) @ SY824 ) )
| ( subset
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) )
@ ( cartprod @ SY823 @ SY824 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(366,plain,
( ( ! [SY859: $i,SY860: $i,SY861: $i > $i] :
( ( ( in @ ( sK93_Xx @ SY861 @ SY860 @ SY859 ) @ SY859 )
& ~ ( in @ ( SY861 @ ( sK93_Xx @ SY861 @ SY860 @ SY859 ) ) @ SY860 ) )
| ( in
@ ( dpsetconstr @ SY859 @ SY860
@ ^ [SY871: $i,SY872: $i] :
( ( SY861 @ SY871 )
= SY872 ) )
@ ( funcSet @ SY859 @ SY860 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(367,plain,
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ~ ( subset @ SY875 @ ( cartprod @ SY873 @ SY874 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ SY873 )
& ( in @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) @ SY874 )
& ( in @ ( kpair @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) ) @ SY875 )
& ~ ( Xphi @ ( kpair @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY875 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(368,plain,
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ~ ( subset @ SY875 @ ( cartprod @ SY873 @ SY874 ) )
| ! [Xphi: $i > $o] :
( ( ( in @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ SY873 )
& ( in @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) @ SY874 )
& ( in @ ( kpair @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) ) @ SY875 )
& ~ ( Xphi @ ( kpair @ ( sK94_Xx @ Xphi @ SY875 @ SY874 @ SY873 ) @ ( sK95_SY1693 @ Xphi @ SY875 @ SY874 @ SY873 ) ) ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY875 )
| ( Xphi @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(369,plain,
( ( ! [SY859: $i,SY860: $i,SY861: $i > $i] :
( ( ( in @ ( sK93_Xx @ SY861 @ SY860 @ SY859 ) @ SY859 )
& ~ ( in @ ( SY861 @ ( sK93_Xx @ SY861 @ SY860 @ SY859 ) ) @ SY860 ) )
| ( in
@ ( dpsetconstr @ SY859 @ SY860
@ ^ [SY871: $i,SY872: $i] :
( ( SY861 @ SY871 )
= SY872 ) )
@ ( funcSet @ SY859 @ SY860 ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(370,plain,
( ( ! [SY823: $i] :
( ! [SY824: $i,SY825: $i > $i] :
( ( ( in @ ( sK92_Xx @ SY825 @ SY824 @ SY823 ) @ SY823 )
& ~ ( in @ ( SY825 @ ( sK92_Xx @ SY825 @ SY824 @ SY823 ) ) @ SY824 ) )
| ! [SY855: $i] :
( ~ ( in @ SY855 @ SY823 )
| ( ( ( dsetconstr @ SY824
@ ^ [SY858: $i] :
( in @ ( kpair @ SY855 @ SY858 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) )
= ( setadjoin @ ( sK91_SY856 @ SY855 @ SY825 @ SY824 @ SY823 ) @ emptyset ) )
& ( in @ ( sK91_SY856 @ SY855 @ SY825 @ SY824 @ SY823 )
@ ( dsetconstr @ SY824
@ ^ [SY857: $i] :
( in @ ( kpair @ SY855 @ SY857 )
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) ) ) ) ) ) ) )
& ! [SY824: $i,SY825: $i > $i] :
( ( ( in @ ( sK90_Xx @ SY825 @ SY824 @ SY823 ) @ SY823 )
& ~ ( in @ ( SY825 @ ( sK90_Xx @ SY825 @ SY824 @ SY823 ) ) @ SY824 ) )
| ( subset
@ ( dpsetconstr @ SY823 @ SY824
@ ^ [SY853: $i,SY854: $i] :
( ( SY825 @ SY853 )
= SY854 ) )
@ ( cartprod @ SY823 @ SY824 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(371,plain,
( ( ! [SY795: $i] :
( ! [SY796: $i,SY797: $i > $i] :
( ( ( in @ ( sK89_Xx @ SY797 @ SY796 @ SY795 ) @ SY795 )
& ~ ( in @ ( SY797 @ ( sK89_Xx @ SY797 @ SY796 @ SY795 ) ) @ SY796 ) )
| ! [SY819: $i] :
( ~ ( in @ SY819 @ SY795 )
| ( ( ( dsetconstr @ SY796
@ ^ [SY822: $i] :
( in @ ( kpair @ SY819 @ SY822 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) )
= ( setadjoin @ ( sK88_SY820 @ SY819 @ SY797 @ SY796 @ SY795 ) @ emptyset ) )
& ( in @ ( sK88_SY820 @ SY819 @ SY797 @ SY796 @ SY795 )
@ ( dsetconstr @ SY796
@ ^ [SY821: $i] :
( in @ ( kpair @ SY819 @ SY821 )
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) ) ) ) ) ) ) )
& ! [SY796: $i,SY797: $i > $i] :
( ( ( in @ ( sK87_Xx @ SY797 @ SY796 @ SY795 ) @ SY795 )
& ~ ( in @ ( SY797 @ ( sK87_Xx @ SY797 @ SY796 @ SY795 ) ) @ SY796 ) )
| ( subset
@ ( dpsetconstr @ SY795 @ SY796
@ ^ [Xx: $i,Xy: $i] :
( ( SY797 @ Xx )
= Xy ) )
@ ( cartprod @ SY795 @ SY796 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(372,plain,
( ( ! [SY770: $i,SY771: $i,SY772: $i] :
( ( ( in @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY770 )
& ! [SY1678: $i] :
( ( ( dsetconstr @ SY771
@ ^ [SY1679: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY1679 ) @ SY772 ) )
!= ( setadjoin @ SY1678 @ emptyset ) )
| ~ ( in @ SY1678
@ ( dsetconstr @ SY771
@ ^ [SY1680: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY772 @ SY771 @ SY770 ) @ SY1680 ) @ SY772 ) ) ) ) )
| ~ ( subset @ SY772 @ ( cartprod @ SY770 @ SY771 ) )
| ( in @ SY772 @ ( funcSet @ SY770 @ SY771 ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(373,plain,
( ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ~ ( in @ SY758 @ ( funcSet @ SY756 @ SY757 ) )
| ! [SY759: $i] :
( ~ ( in @ SY759 @ SY756 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY757
@ ^ [SY769: $i] : ( in @ ( kpair @ SY759 @ SY769 ) @ SY758 ) ) )
@ SY757 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(374,plain,
( ( ! [SY731: $i] :
( ! [SY732: $i,SY733: $i] :
( ~ ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
| ! [SY752: $i] :
( ~ ( in @ SY752 @ SY731 )
| ( ( ( dsetconstr @ SY732
@ ^ [SY755: $i] : ( in @ ( kpair @ SY752 @ SY755 ) @ SY733 ) )
= ( setadjoin @ ( sK85_SY753 @ SY752 @ SY733 @ SY732 @ SY731 ) @ emptyset ) )
& ( in @ ( sK85_SY753 @ SY752 @ SY733 @ SY732 @ SY731 )
@ ( dsetconstr @ SY732
@ ^ [SY754: $i] : ( in @ ( kpair @ SY752 @ SY754 ) @ SY733 ) ) ) ) ) )
& ! [SY732: $i,SY733: $i] :
( ~ ( in @ SY733 @ ( funcSet @ SY731 @ SY732 ) )
| ( subset @ SY733 @ ( cartprod @ SY731 @ SY732 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(375,plain,
( ( ! [SY695: $i,SY696: $i,SY697: $i] :
( ( ( in @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY695 )
& ! [SY1673: $i] :
( ( ( dsetconstr @ SY696
@ ^ [SY1674: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY1674 ) @ SY697 ) )
!= ( setadjoin @ SY1673 @ emptyset ) )
| ~ ( in @ SY1673
@ ( dsetconstr @ SY696
@ ^ [SY1675: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY697 @ SY696 @ SY695 ) @ SY1675 ) @ SY697 ) ) ) ) )
| ~ ( subset @ SY697 @ ( cartprod @ SY695 @ SY696 ) )
| ! [SY720: $i] :
( ~ ( in @ SY720 @ SY695 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY696
@ ^ [SY730: $i] : ( in @ ( kpair @ SY720 @ SY730 ) @ SY697 ) ) )
@ SY696 ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(376,plain,
( ( ! [SY668: $i,SY669: $i,SY670: $i] :
( ( ( in @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY668 )
& ! [SY1670: $i] :
( ( ( dsetconstr @ SY669
@ ^ [SY1671: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY1671 ) @ SY670 ) )
!= ( setadjoin @ SY1670 @ emptyset ) )
| ~ ( in @ SY1670
@ ( dsetconstr @ SY669
@ ^ [SY1672: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY670 @ SY669 @ SY668 ) @ SY1672 ) @ SY670 ) ) ) ) )
| ~ ( subset @ SY670 @ ( cartprod @ SY668 @ SY669 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY668 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY669
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ SY670 ) ) )
@ SY669 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(377,plain,
( ( ! [SY640: $i,SY641: $i,SY642: $i] :
( ( ( in @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY640 )
& ! [SY1667: $i] :
( ( ( dsetconstr @ SY641
@ ^ [SY1668: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY1668 ) @ SY642 ) )
!= ( setadjoin @ SY1667 @ emptyset ) )
| ~ ( in @ SY1667
@ ( dsetconstr @ SY641
@ ^ [SY1669: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY642 @ SY641 @ SY640 ) @ SY1669 ) @ SY642 ) ) ) ) )
| ~ ( subset @ SY642 @ ( cartprod @ SY640 @ SY641 ) )
| ! [SY665: $i] :
( ~ ( in @ SY665 @ SY640 )
| ( ( ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) )
= ( setadjoin @ ( sK81_SY667 @ SY665 @ SY642 @ SY641 @ SY640 ) @ emptyset ) )
& ( in @ ( sK81_SY667 @ SY665 @ SY642 @ SY641 @ SY640 )
@ ( dsetconstr @ SY641
@ ^ [Xy: $i] : ( in @ ( kpair @ SY665 @ Xy ) @ SY642 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(378,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)],[357]) ).
thf(379,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)],[356]) ).
thf(380,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)],[355]) ).
thf(381,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)],[354]) ).
thf(382,plain,
( ( ! [SY604: $i,SY605: $i,SY606: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SY604 @ SY605
@ ^ [Xx: $i,Xy: $i] : ( SY606 @ Xx @ Xy ) )
@ ( cartprod @ SY604 @ SY605 ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(383,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(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(copy,[status(thm)],[353]) ).
thf(385,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(386,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)],[351]) ).
thf(387,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)],[350]) ).
thf(388,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(389,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(390,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ! [Xy: $i] :
~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(391,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(392,plain,
( ( ! [Xu: $i] :
( ~ ( iskpair @ Xu )
| ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(393,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(394,plain,
( ( ! [SY560: $i] :
( ~ ( iskpair @ SY560 )
| ( ( ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) )
= ( setadjoin @ ( sK80_SY562 @ SY560 ) @ emptyset ) )
& ( in @ ( sK80_SY562 @ SY560 )
@ ( dsetconstr @ ( setunion @ SY560 )
@ ^ [Xx: $i] :
( SY560
= ( kpair @ ( kfst @ SY560 ) @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(395,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(396,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)],[342]) ).
thf(397,plain,
( ( ! [Xx: $i,Xy: $i] :
( ! [Xz: $i] :
( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
!= ( setadjoin @ Xz @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(398,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)],[340]) ).
thf(399,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)],[339]) ).
thf(400,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(401,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ! [Xu: $i] :
( ( kpair @ Xx @ Xy )
!= ( kpair @ Xz @ Xu ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[337]) ).
thf(402,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)],[336]) ).
thf(403,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(404,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(405,plain,
( ( ! [SY526: $i] :
( ! [SY527: $i] :
( ( SY526
!= ( setadjoin @ SY527 @ emptyset ) )
| ~ ( in @ SY527 @ SY526 ) )
| ( in @ ( setunion @ SY526 ) @ SY526 ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(406,plain,
( ( ! [SY523: $i] :
( ~ ( iskpair @ SY523 )
| ( ( ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) )
= ( setadjoin @ ( sK79_SY525 @ SY523 ) @ emptyset ) )
& ( in @ ( sK79_SY525 @ SY523 )
@ ( dsetconstr @ ( setunion @ SY523 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY523 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(407,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)],[332]) ).
thf(408,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(409,plain,
( ( ! [SY506: $i,SY507: $i > $o] :
( ( ( in @ ( sK77_Xx @ SY507 @ SY506 ) @ SY506 )
& ( in @ ( sK78_SY1660 @ SY507 @ SY506 ) @ SY506 )
& ( SY507 @ ( sK77_Xx @ SY507 @ SY506 ) )
& ( SY507 @ ( sK78_SY1660 @ SY507 @ SY506 ) )
& ( ( sK77_Xx @ SY507 @ SY506 )
!= ( sK78_SY1660 @ SY507 @ SY506 ) ) )
| ! [Xx: $i] :
( ~ ( SY507 @ Xx )
| ~ ( in @ Xx @ SY506 ) )
| ( ( ( dsetconstr @ SY506
@ ^ [SY517: $i] : ( SY507 @ SY517 ) )
= ( setadjoin @ ( sK76_SY515 @ SY507 @ SY506 ) @ emptyset ) )
& ( in @ ( sK76_SY515 @ SY507 @ SY506 )
@ ( dsetconstr @ SY506
@ ^ [SY516: $i] : ( SY507 @ SY516 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(410,plain,
( ( ! [SY495: $i,SY496: $i > $o,SY497: $i] :
( ~ ( in @ SY497 @ SY495 )
| ~ ( SY496 @ SY497 )
| ( ( in @ ( sK75_Xy @ SY497 @ SY496 @ SY495 ) @ SY495 )
& ( SY496 @ ( sK75_Xy @ SY497 @ SY496 @ SY495 ) )
& ( ( sK75_Xy @ SY497 @ SY496 @ SY495 )
!= SY497 ) )
| ( ( ( dsetconstr @ SY495
@ ^ [SY505: $i] : ( SY496 @ SY505 ) )
= ( setadjoin @ ( sK74_SY503 @ SY497 @ SY496 @ SY495 ) @ emptyset ) )
& ( in @ ( sK74_SY503 @ SY497 @ SY496 @ SY495 )
@ ( dsetconstr @ SY495
@ ^ [SY504: $i] : ( SY496 @ SY504 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(411,plain,
( ( ! [SY485: $i,SY486: $i > $o] :
( ! [SY491: $i] :
( ( ( dsetconstr @ SY485
@ ^ [SY493: $i] : ( SY486 @ SY493 ) )
!= ( setadjoin @ SY491 @ emptyset ) )
| ~ ( in @ SY491
@ ( dsetconstr @ SY485
@ ^ [SY492: $i] : ( SY486 @ SY492 ) ) ) )
| ( ( SY486 @ ( sK73_Xx @ SY486 @ SY485 ) )
& ( in @ ( sK73_Xx @ SY486 @ SY485 ) @ SY485 ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(412,plain,
( ( ! [SY478: $i,SY479: $i > $o] :
( ( ( in @ ( sK71_Xx @ SY479 @ SY478 ) @ SY478 )
& ( in @ ( sK72_SY1655 @ SY479 @ SY478 ) @ SY478 )
& ( SY479 @ ( sK71_Xx @ SY479 @ SY478 ) )
& ( SY479 @ ( sK72_SY1655 @ SY479 @ SY478 ) )
& ( ( sK71_Xx @ SY479 @ SY478 )
!= ( sK72_SY1655 @ SY479 @ SY478 ) ) )
| ! [Xx: $i] :
( ~ ( SY479 @ Xx )
| ~ ( in @ Xx @ SY478 ) )
| ( ( ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) )
= ( setadjoin @ ( sK70_SY484 @ SY479 @ SY478 ) @ emptyset ) )
& ( in @ ( sK70_SY484 @ SY479 @ SY478 )
@ ( dsetconstr @ SY478
@ ^ [Xx: $i] : ( SY479 @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(413,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(414,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(415,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(416,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK69_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK69_X @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(417,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(418,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK67_Xx @ Xu @ B @ A ) @ ( sK68_SY1652 @ Xu @ B @ A ) ) )
& ( in @ ( sK68_SY1652 @ Xu @ B @ A ) @ B )
& ( in @ ( sK67_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(419,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)],[323]) ).
thf(420,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)],[322]) ).
thf(421,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)],[321]) ).
thf(422,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)],[320]) ).
thf(423,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)],[319]) ).
thf(424,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)],[318]) ).
thf(425,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(426,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(427,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(428,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(429,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(430,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(431,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(432,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(433,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(434,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(435,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(436,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(437,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(438,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)],[309]) ).
thf(439,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(441,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(442,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(444,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(446,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(447,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(448,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(449,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(450,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK66_Xx @ B @ A ) @ A )
& ( in @ ( sK66_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(454,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(456,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(459,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(460,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(461,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(463,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(464,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)],[289]) ).
thf(465,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(466,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(467,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(468,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(469,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(470,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(471,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(474,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(475,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(476,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(477,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(478,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(480,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(481,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(482,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(483,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(484,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(486,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK65_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(489,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK62_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK63_SY1651 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(492,plain,
( ( ! [SY256: $i > $o,SY257: $i > $o] :
( ( ( ( sK60_Xx @ SY257 @ SY256 )
= ( sK61_SY1650 @ SY257 @ SY256 ) )
& ( ~ ( SY256 @ ( sK60_Xx @ SY257 @ SY256 ) )
| ~ ( SY257 @ ( sK61_SY1650 @ SY257 @ SY256 ) ) )
& ( ( SY256 @ ( sK60_Xx @ SY257 @ SY256 ) )
| ( SY257 @ ( sK61_SY1650 @ SY257 @ SY256 ) ) ) )
| ! [SY261: $i] :
( ( ( SY256 @ ( sK59_SY262 @ SY261 @ SY257 @ SY256 ) )
& ( SY261
!= ( sK59_SY262 @ SY261 @ SY257 @ SY256 ) ) )
| ~ ( SY256 @ SY261 ) )
| ! [SY264: $i] :
( ( ( SY257 @ ( sK58_SY265 @ SY264 @ SY257 @ SY256 ) )
& ( SY264
!= ( sK58_SY265 @ SY264 @ SY257 @ SY256 ) ) )
| ~ ( SY257 @ SY264 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY256 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY257 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(493,plain,
( ( ! [SY250: $i > $o] :
( ! [SY252: $i] :
( ( ( SY250 @ ( sK57_SY253 @ SY252 @ SY250 ) )
& ( SY252
!= ( sK57_SY253 @ SY252 @ SY250 ) ) )
| ~ ( SY250 @ SY252 ) )
| ! [Xx: $i] :
( ~ ( SY250 @ Xx )
| ! [Xy: $i] :
( ~ ( SY250 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(494,plain,
$true = $true,
inference(copy,[status(thm)],[266]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(497,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ! [Xz: $i,Xu: $i] :
( ( Xz != Xu )
| ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(498,plain,
$true = $true,
inference(copy,[status(thm)],[262]) ).
thf(499,plain,
( ( ! [SY232: $i > $o,SY233: $i > $o] :
( ( ( ( sK55_Xx @ SY233 @ SY232 )
= ( sK56_SY1649 @ SY233 @ SY232 ) )
& ( ~ ( SY232 @ ( sK55_Xx @ SY233 @ SY232 ) )
| ~ ( SY233 @ ( sK56_SY1649 @ SY233 @ SY232 ) ) )
& ( ( SY232 @ ( sK55_Xx @ SY233 @ SY232 ) )
| ( SY233 @ ( sK56_SY1649 @ SY233 @ SY232 ) ) ) )
| ! [SY237: $i] :
( ( ( SY232 @ ( sK54_SY238 @ SY237 @ SY233 @ SY232 ) )
& ( SY237
!= ( sK54_SY238 @ SY237 @ SY233 @ SY232 ) ) )
| ~ ( SY232 @ SY237 ) )
| ( ! [SY1648: $i] :
( ~ ( SY233 @ SY1648 )
| ( ( sK53_SY240 @ SY233 @ SY232 )
= SY1648 ) )
& ( SY233 @ ( sK53_SY240 @ SY233 @ SY232 ) ) ) )
& ! [SY232: $i > $o,SY233: $i > $o] :
( ( ( ( sK51_Xx @ SY233 @ SY232 )
= ( sK52_SY1647 @ SY233 @ SY232 ) )
& ( ~ ( SY232 @ ( sK51_Xx @ SY233 @ SY232 ) )
| ~ ( SY233 @ ( sK52_SY1647 @ SY233 @ SY232 ) ) )
& ( ( SY232 @ ( sK51_Xx @ SY233 @ SY232 ) )
| ( SY233 @ ( sK52_SY1647 @ SY233 @ SY232 ) ) ) )
| ! [SY240: $i] :
( ( ( SY233 @ ( sK50_SY241 @ SY240 @ SY233 @ SY232 ) )
& ( SY240
!= ( sK50_SY241 @ SY240 @ SY233 @ SY232 ) ) )
| ~ ( SY233 @ SY240 ) )
| ( ! [SY1646: $i] :
( ~ ( SY232 @ SY1646 )
| ( ( sK49_SY237 @ SY233 @ SY232 )
= SY1646 ) )
& ( SY232 @ ( sK49_SY237 @ SY233 @ SY232 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(500,plain,
( ( ! [SY226: $i > $o] :
( ! [SY228: $i] :
( ( ( SY226 @ ( sK48_SY229 @ SY228 @ SY226 ) )
& ( SY228
!= ( sK48_SY229 @ SY228 @ SY226 ) ) )
| ~ ( SY226 @ SY228 ) )
| ! [Xx: $i] :
( ~ ( SY226 @ Xx )
| ! [Xy: $i] :
( ~ ( SY226 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(501,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)],[259]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(503,plain,
( ( ! [SY212: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK47_Xy @ Xx @ SY212 )
!= Xx )
| ~ ( SY212 @ ( sK47_Xy @ Xx @ SY212 ) ) )
& ( ( ( sK47_Xy @ Xx @ SY212 )
= Xx )
| ( SY212 @ ( sK47_Xy @ Xx @ SY212 ) ) ) )
| ( ! [SY1645: $i] :
( ~ ( SY212 @ SY1645 )
| ( ( sK46_SY216 @ SY212 )
= SY1645 ) )
& ( SY212 @ ( sK46_SY216 @ SY212 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(504,plain,
( ( ! [SY205: $i > $o] :
( ! [Xx: $i] :
~ ( SY205 @ Xx )
| ( ( SY205 @ ( sK44_Xx @ SY205 ) )
& ( SY205 @ ( sK45_SY1644 @ SY205 ) )
& ( ( sK44_Xx @ SY205 )
!= ( sK45_SY1644 @ SY205 ) ) )
| ( ! [SY1643: $i] :
( ~ ( SY205 @ SY1643 )
| ( ( sK43_SY210 @ SY205 )
= SY1643 ) )
& ( SY205 @ ( sK43_SY210 @ SY205 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(505,plain,
( ( ! [SY199: $i > $o] :
( ! [Xx: $i] :
( ( ( SY199 @ ( sK42_Xy @ Xx @ SY199 ) )
& ( Xx
!= ( sK42_Xy @ Xx @ SY199 ) ) )
| ~ ( SY199 @ Xx ) )
| ( ! [SY1642: $i] :
( ~ ( SY199 @ SY1642 )
| ( ( sK41_SY203 @ SY199 )
= SY1642 ) )
& ( SY199 @ ( sK41_SY203 @ SY199 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(506,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK40_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK40_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(507,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK39_Xx @ Xphi @ A ) )
& ( in @ ( sK39_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(508,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(509,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(510,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)],[250]) ).
thf(511,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)],[249]) ).
thf(512,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(513,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(514,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(515,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)],[245]) ).
thf(516,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(517,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
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)],[244]) ).
thf(519,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(520,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(521,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(522,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(523,plain,
( ( ! [SY150: $i] :
( ( SY150 = emptyset )
| ( in @ ( sK34_Xx @ SY150 ) @ SY150 ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(524,plain,
( ( ! [SY144: $i > $o] :
( ! [SY146: $i] :
( ( ( SY144 @ ( sK33_SY147 @ SY146 @ SY144 ) )
& ( SY146
!= ( sK33_SY147 @ SY146 @ SY144 ) ) )
| ~ ( SY144 @ SY146 ) )
| ( ! [SY1640: $i] :
( ( SY1640
!= ( sK32_Xx @ SY144 ) )
| ( SY144 @ SY1640 ) )
& ! [SY1641: $i] :
( ~ ( SY144 @ SY1641 )
| ( SY1641
= ( sK32_Xx @ SY144 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(525,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(526,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK31_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK31_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(527,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(529,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(530,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK30_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK30_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(532,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(533,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(534,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)],[231]) ).
thf(535,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(536,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(537,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(538,plain,
( ( ! [SY111: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY111 )
| ( SY111 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(539,plain,
( ( ! [SY107: $i,SY108: $i > $o,SY109: $i] :
( ~ ( in @ SY109 @ SY107 )
| ~ ( SY108 @ SY109 )
| ( ( dsetconstr @ SY107
@ ^ [Xy: $i] : ( SY108 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(540,plain,
( ( ! [SY105: $i] :
( ( SY105 = emptyset )
| ( in @ ( sK29_Xx @ SY105 ) @ SY105 ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(541,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)],[226]) ).
thf(542,plain,
( ( ! [A: $i] :
( ( in @ ( sK28_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(543,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK26_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK26_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK25_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK25_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(545,plain,
( ( ! [SY88: $i > $o] :
( ! [SY90: $i] :
( ( ( SY88 @ ( sK24_SY91 @ SY90 @ SY88 ) )
& ( SY90
!= ( sK24_SY91 @ SY90 @ SY88 ) ) )
| ~ ( SY88 @ SY90 ) )
| ( SY88 @ ( sK23_Xx @ SY88 ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(546,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(547,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(548,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(549,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(550,plain,
( ( ! [SY76: $i > $o] :
( ! [SY78: $i] :
( ( ( SY76 @ ( sK22_SY79 @ SY78 @ SY76 ) )
& ( SY78
!= ( sK22_SY79 @ SY78 @ SY76 ) ) )
| ~ ( SY76 @ SY78 ) )
| ( ! [SY1639: $i] :
( ~ ( SY76 @ SY1639 )
| ( ( sK21_Xx @ SY76 )
= SY1639 ) )
& ( SY76 @ ( sK21_Xx @ SY76 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(551,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(552,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(553,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)],[215]) ).
thf(554,plain,
( ( ! [SY59: $i > $o] :
( ! [SY61: $i] :
( ( ( SY59 @ ( sK20_SY62 @ SY61 @ SY59 ) )
& ( SY61
!= ( sK20_SY62 @ SY61 @ SY59 ) ) )
| ~ ( SY59 @ SY61 ) )
| ( SY59
@ ( descr
@ ^ [Xx: $i] : ( SY59 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(555,plain,
( ( ! [A: $i] :
( ! [SY1615: $i] :
( ( ( in @ ( sK19_Xx @ SY1615 @ A ) @ SY1615 )
& ~ ( in @ ( sK19_Xx @ SY1615 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1615 )
| ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK15_B @ A ) )
| ! [SY1634: $i] :
( ~ ( in @ SY1634 @ SY1636 )
| ( in @ SY1634 @ ( sK17_SY1618 @ SY1615 @ A ) ) )
| ( in @ ( sK18_SY1632 @ SY1615 @ A ) @ SY1636 ) )
& ( in @ ( sK17_SY1618 @ SY1615 @ A ) @ ( sK15_B @ A ) )
& ( in @ ( sK18_SY1632 @ SY1615 @ A ) @ SY1615 )
& ! [SY1635: $i] :
( ~ ( in @ SY1635 @ ( sK17_SY1618 @ SY1615 @ A ) )
| ~ ( in @ SY1635 @ SY1615 ) ) ) )
& ! [SY1623: $i,SY1624: $i] :
( ~ ( in @ SY1623 @ ( sK15_B @ A ) )
| ~ ( in @ SY1624 @ ( sK15_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1623 )
| ( in @ Xx @ SY1624 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1624 )
| ( in @ Xx @ SY1623 ) ) )
& ! [SY1627: $i] :
( ~ ( in @ SY1627 @ ( sK15_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1627 )
| ( in @ Xx @ A ) ) )
& ! [SY1629: $i,SY1630: $i] :
( ~ ( in @ SY1629 @ A )
| ~ ( in @ SY1630 @ A )
| ( ( in @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) @ ( sK15_B @ A ) )
& ( ~ ( in @ SY1629 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) )
| ~ ( in @ SY1630 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) ) )
& ( ( in @ SY1629 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) )
| ( in @ SY1630 @ ( sK16_SY1631 @ SY1630 @ SY1629 @ A ) ) ) )
| ( SY1629 = SY1630 ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(556,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK14_B @ A ) @ A )
& ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK14_B @ A ) )
| ~ ( in @ SY1614 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(557,plain,
( ( ! [SY27: $i > $i > $o,SY28: $i] :
( ( ( in @ ( sK12_SY29 @ SY28 @ SY27 ) @ SY28 )
& ! [SY1612: $i] :
( ( ( SY27 @ ( sK12_SY29 @ SY28 @ SY27 ) @ ( sK13_SY1613 @ SY1612 @ SY28 @ SY27 ) )
& ( SY1612
!= ( sK13_SY1613 @ SY1612 @ SY28 @ SY27 ) ) )
| ~ ( SY27 @ ( sK12_SY29 @ SY28 @ SY27 ) @ SY1612 ) ) )
| ( ! [SY1608: $i] :
( ! [Xy: $i] :
( ~ ( SY27 @ Xy @ SY1608 )
| ~ ( in @ Xy @ SY28 ) )
| ( in @ SY1608 @ ( sK10_B @ SY28 @ SY27 ) ) )
& ! [SY1610: $i] :
( ~ ( in @ SY1610 @ ( sK10_B @ SY28 @ SY27 ) )
| ( ( SY27 @ ( sK11_Xy @ SY1610 @ SY28 @ SY27 ) @ SY1610 )
& ( in @ ( sK11_Xy @ SY1610 @ SY28 @ SY27 ) @ SY28 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(558,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK9_Xx @ A ) @ omega )
& ( in @ ( sK9_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK9_Xx @ A ) @ ( sK9_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(559,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(560,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(561,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 @ ( sK8_B @ Xx @ A ) )
& ( in @ ( sK8_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(562,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK7_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK7_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)],[207]) ).
thf(563,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)],[206]) ).
thf(564,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK6_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK6_Xx @ B @ A ) @ A )
| ( in @ ( sK6_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(566,plain,
( ( ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) )
& ! [SY1605: $i] :
( ~ ( in @ SY1605 @ sK1_SY0 )
| ! [SY1606: $i] :
( ~ ( in @ SY1606 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SY1605 @ SY1606 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SY1605 @ SY1606 ) ) ) )
& ( in @ sK5_SY1607 @ sK3_SY1596 )
& ~ ( sK4_SY1601 @ sK5_SY1607 ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(567,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)],[510,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(568,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK33_SY147 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK33_SY147 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ( SX1
!= ( sK32_Xx @ SX0 ) )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( SX1
= ( sK32_Xx @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(569,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK30_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK30_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(570,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ( ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) )
!= ( setadjoin @ ( sK79_SY525 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY525 @ SX0 )
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( ~ ( in @ ( sK75_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK75_Xy @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( ( sK75_Xy @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ ( sK74_SY503 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(572,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ( ~ ( SX1 @ ( sK73_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK73_Xx @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK93_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK93_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) )
@ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(574,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)],[501,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(575,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ( ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK80_SY562 @ SX0 )
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(576,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( kpair @ ( sK67_Xx @ SX2 @ SX1 @ SX0 ) @ ( sK68_SY1652 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK67_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK40_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK40_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(578,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)],[541,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(579,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0 @ ( sK44_Xx @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK45_SY1644 @ SX0 ) )
| ~ ( ( ( sK44_Xx @ SX0 )
!= ( sK45_SY1644 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK43_SY210 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK43_SY210 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(581,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)],[464,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK95_SY1693 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ~ ( SX3 @ ( kpair @ ( sK94_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK95_SY1693 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(583,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK42_Xy @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK42_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK41_SY203 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK41_SY203 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(584,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
!= ( setadjoin @ ( sK85_SY753 @ SX3 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SX3 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK39_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ( ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK63_SY1651 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX2 @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( SX3 @ ( sK63_SY1651 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2 @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( SX3 @ ( sK63_SY1651 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(587,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK89_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] :
( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] :
( ( SX2 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SX3 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SX3 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] :
( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] :
( ( SX2 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK87_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(588,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(589,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)],[511,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(590,plain,
( ( ~ ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
!= ( sK56_SY1649 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK53_SY240 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK53_SY240 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
!= ( sK52_SY1647 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK49_SY237 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK49_SY237 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(591,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK19_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK19_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK15_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK17_SY1618 @ SX1 @ SX0 ) ) )
| ( in @ ( sK18_SY1632 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SX1 @ SX0 ) @ ( sK15_B @ SX0 ) )
| ~ ( in @ ( sK18_SY1632 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK17_SY1618 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK15_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK15_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK15_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SX2 @ SX1 @ SX0 ) @ ( sK15_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK16_SY1631 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK16_SY1631 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK16_SY1631 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK16_SY1631 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( in @ ( sK82_SY661 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ! [SX3: $i] :
( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) )
!= ( setadjoin @ SX3 @ emptyset ) )
| ~ ( in @ SX3
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) )
| ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
!= ( setadjoin @ ( sK81_SY667 @ SX3 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SX3 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(593,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK12_SY29 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK12_SY29 @ SX1 @ SX0 ) @ ( sK13_SY1613 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK13_SY1613 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK12_SY29 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK10_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK10_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK11_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK11_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(594,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)],[438,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(595,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK48_SY229 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK48_SY229 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ( ~ ( in @ SX1 @ ( sK31_B @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ SX2 ) )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(597,plain,
( ( ~ ( ~ ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(598,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK57_SY253 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK57_SY253 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( in @ ( sK83_SY689 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ! [SX3: $i] :
( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) )
!= ( setadjoin @ SX3 @ emptyset ) )
| ~ ( in @ SX3
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) )
| ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in
@ ( setunion
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
@ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK77_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK78_SY1660 @ SX1 @ SX0 ) )
| ~ ( ( ( sK77_Xx @ SX1 @ SX0 )
!= ( sK78_SY1660 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= ( setadjoin @ ( sK76_SY515 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(601,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
~ ( ~ ( ( ( sK47_Xy @ SX1 @ SX0 )
!= SX1 )
| ~ ( SX0 @ ( sK47_Xy @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK47_Xy @ SX1 @ SX0 )
= SX1 )
| ( SX0 @ ( sK47_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK46_SY216 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK46_SY216 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(602,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK24_SY91 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK24_SY91 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK23_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(603,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK35_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK35_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK71_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK71_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK72_SY1655 @ SX1 @ SX0 ) )
| ~ ( ( ( sK71_Xx @ SX1 @ SX0 )
!= ( sK72_SY1655 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= ( setadjoin @ ( sK70_SY484 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(606,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] :
( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] :
( ( SX2 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SX3 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SX3 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] :
( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] :
( ( SX2 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SX1: $i,SX2: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( SX2 @ ( sK90_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK66_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK66_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK36_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( SX1 @ ( sK36_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( in @ ( sK86_SY791 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ! [SX3: $i] :
( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) )
!= ( setadjoin @ SX3 @ emptyset ) )
| ~ ( in @ SX3
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) )
| ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(610,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SX0 ) @ ( sK9_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ( in @ ( sK84_SY716 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ! [SX3: $i] :
( ( ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) )
!= ( setadjoin @ SX3 @ emptyset ) )
| ~ ( in @ SX3
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX2 ) ) ) ) )
| ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in
@ ( setunion
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
@ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(612,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK14_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(613,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK20_SY62 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK20_SY62 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(614,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)],[534,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(617,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK60_Xx @ SX1 @ SX0 )
!= ( sK61_SY1650 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK60_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK61_SY1650 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK60_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK61_SY1650 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK59_SY262 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK59_SY262 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK58_SY265 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK58_SY265 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(618,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK7_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)],[562,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ ( sK69_X @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ SX1 @ ( sK69_X @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(620,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK22_SY79 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK22_SY79 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK21_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK21_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(621,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)],[563,ap,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,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,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,func,funcImageSingleton,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,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,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(622,plain,
! [SV1: $i] :
( ( ! [SY1694: $i,SY1695: $i] :
( ~ ( in @ SY1695 @ ( funcSet @ SV1 @ SY1694 ) )
| ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY1694
@ ^ [SY769: $i] : ( in @ ( kpair @ SY1696 @ SY769 ) @ SY1695 ) ) )
@ SY1694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(623,plain,
! [SV2: $i] :
( ( ! [SY1698: $i,SY1699: $i > $i > $o,SY1700: $i,SY1701: $i] :
( ~ ( in @ ( kpair @ SY1700 @ SY1701 )
@ ( dpsetconstr @ SV2 @ SY1698
@ ^ [Xz: $i,Xu: $i] : ( SY1699 @ Xz @ Xu ) ) )
| ( SY1699 @ SY1700 @ SY1701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(624,plain,
! [SV3: $i] :
( ( ! [SY1704: $i,SY1705: $i > $i > $o,SY1706: $i,SY1707: $i] :
( ~ ( in @ ( kpair @ SY1706 @ SY1707 )
@ ( dpsetconstr @ SV3 @ SY1704
@ ^ [Xz: $i,Xu: $i] : ( SY1705 @ Xz @ Xu ) ) )
| ( in @ SY1707 @ SY1704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(625,plain,
! [SV4: $i] :
( ( ! [SY1710: $i,SY1711: $i > $i > $o,SY1712: $i] :
( ! [SY1713: $i] :
~ ( in @ ( kpair @ SY1712 @ SY1713 )
@ ( dpsetconstr @ SV4 @ SY1710
@ ^ [Xz: $i,Xu: $i] : ( SY1711 @ Xz @ Xu ) ) )
| ( in @ SY1712 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(626,plain,
! [SV5: $i] :
( ( ! [SY1716: $i,SY1717: $i > $i > $o,SY1718: $i] :
( ~ ( in @ SY1718 @ SV5 )
| ! [SY1719: $i] :
( ~ ( in @ SY1719 @ SY1716 )
| ~ ( in @ ( kpair @ SY1718 @ SY1719 )
@ ( dpsetconstr @ SV5 @ SY1716
@ ^ [Xz: $i,Xu: $i] : ( SY1717 @ Xz @ Xu ) ) )
| ( SY1717 @ SY1718 @ SY1719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(627,plain,
! [SV6: $i] :
( ( ! [SY1722: $i,SY1723: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV6 @ SY1722
@ ^ [Xx: $i,Xy: $i] : ( SY1723 @ Xx @ Xy ) )
@ ( cartprod @ SV6 @ SY1722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(628,plain,
! [SV7: $i] :
( ( ! [SY1726: $i,SY1727: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV7 @ SY1726
@ ^ [Xx: $i,Xy: $i] : ( SY1727 @ Xx @ Xy ) )
@ ( cartprod @ SV7 @ SY1726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(629,plain,
! [SV8: $i] :
( ( ! [SY1730: $i,SY1731: $i > $i > $o,SY1732: $i] :
( ~ ( in @ SY1732 @ SV8 )
| ! [SY1733: $i] :
( ~ ( in @ SY1733 @ SY1730 )
| ~ ( SY1731 @ SY1732 @ SY1733 )
| ( in @ ( kpair @ SY1732 @ SY1733 )
@ ( dpsetconstr @ SV8 @ SY1730
@ ^ [Xz: $i,Xu: $i] : ( SY1731 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(630,plain,
! [SV9: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ~ ( in @ SY1737 @ ( cartprod @ SV9 @ SY1736 ) )
| ( ( kpair @ ( kfst @ SY1737 ) @ ( ksnd @ SY1737 ) )
= SY1737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(631,plain,
! [SV10: $i] :
( ( ! [SY1738: $i,SY1739: $i] :
( ~ ( in @ SY1739 @ SV10 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY1738 )
| ( ( ksnd @ ( kpair @ SY1739 @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(632,plain,
! [SV11: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
( ~ ( in @ SY1742 @ SV11 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY1741 )
| ( ( kfst @ ( kpair @ SY1742 @ Xy ) )
= SY1742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(633,plain,
! [SV12: $i] :
( ( ! [SY1744: $i] :
~ ( in @ SY1744 @ SV12 )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(634,plain,
! [SV13: $i] :
( ( ! [SY1747: $i,SY1748: $i,SY1749: $i] :
( ~ ( in @ ( kpair @ SY1748 @ SY1749 ) @ ( cartprod @ SV13 @ SY1747 ) )
| ( in @ SY1749 @ SY1747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(635,plain,
! [SV14: $i] :
( ( ! [SY1750: $i,SY1751: $i] :
( ! [SY1752: $i] :
~ ( in @ ( kpair @ SY1751 @ SY1752 ) @ ( cartprod @ SV14 @ SY1750 ) )
| ( in @ SY1751 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(636,plain,
! [SV15: $i] :
( ( ! [SY1753: $i,SY1754: $i] :
( ~ ( in @ SY1754 @ ( cartprod @ SV15 @ SY1753 ) )
| ( in @ ( ksnd @ SY1754 ) @ SY1753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(637,plain,
! [SV16: $i] :
( ( ~ ( iskpair @ SV16 )
| ( ( kpair @ ( kfst @ SV16 ) @ ( ksnd @ SV16 ) )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(638,plain,
! [SV17: $i] :
( ( ! [SY1755: $i] :
( ( ksnd @ ( kpair @ SV17 @ SY1755 ) )
= SY1755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(639,plain,
! [SV18: $i] :
( ( ! [SY1756: $i,SY1757: $i,SY1758: $i] :
( ( ( kpair @ SV18 @ SY1756 )
!= ( kpair @ SY1757 @ SY1758 ) )
| ( SY1756 = SY1758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(640,plain,
! [SV19: $i] :
( ( ! [SY1759: $i,SY1760: $i,SY1761: $i] :
( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SY1759 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1760 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1760 @ ( setadjoin @ SY1761 @ emptyset ) ) @ emptyset ) ) )
| ( SY1759 = SY1761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(641,plain,
! [SV20: $i] :
( ( ! [SY1762: $i] :
( ! [SY1763: $i] :
( ( setadjoin @ SV20 @ ( setadjoin @ SY1762 @ emptyset ) )
!= ( setadjoin @ SY1763 @ emptyset ) )
| ( SV20 = SY1762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(642,plain,
! [SV21: $i] :
( ( ! [SY1764: $i,SY1765: $i,SY1766: $i] :
( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SY1764 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1765 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1765 @ ( setadjoin @ SY1766 @ emptyset ) ) @ emptyset ) ) )
| ( SY1765 != SY1766 )
| ( SY1764 = SY1766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(643,plain,
! [SV22: $i] :
( ( ! [SY1767: $i] :
( ( SV22 != SY1767 )
| ( ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV22 @ ( setadjoin @ SY1767 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(644,plain,
! [SV23: $i] :
( ( ! [SY1768: $i] :
( ( SV23 != SY1768 )
| ( ( setadjoin @ SV23 @ ( setadjoin @ SY1768 @ emptyset ) )
= ( setadjoin @ SV23 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(645,plain,
! [SV24: $i] :
( ( ! [SY1769: $i,SY1770: $i] :
( ! [SY1771: $i] :
( ( kpair @ SV24 @ SY1769 )
!= ( kpair @ SY1770 @ SY1771 ) )
| ( SV24 = SY1770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(646,plain,
! [SV25: $i] :
( ( ! [SY1772: $i,SY1773: $i] :
( ! [SY1774: $i] :
( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SY1772 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1773 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1773 @ ( setadjoin @ SY1774 @ emptyset ) ) @ emptyset ) ) )
| ( SV25 = SY1773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(647,plain,
! [SV26: $i] :
( ( ! [SY1775: $i,SY1776: $i] :
( ~ ( in @ SY1776 @ ( cartprod @ SV26 @ SY1775 ) )
| ( in @ ( kfst @ SY1776 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(648,plain,
! [SV27: $i] :
( ( ! [SY1777: $i] :
( ( kfst @ ( kpair @ SV27 @ SY1777 ) )
= SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(649,plain,
! [SV28: $i] :
( ( ! [SY1778: $i] :
( ( SV28
!= ( setadjoin @ SY1778 @ emptyset ) )
| ~ ( in @ SY1778 @ SV28 ) )
| ( in @ ( setunion @ SV28 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(650,plain,
! [SV29: $i] :
( ( ! [SY1779: $i,SY1780: $i] :
( ~ ( in @ ( setadjoin @ SY1780 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ ( setadjoin @ SY1779 @ emptyset ) ) @ emptyset ) ) )
| ( SV29 = SY1780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(651,plain,
! [SV30: $i] :
( ( ! [SY1781: $i] :
( ( ( setadjoin @ SV30 @ emptyset )
!= ( setadjoin @ SY1781 @ emptyset ) )
| ( SV30 = SY1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(652,plain,
! [SV31: $i] :
( ( ( setunion @ ( setadjoin @ SV31 @ emptyset ) )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(653,plain,
! [SV32: $i] :
( ( subset @ SV32 @ ( setunion @ ( setadjoin @ SV32 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(654,plain,
! [SV33: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV33 @ emptyset ) ) @ SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(655,plain,
! [SV34: $i] :
( ( ! [SY1782: $i,SY1783: $i] :
( ~ ( in @ SY1783 @ ( cartprod @ SV34 @ SY1782 ) )
| ( iskpair @ SY1783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(656,plain,
! [SV35: $i] :
( ( ! [SY1784: $i,SY1785: $i] :
( ~ ( in @ SY1785 @ SV35 )
| ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SY1784 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ ( cartprod @ SV35 @ SY1784 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(657,plain,
! [SV36: $i] :
( ( ! [SY1787: $i,SY1788: $i] :
( ~ ( in @ SY1788 @ SV36 )
| ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SY1787 )
| ( in @ ( kpair @ SY1788 @ SY1789 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SY1787 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(658,plain,
! [SV37: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ~ ( in @ SY1791 @ SV37 )
| ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SY1790 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1791 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1791 @ ( setadjoin @ SY1792 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SY1790 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(659,plain,
! [SV38: $i] :
( ( ! [SY1793: $i,SY1794: $i] :
( ~ ( in @ SY1794 @ SV38 )
| ! [SY1795: $i] :
( ~ ( in @ SY1795 @ SY1793 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1794 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1794 @ ( setadjoin @ SY1795 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SY1793 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(660,plain,
! [SV39: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ~ ( in @ SY1797 @ SV39 )
| ! [SY1798: $i] :
( ~ ( in @ SY1798 @ SY1796 )
| ( in @ ( setadjoin @ SY1797 @ ( setadjoin @ SY1798 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SY1796 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(661,plain,
! [SV40: $i] :
( ( ! [SY1799: $i,SY1800: $i] :
( ~ ( in @ SY1800 @ SV40 )
| ! [SY1801: $i] :
( ~ ( in @ SY1801 @ SY1799 )
| ( subset @ ( setadjoin @ SY1800 @ ( setadjoin @ SY1801 @ emptyset ) ) @ ( binunion @ SV40 @ SY1799 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(662,plain,
! [SV41: $i] :
( ( ! [SY1802: $i,SY1803: $i] :
( ~ ( in @ SY1803 @ ( setadjoin @ SV41 @ ( setadjoin @ SY1802 @ emptyset ) ) )
| ( SY1803 = SV41 )
| ( SY1803 = SY1802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(663,plain,
! [SV42: $i] :
( ( ! [SY1804: $i,SY1805: $i] :
( ~ ( in @ SY1805 @ SV42 )
| ( in @ ( setadjoin @ SY1805 @ emptyset ) @ ( powerset @ ( binunion @ SV42 @ SY1804 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(664,plain,
! [SV43: $i] :
( ( ! [SY1806: $i] :
( ~ ( in @ SY1806 @ SV43 )
| ( in @ ( setadjoin @ SY1806 @ emptyset ) @ ( powerset @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(665,plain,
! [SV44: $i] :
( ( ! [SY1807: $i] :
( ~ ( in @ SY1807 @ SV44 )
| ( subset @ ( setadjoin @ SY1807 @ emptyset ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(666,plain,
! [SV45: $i] :
( ( ! [SY1808: $i] : ( iskpair @ ( kpair @ SV45 @ SY1808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(667,plain,
! [SV46: $i] :
( ( ! [SY1809: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV46 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV46 @ ( setadjoin @ SY1809 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(668,plain,
! [SV47: $i] :
( ( ! [SY1810: $i] : ( in @ SY1810 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV47 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV47 @ ( setadjoin @ SY1810 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(669,plain,
! [SV48: $i] :
( ( ! [SY1811: $i] : ( in @ SV48 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SY1811 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(670,plain,
! [SV49: $i] :
( ( ! [SY1812: $i] : ( in @ SY1812 @ ( setadjoin @ SV49 @ ( setadjoin @ SY1812 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(671,plain,
! [SV50: $i] :
( ( ! [SY1813: $i,SY1814: $i] :
( ( in @ SY1814 @ SV50 )
| ( in @ SY1814 @ SY1813 )
| ~ ( in @ SY1814 @ ( symdiff @ SV50 @ SY1813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(672,plain,
! [SV51: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ~ ( in @ SY1816 @ SV51 )
| ~ ( in @ SY1816 @ SY1815 )
| ~ ( in @ SY1816 @ ( symdiff @ SV51 @ SY1815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(673,plain,
! [SV52: $i] :
( ( ! [SY1817: $i,SY1818: $i] :
( ( in @ SY1818 @ SV52 )
| ~ ( in @ SY1818 @ SY1817 )
| ( in @ SY1818 @ ( symdiff @ SV52 @ SY1817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(674,plain,
! [SV53: $i] :
( ( ! [SY1819: $i,SY1820: $i] :
( ~ ( in @ SY1820 @ SV53 )
| ( in @ SY1820 @ SY1819 )
| ( in @ SY1820 @ ( symdiff @ SV53 @ SY1819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(675,plain,
! [SV54: $i] :
( ( ! [SY1821: $i] :
( ( ( setminus @ SV54 @ SY1821 )
!= emptyset )
| ( subset @ SV54 @ SY1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(676,plain,
! [SV55: $i] :
( ( ! [SY1822: $i] : ( subset @ ( setminus @ SV55 @ SY1822 ) @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(677,plain,
! [SV56: $i] :
( ( ! [SY1823: $i,SY1824: $i] :
( ~ ( in @ SY1824 @ SY1823 )
| ~ ( in @ SY1824 @ ( setminus @ SV56 @ SY1823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(678,plain,
! [SV57: $i] :
( ( ! [SY1825: $i,SY1826: $i] :
( ( in @ SY1826 @ SV57 )
| ~ ( in @ SY1826 @ ( setminus @ SV57 @ SY1825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(679,plain,
! [SV58: $i] :
( ( ! [SY1827: $i,SY1828: $i] :
( ( in @ SY1828 @ ( setminus @ SV58 @ SY1827 ) )
| ( in @ SY1828 @ SY1827 )
| ~ ( in @ SY1828 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(680,plain,
! [SV59: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ( in @ SY1830 @ ( setminus @ SV59 @ SY1829 ) )
| ~ ( in @ SY1830 @ SV59 )
| ( in @ SY1830 @ SY1829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(681,plain,
! [SV60: $i] :
( ( ! [SY1831: $i] :
( ~ ( subset @ SV60 @ SY1831 )
| ( ( setminus @ SV60 @ SY1831 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(682,plain,
! [SV61: $i] :
( ( ! [SY1832: $i,SY1833: $i] :
( ~ ( in @ SY1833 @ ( setminus @ SV61 @ SY1832 ) )
| ~ ( in @ SY1833 @ SY1832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(683,plain,
! [SV62: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ~ ( in @ SY1835 @ ( setminus @ SV62 @ SY1834 ) )
| ( in @ SY1835 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(684,plain,
! [SV63: $i] :
( ( ! [SY1836: $i,SY1837: $i] :
( ~ ( in @ SY1837 @ SV63 )
| ( in @ SY1837 @ SY1836 )
| ( in @ SY1837 @ ( setminus @ SV63 @ SY1836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(685,plain,
! [SV64: $i] :
( ( ! [SY1838: $i,SY1839: $i] :
( ( binintersect @ SV64 @ ( binunion @ SY1838 @ SY1839 ) )
= ( binunion @ ( binintersect @ SV64 @ SY1838 ) @ ( binintersect @ SV64 @ SY1839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(686,plain,
! [SV65: $i] :
( ( ! [SY1840: $i] :
( ( ( binintersect @ SV65 @ SY1840 )
!= SV65 )
| ( subset @ SV65 @ SY1840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(687,plain,
! [SV66: $i] :
( ( ! [SY1841: $i] :
( ~ ( subset @ SY1841 @ SV66 )
| ( ( binintersect @ SV66 @ SY1841 )
= SY1841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(688,plain,
! [SV67: $i] :
( ( ! [SY1842: $i] : ( subset @ ( binintersect @ SV67 @ SY1842 ) @ SY1842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(689,plain,
! [SV68: $i] :
( ( ! [SY1843: $i,SY1844: $i] :
( ~ ( in @ SY1844 @ ( binintersect @ SV68 @ SY1843 ) )
| ( in @ SY1844 @ SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(690,plain,
! [SV69: $i] :
( ( ! [SY1845: $i] :
( ( ( binintersect @ SV69 @ SY1845 )
!= SY1845 )
| ( subset @ SY1845 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(691,plain,
! [SV70: $i] :
( ( ! [SY1846: $i] :
( ~ ( subset @ SV70 @ SY1846 )
| ( ( binintersect @ SV70 @ SY1846 )
= SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(692,plain,
! [SV71: $i] :
( ( ! [SY1847: $i] : ( subset @ ( binintersect @ SV71 @ SY1847 ) @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(693,plain,
! [SV72: $i] :
( ( ! [SY1848: $i,SY1849: $i] :
( ~ ( in @ SY1849 @ ( binintersect @ SV72 @ SY1848 ) )
| ( in @ SY1849 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(694,plain,
! [SV73: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( subset @ SY1851 @ SV73 )
| ~ ( subset @ SY1851 @ SY1850 )
| ( subset @ SY1851 @ ( binintersect @ SV73 @ SY1850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(695,plain,
! [SV74: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( in @ SY1853 @ SV74 )
| ~ ( in @ SY1853 @ SY1852 )
| ( in @ SY1853 @ ( binintersect @ SV74 @ SY1852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(696,plain,
! [SV75: $i] :
( ( ! [SY1854: $i] : ( subset @ SY1854 @ ( binunion @ SV75 @ SY1854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(697,plain,
! [SV76: $i] :
( ( ! [SY1855: $i] : ( subset @ SV76 @ ( binunion @ SV76 @ SY1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(698,plain,
! [SV77: $i] :
( ( ! [SY1856: $i,SY1857: $i] :
( ~ ( in @ SY1857 @ ( binunion @ SV77 @ SY1856 ) )
| ( in @ SY1857 @ SV77 )
| ( in @ SY1857 @ SY1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(699,plain,
! [SV78: $i] :
( ( ! [SY1858: $i,SY1859: $i] :
( ~ ( in @ SY1859 @ SY1858 )
| ( in @ SY1859 @ ( binunion @ SV78 @ SY1858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(700,plain,
! [SV79: $i] :
( ( ! [SY1860: $i] : ( in @ SY1860 @ ( setadjoin @ SV79 @ ( setadjoin @ SY1860 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(701,plain,
! [SV80: $i] :
( ( ! [SY1861: $i,SY1862: $i] :
( ~ ( in @ SY1862 @ SV80 )
| ( in @ SY1862 @ ( binunion @ SV80 @ SY1861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(702,plain,
! [SV81: $i] :
( ( ! [SY1863: $i > $o] :
( subset
@ ( dsetconstr @ SV81
@ ^ [Xx: $i] : ( SY1863 @ Xx ) )
@ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(703,plain,
! [SV82: $i] :
( ( ! [SY1865: $i > $o] :
( in
@ ( dsetconstr @ SV82
@ ^ [Xx: $i] : ( SY1865 @ Xx ) )
@ ( powerset @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(704,plain,
! [SV83: $i] :
( ( ! [SY1867: $i] :
( ~ ( subset @ SV83 @ SY1867 )
| ( subset @ ( powerset @ SV83 ) @ ( powerset @ SY1867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(705,plain,
! [SV84: $i] :
( ( in @ SV84 @ ( powerset @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(706,plain,
! [SV85: $i] :
( ( ! [SY1868: $i] :
( ~ ( in @ SY1868 @ ( powerset @ SV85 ) )
| ( subset @ SY1868 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(707,plain,
! [SV86: $i] :
( ( ! [SY1869: $i] :
( ~ ( subset @ SY1869 @ SV86 )
| ( in @ SY1869 @ ( powerset @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(708,plain,
! [SV87: $i] :
( ( ~ ( subset @ SV87 @ emptyset )
| ( SV87 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(709,plain,
! [SV88: $i] :
( ( ! [SY1870: $i] :
( ~ ( subset @ SV88 @ SY1870 )
| ~ ( subset @ SY1870 @ SV88 )
| ( SV88 = SY1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(710,plain,
! [SV89: $i] :
( ( ! [SY1871: $i] :
( ~ ( subset @ SV89 @ SY1871 )
| ( in @ SV89 @ ( powerset @ SY1871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(711,plain,
! [SV90: $i] :
( ( ! [SY1872: $i,SY1873: $i] :
( ~ ( subset @ SV90 @ SY1873 )
| ( subset @ SV90 @ ( setadjoin @ SY1872 @ SY1873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(712,plain,
! [SV91: $i] :
( ( ! [SY1874: $i] : ( subset @ SY1874 @ ( setadjoin @ SV91 @ SY1874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(713,plain,
! [SV92: $i] :
( ( ! [SY1875: $i] :
( ~ ( subset @ SV92 @ SY1875 )
| ! [SY1876: $i] :
( ~ ( subset @ SY1875 @ SY1876 )
| ( subset @ SV92 @ SY1876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(714,plain,
! [SV93: $i] :
( ( subset @ SV93 @ SV93 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(715,plain,
! [SV94: $i] :
( ( ! [SY1877: $i,SY1878: $i] :
( ~ ( in @ SY1878 @ SV94 )
| ( in @ SY1878 @ SY1877 )
| ( SV94 != SY1877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(716,plain,
! [SV95: $i] :
( ( ! [SY1879: $i] :
( ( subset @ SV95 @ SY1879 )
| ( SV95 != SY1879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(717,plain,
! [SV96: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
( ~ ( in @ SY1881 @ SV96 )
| ( in @ SY1881 @ SY1880 )
| ~ ( subset @ SV96 @ SY1880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(718,plain,
! [SV97: $i] :
( ( ! [SY1882: $i] :
( ~ ( subset @ SV97 @ SY1882 )
| ! [SY1883: $i] :
( ( in @ SY1883 @ SY1882 )
| ~ ( in @ SY1883 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(719,plain,
! [SV98: $i] :
( ( ! [SY1884: $i] :
( ~ ( subset @ SV98 @ SY1884 )
| ! [SY1885: $i] :
( ~ ( in @ SY1885 @ SV98 )
| ( in @ SY1885 @ SY1884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(720,plain,
! [SV99: $i] :
( ( subset @ emptyset @ SV99 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(721,plain,
! [SV100: $i] :
( ( ! [SY1886: $i] :
( ( SV100 != SY1886 )
| ( subset @ SV100 @ SY1886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(722,plain,
! [SV101: $i] :
( ( ! [SY1887: $i] :
( ( SV101 != SY1887 )
| ( subset @ SY1887 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(723,plain,
! [SV102: $i] :
( ( ! [SY1888: $i] :
( ( SV102 != SY1888 )
| ( ( setunion @ SV102 )
= ( setunion @ SY1888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(724,plain,
! [SV103: $i] :
( ( ! [SY1889: $i] :
( ( SV103 != SY1889 )
| ( ( powerset @ SV103 )
= ( powerset @ SY1889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(725,plain,
! [SV104: $i] :
( ( ! [SY1890: $i] :
( ( SV104 != SY1890 )
| ! [SY1891: $i,SY1892: $i] :
( ( SY1891 != SY1892 )
| ( ( setadjoin @ SV104 @ SY1891 )
= ( setadjoin @ SY1890 @ SY1892 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(726,plain,
! [SV105: $i] :
( ( ! [SY1893: $i] :
( ( SV105 != SY1893 )
| ! [SY1894: $i,SY1895: $i] :
( ( SY1894 != SY1895 )
| ~ ( in @ SY1894 @ SV105 )
| ( in @ SY1895 @ SY1893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(727,plain,
! [SV106: $o] :
( ( ~ SV106
| ( set2prop @ ( prop2set @ SV106 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[508]) ).
thf(728,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[508]) ).
thf(729,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[508]) ).
thf(730,plain,
! [SV107: $o] :
( ( ~ SV107
| ( in @ emptyset @ ( prop2set @ SV107 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[509]) ).
thf(731,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[509]) ).
thf(732,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[509]) ).
thf(733,plain,
! [SV108: $i > $o] :
( ( ! [SY1896: $i] :
( ~ ( in @ SY1896 @ emptyset )
| ( SV108 @ SY1896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(734,plain,
! [SV109: $i] :
( ( ! [SY1897: $i > $o] :
( ! [SY1898: $i] :
( ~ ( SY1897 @ SY1898 )
| ~ ( in @ SY1898 @ SV109 ) )
| ( ( dsetconstr @ SV109
@ ^ [Xx: $i] : ( SY1897 @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(735,plain,
! [SV110: $i] :
( ( ! [SY1900: $i] : ( in @ SY1900 @ ( setadjoin @ SV110 @ ( setadjoin @ SY1900 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(736,plain,
! [SV111: $i] :
( ( ! [SY1901: $i] : ( in @ SV111 @ ( setadjoin @ SV111 @ ( setadjoin @ SY1901 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(737,plain,
! [SV112: $i] :
( ( ! [SY1902: $i,SY1903: $i] :
( ~ ( in @ SY1903 @ ( setadjoin @ SV112 @ ( setadjoin @ SY1902 @ emptyset ) ) )
| ( SY1903 = SV112 )
| ( SY1903 = SY1902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(738,plain,
! [SV113: $i] :
( ( ! [SY1904: $i] :
( ~ ( in @ SV113 @ ( setadjoin @ SY1904 @ emptyset ) )
| ( in @ SY1904 @ ( setadjoin @ SV113 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(739,plain,
! [SV114: $i] :
( ( ! [SY1905: $i] :
( ( SV114 != SY1905 )
| ( in @ SV114 @ ( setadjoin @ SY1905 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(740,plain,
! [SV115: $i] :
( ( ! [SY1906: $i] :
( ( SV115 = SY1906 )
| ~ ( in @ SY1906 @ ( setadjoin @ SV115 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(741,plain,
! [SV116: $i] :
( ( ! [SY1907: $i] :
( ~ ( in @ SV116 @ ( setadjoin @ SY1907 @ emptyset ) )
| ( SV116 = SY1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(742,plain,
! [SV117: $i] :
( ( ( SV117 = emptyset )
| ( in @ ( sK34_Xx @ SV117 ) @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(743,plain,
! [SV118: $i] :
( ( ! [SY1908: $i] :
( ~ ( in @ SY1908 @ SV118 )
| ( in @ SY1908 @ ( powerset @ ( setunion @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(744,plain,
! [SV119: $i] :
( ( ! [SY1909: $i,SY1910: $i] :
( ~ ( in @ SY1909 @ SY1910 )
| ~ ( in @ SY1910 @ SV119 )
| ( in @ SY1909 @ ( setunion @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(745,plain,
! [SV120: $i] :
( ( ! [SY1911: $i] :
( ~ ( in @ SY1911 @ ( powerset @ SV120 ) )
| ! [SY1912: $i] :
( ~ ( in @ SY1912 @ SY1911 )
| ( in @ SY1912 @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(746,plain,
! [SV121: $i] :
( ( in @ emptyset @ ( powerset @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(747,plain,
! [SV122: $i] :
( ( in @ emptyset @ ( powerset @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(748,plain,
! [SV123: $i] :
( ( ( dsetconstr @ SV123
@ ^ [Xx: $i] : $true )
= SV123 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(749,plain,
! [SV124: $i] :
( ( ! [SY1914: $i,SY1915: $i] :
( ~ ( in @ SY1915 @ ( setadjoin @ SV124 @ SY1914 ) )
| ( SY1915 = SV124 )
| ( in @ SY1915 @ SY1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(750,plain,
! [SV125: $i] :
( ( ! [SY1916: $i,SY1917: $i] :
( ~ ( in @ SY1917 @ SY1916 )
| ( in @ SY1917 @ ( setadjoin @ SV125 @ SY1916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(751,plain,
! [SV126: $i] :
( ( ! [SY1918: $i] : ( in @ SV126 @ ( setadjoin @ SV126 @ SY1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(752,plain,
! [SV127: $i] :
( ( ! [SY1919: $i] :
~ ( in @ SY1919 @ SV127 )
| ( SV127 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(753,plain,
! [SV128: $i] :
( ( ! [SY1920: $i > $o,SY1921: $i] :
( ~ ( in @ SY1921 @ SV128 )
| ~ ( SY1920 @ SY1921 )
| ( ( dsetconstr @ SV128
@ ^ [Xy: $i] : ( SY1920 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(754,plain,
! [SV129: $i] :
( ( ( SV129 = emptyset )
| ( in @ ( sK29_Xx @ SV129 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(755,plain,
! [SV130: $i] :
( ( ( in @ ( sK28_Xx @ SV130 ) @ SV130 )
| ( SV130 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(756,plain,
! [SV131: $i] :
( ( ( in @ ( sK27_Xx @ SV131 ) @ SV131 )
| ( SV131 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(757,plain,
! [SV132: $i] :
( ( ~ ( in @ SV132 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(758,plain,
! [SV133: $i] :
( ( ~ ( in @ SV133 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(759,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(760,plain,
! [SV134: $o] :
( ( ! [SY1923: $i] :
~ ( in @ SY1923 @ ( prop2set @ SV134 ) )
| SV134 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[549]) ).
thf(761,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[549]) ).
thf(762,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[549]) ).
thf(763,plain,
! [SV135: $i] :
( ( ! [SY1924: $i > $o,SY1925: $i] :
( ~ ( in @ SY1925
@ ( dsetconstr @ SV135
@ ^ [Xy: $i] : ( SY1924 @ Xy ) ) )
| ( SY1924 @ SY1925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(764,plain,
! [SV136: $i] :
( ( ! [SY1927: $i > $o,SY1928: $i] :
( ~ ( in @ SY1928
@ ( dsetconstr @ SV136
@ ^ [Xy: $i] : ( SY1927 @ Xy ) ) )
| ( in @ SY1928 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(765,plain,
! [SV137: $i] :
( ( ! [SY1930: $i > $o,SY1931: $i] :
( ~ ( in @ SY1931 @ SV137 )
| ~ ( SY1930 @ SY1931 )
| ( in @ SY1931
@ ( dsetconstr @ SV137
@ ^ [Xy: $i] : ( SY1930 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(766,plain,
! [SV138: $i] :
( ( ~ ( in @ SV138 @ omega )
| ( in @ ( setadjoin @ SV138 @ SV138 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(767,plain,
! [SV139: $i] :
( ( ~ ( in @ SV139 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(768,plain,
! [SV140: $i] :
( ( ! [SY1933: $i > $o] :
( ! [SY1934: $i] :
( ~ ( in @ SY1934 @ SV140 )
| ( SY1933 @ SY1934 ) )
| ~ ( ~ ( in @ ( sK38_Xx @ SY1933 @ SV140 ) @ SV140 )
| ~ ~ ( SY1933 @ ( sK38_Xx @ SY1933 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(769,plain,
! [SV141: $i > $o] :
( ( ! [SY1935: $i] :
( ~ ( ~ ( SV141 @ ( sK33_SY147 @ SY1935 @ SV141 ) )
| ~ ( ( SY1935
!= ( sK33_SY147 @ SY1935 @ SV141 ) ) ) )
| ~ ( SV141 @ SY1935 ) )
| ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(770,plain,
! [SV142: $i] :
( ( ! [SY1938: $i] :
( ~ ( ~ ( in @ ( sK30_Xx @ SY1938 @ SV142 ) @ SY1938 )
| ~ ~ ( in @ ( sK30_Xx @ SY1938 @ SV142 ) @ SV142 ) )
| ( in @ SY1938 @ ( powerset @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(771,plain,
! [SV143: $i] :
( ( ~ ( iskpair @ SV143 )
| ~ ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
!= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(772,plain,
! [SV144: $i] :
( ( ! [SY1941: $i > $o,SY1942: $i] :
( ~ ( in @ SY1942 @ SV144 )
| ~ ( SY1941 @ SY1942 )
| ~ ( ~ ( in @ ( sK75_Xy @ SY1942 @ SY1941 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SY1941 @ ( sK75_Xy @ SY1942 @ SY1941 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SY1942 @ SY1941 @ SV144 )
!= SY1942 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1941 @ SX3 ) )
!= ( setadjoin @ ( sK74_SY503 @ SY1942 @ SY1941 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SY1942 @ SY1941 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1941 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(773,plain,
! [SV145: $i] :
( ( ! [SY1945: $i > $o] :
( ! [SY1946: $i] :
( ( ( dsetconstr @ SV145
@ ^ [SX3: $i] : ( SY1945 @ SX3 ) )
!= ( setadjoin @ SY1946 @ emptyset ) )
| ~ ( in @ SY1946
@ ( dsetconstr @ SV145
@ ^ [SX3: $i] : ( SY1945 @ SX3 ) ) ) )
| ~ ( ~ ( SY1945 @ ( sK73_Xx @ SY1945 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SY1945 @ SV145 ) @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(774,plain,
! [SV146: $i] :
( ( ! [SY1949: $i,SY1950: $i > $i] :
( ~ ( ~ ( in @ ( sK93_Xx @ SY1950 @ SY1949 @ SV146 ) @ SV146 )
| ~ ~ ( in @ ( SY1950 @ ( sK93_Xx @ SY1950 @ SY1949 @ SV146 ) ) @ SY1949 ) )
| ( in
@ ( dpsetconstr @ SV146 @ SY1949
@ ^ [SX3: $i,SX4: $i] :
( ( SY1950 @ SX3 )
= SX4 ) )
@ ( funcSet @ SV146 @ SY1949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(775,plain,
! [SV147: $i] :
( ( ! [SY1953: $i] :
( ( SV147 != SY1953 )
| ~ ( ~ ! [SY1954: $i,SY1955: $i] :
( ( SY1954 != SY1955 )
| ~ ( in @ SY1954 @ SV147 )
| ( in @ SY1955 @ SY1953 ) )
| ~ ! [SY1956: $i,SY1957: $i] :
( ( SY1956 != SY1957 )
| ~ ( in @ SY1957 @ SY1953 )
| ( in @ SY1956 @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(776,plain,
! [SV148: $i] :
( ( ~ ( iskpair @ SV148 )
| ~ ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
| ~ ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(777,plain,
! [SV149: $i] :
( ( ! [SY1960: $i,SY1961: $i] :
( ~ ( in @ SY1961 @ ( cartprod @ SV149 @ SY1960 ) )
| ~ ( ~ ~ ( ( SY1961
!= ( kpair @ ( sK67_Xx @ SY1961 @ SY1960 @ SV149 ) @ ( sK68_SY1652 @ SY1961 @ SY1960 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SY1961 @ SY1960 @ SV149 ) @ SY1960 ) )
| ~ ( in @ ( sK67_Xx @ SY1961 @ SY1960 @ SV149 ) @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(778,plain,
! [SV150: $i] :
( ( ! [SY1962: $i > $o] :
( ! [SY1963: $i] :
( ~ ( in @ SY1963 @ SV150 )
| ( SY1962 @ SY1963 ) )
| ~ ( ~ ( in @ ( sK40_Xx @ SY1962 @ SV150 ) @ SV150 )
| ~ ~ ( SY1962 @ ( sK40_Xx @ SY1962 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(779,plain,
! [SV151: $i] :
( ( ~ ( ~ ! [SY1964: $i > $o,SY1965: $i] :
( ~ ( in @ SY1965 @ SV151 )
| ~ ( SY1964 @ SY1965 )
| ( in @ SY1965
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1964 @ SX3 ) ) ) )
| ~ ! [SY1967: $i > $o,SY1968: $i] :
( ~ ( in @ SY1968 @ SV151 )
| ~ ( in @ SY1968
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1967 @ SX3 ) ) )
| ( SY1967 @ SY1968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(780,plain,
! [SV152: $i > $o] :
( ( ! [SY1970: $i] :
~ ( SV152 @ SY1970 )
| ~ ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
| ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(781,plain,
! [SV153: $i] :
( ( ! [SY1972: $i] :
( ~ ( ~ ( in @ ( sK26_Xx @ SY1972 @ SV153 ) @ SV153 )
| ~ ~ ( in @ ( sK26_Xx @ SY1972 @ SV153 ) @ SY1972 ) )
| ~ ( ~ ( in @ ( sK25_Xx @ SY1972 @ SV153 ) @ SY1972 )
| ~ ~ ( in @ ( sK25_Xx @ SY1972 @ SV153 ) @ SV153 ) )
| ( SV153 = SY1972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(782,plain,
! [SV154: $i] :
( ( ! [SY1973: $i] :
~ ( ~ ~ ( ~ ! [SY1974: $i] :
( ~ ( in @ SY1974 @ ( binunion @ SV154 @ SY1973 ) )
| ( in @ SY1974 @ SV154 )
| ( in @ SY1974 @ SY1973 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1976: $i] :
( ~ ( in @ SY1976 @ ( binunion @ SV154 @ SY1973 ) )
| ( in @ SY1976 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1978: $i] :
( ~ ( in @ SY1978 @ ( binunion @ SV154 @ SY1973 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SY1978 @ SY1973 )
| SX3 ) )
| ~ ( ! [SY1980: $i] :
~ ( in @ SY1980 @ ( binunion @ SV154 @ SY1973 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(783,plain,
! [SV155: $i] :
( ( ! [SY1982: $i,SY1983: $i] :
( ~ ( subset @ SY1983 @ ( cartprod @ SV155 @ SY1982 ) )
| ! [SY1984: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SY1984 @ SY1983 @ SY1982 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SY1984 @ SY1983 @ SY1982 @ SV155 ) @ SY1982 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SY1984 @ SY1983 @ SY1982 @ SV155 ) @ ( sK95_SY1693 @ SY1984 @ SY1983 @ SY1982 @ SV155 ) ) @ SY1983 )
| ~ ~ ( SY1984 @ ( kpair @ ( sK94_Xx @ SY1984 @ SY1983 @ SY1982 @ SV155 ) @ ( sK95_SY1693 @ SY1984 @ SY1983 @ SY1982 @ SV155 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1983 )
| ( SY1984 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(784,plain,
! [SV156: $i > $o] :
( ( ! [SY1986: $i] :
( ~ ( ~ ( SV156 @ ( sK42_Xy @ SY1986 @ SV156 ) )
| ~ ( ( SY1986
!= ( sK42_Xy @ SY1986 @ SV156 ) ) ) )
| ~ ( SV156 @ SY1986 ) )
| ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(785,plain,
! [SV157: $i] :
( ( ~ ( ~ ! [SY1988: $i,SY1989: $i] :
( ~ ( in @ SY1989 @ ( funcSet @ SV157 @ SY1988 ) )
| ! [SY1990: $i] :
( ~ ( in @ SY1990 @ SV157 )
| ~ ( ( ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 )
@ ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) ) ) ) ) )
| ~ ! [SY1993: $i,SY1994: $i] :
( ~ ( in @ SY1994 @ ( funcSet @ SV157 @ SY1993 ) )
| ( subset @ SY1994 @ ( cartprod @ SV157 @ SY1993 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(786,plain,
! [SV158: $i] :
( ( ! [SY1995: $i > $o] :
( ~ ( ~ ( SY1995 @ ( sK39_Xx @ SY1995 @ SV158 ) )
| ~ ( in @ ( sK39_Xx @ SY1995 @ SV158 ) @ SV158 ) )
| ! [SY1996: $i] :
( ~ ( in @ SY1996 @ SV158 )
| ~ ( SY1995 @ SY1996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(787,plain,
! [SV159: $i] :
( ( ! [SY1997: $i] :
( ( SV159 != SY1997 )
| ! [SY1998: $i > $o,SY1999: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY1999 @ SY1998 @ SY1997 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SY1999 @ SY1998 @ SY1997 @ SV159 ) @ SY1997 )
| ~ ~ ( ( ( sK62_Xx @ SY1999 @ SY1998 @ SY1997 @ SV159 )
!= ( sK63_SY1651 @ SY1999 @ SY1998 @ SY1997 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SY1998 @ ( sK62_Xx @ SY1999 @ SY1998 @ SY1997 @ SV159 ) )
| ~ ( SY1999 @ ( sK63_SY1651 @ SY1999 @ SY1998 @ SY1997 @ SV159 ) ) )
| ~ ( ( SY1998 @ ( sK62_Xx @ SY1999 @ SY1998 @ SY1997 @ SV159 ) )
| ( SY1999 @ ( sK63_SY1651 @ SY1999 @ SY1998 @ SY1997 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SX4: $i] : ( SY1998 @ SX4 ) )
= ( dsetconstr @ SY1997
@ ^ [SX4: $i] : ( SY1999 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(788,plain,
! [SV160: $i] :
( ( ~ ( ~ ! [SY2002: $i,SY2003: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2003 @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) ) @ SY2002 ) )
| ! [SY2004: $i] :
( ~ ( in @ SY2004 @ SV160 )
| ~ ( ( ( dsetconstr @ SY2002
@ ^ [SY2005: $i] :
( in @ ( kpair @ SY2004 @ SY2005 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 )
@ ( dsetconstr @ SY2002
@ ^ [SY2008: $i] :
( in @ ( kpair @ SY2004 @ SY2008 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SY2011: $i,SY2012: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2012 @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) ) @ SY2011 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SY2011
@ ^ [SX3: $i,SX4: $i] :
( ( SY2012 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV160 @ SY2011 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(789,plain,
! [SV161: $i] :
( ( ! [SY2015: $i] :
( ~ ( ~ ( in @ ( sK64_Xx @ SY2015 @ SV161 ) @ SV161 )
| ~ ~ ( in @ ( sK64_Xx @ SY2015 @ SV161 ) @ SY2015 ) )
| ( subset @ SV161 @ SY2015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(790,plain,
! [SV162: $i] :
( ( ! [SY2016: $i > $o] :
( ~ ( ~ ( SY2016 @ ( sK37_Xx @ SY2016 @ SV162 ) )
| ~ ( in @ ( sK37_Xx @ SY2016 @ SV162 ) @ SV162 ) )
| ! [SY2017: $i] :
( ~ ( in @ SY2017 @ SV162 )
| ~ ( SY2016 @ SY2017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(791,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
!= ( sK56_SY1649 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK53_SY240 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK53_SY240 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
!= ( sK52_SY1647 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK49_SY237 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK49_SY237 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(792,plain,
! [SV163: $i] :
( ( ~ ( ~ ! [SY2018: $i] :
( ~ ( ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SY2018 )
| ~ ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SV163 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2018 )
| ~ ( ~ ! [SY2020: $i] :
( ~ ( in @ SY2020 @ ( sK15_B @ SV163 ) )
| ! [SY2021: $i] :
( ~ ( in @ SY2021 @ SY2020 )
| ( in @ SY2021 @ ( sK17_SY1618 @ SY2018 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2020 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SY2018 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2018 ) )
| ~ ! [SY2022: $i] :
( ~ ( in @ SY2022 @ ( sK17_SY1618 @ SY2018 @ SV163 ) )
| ~ ( in @ SY2022 @ SY2018 ) ) ) ) )
| ~ ~ ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) )
| ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(793,plain,
! [SV164: $i] :
( ( ! [SY2031: $i,SY2032: $i] :
( ~ ( ~ ( in @ ( sK82_SY661 @ SY2032 @ SY2031 @ SV164 ) @ SV164 )
| ~ ! [SY2033: $i] :
( ( ( dsetconstr @ SY2031
@ ^ [SY2034: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY2032 @ SY2031 @ SV164 ) @ SY2034 ) @ SY2032 ) )
!= ( setadjoin @ SY2033 @ emptyset ) )
| ~ ( in @ SY2033
@ ( dsetconstr @ SY2031
@ ^ [SY2035: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY2032 @ SY2031 @ SV164 ) @ SY2035 ) @ SY2032 ) ) ) ) )
| ~ ( subset @ SY2032 @ ( cartprod @ SV164 @ SY2031 ) )
| ! [SY2036: $i] :
( ~ ( in @ SY2036 @ SV164 )
| ~ ( ( ( dsetconstr @ SY2031
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2036 @ SX4 ) @ SY2032 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2036 @ SY2032 @ SY2031 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2036 @ SY2032 @ SY2031 @ SV164 )
@ ( dsetconstr @ SY2031
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2036 @ SX4 ) @ SY2032 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(794,plain,
! [SV165: $i > $i > $o] :
( ( ! [SY2039: $i] :
( ~ ( ~ ( in @ ( sK12_SY29 @ SY2039 @ SV165 ) @ SY2039 )
| ~ ! [SY2040: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SY2039 @ SV165 ) @ ( sK13_SY1613 @ SY2040 @ SY2039 @ SV165 ) )
| ~ ( ( SY2040
!= ( sK13_SY1613 @ SY2040 @ SY2039 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SY2039 @ SV165 ) @ SY2040 ) ) )
| ~ ( ~ ! [SY2041: $i] :
( ! [SY2042: $i] :
( ~ ( SV165 @ SY2042 @ SY2041 )
| ~ ( in @ SY2042 @ SY2039 ) )
| ( in @ SY2041 @ ( sK10_B @ SY2039 @ SV165 ) ) )
| ~ ! [SY2043: $i] :
( ~ ( in @ SY2043 @ ( sK10_B @ SY2039 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2043 @ SY2039 @ SV165 ) @ SY2043 )
| ~ ( in @ ( sK11_Xy @ SY2043 @ SY2039 @ SV165 ) @ SY2039 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(795,plain,
! [SV166: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ~ ( in @ SY2045 @ ( symdiff @ SV166 @ SY2044 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY2045 @ SV166 )
| ~ ( in @ SY2045 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY2045 @ SV166 )
| ( in @ SY2045 @ SY2044 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY2045 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY2045 @ SY2044 )
| ~ ( in @ SY2045 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY2045 @ SY2044 )
| ( in @ SY2045 @ SY2044 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY2045 @ SY2044 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2052: $o] :
( ~ SY2052
| ~ ( in @ SY2045 @ SV166 )
| SY2052 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY2045 @ SY2044 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(796,plain,
! [SV167: $i > $o] :
( ( ! [SY2055: $i] :
( ~ ( ~ ( SV167 @ ( sK48_SY229 @ SY2055 @ SV167 ) )
| ~ ( ( SY2055
!= ( sK48_SY229 @ SY2055 @ SV167 ) ) ) )
| ~ ( SV167 @ SY2055 ) )
| ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(797,plain,
! [SV168: $i] :
( ( ! [SY2058: $i] :
( ~ ( in @ SY2058 @ ( setunion @ SV168 ) )
| ! [SY2059: $o] :
( ~ ( ~ ( in @ SY2058 @ ( sK31_B @ SY2059 @ SY2058 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SY2059 @ SY2058 @ SV168 ) @ SV168 )
| ~ ~ SY2059 ) )
| SY2059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(798,plain,
( ( ~ ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(799,plain,
! [SV169: $i > $o] :
( ( ! [SY2060: $i] :
( ~ ( ~ ( SV169 @ ( sK57_SY253 @ SY2060 @ SV169 ) )
| ~ ( ( SY2060
!= ( sK57_SY253 @ SY2060 @ SV169 ) ) ) )
| ~ ( SV169 @ SY2060 ) )
| ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(800,plain,
! [SV170: $i] :
( ( ! [SY2063: $i,SY2064: $i] :
( ~ ( ~ ( in @ ( sK83_SY689 @ SY2064 @ SY2063 @ SV170 ) @ SV170 )
| ~ ! [SY2065: $i] :
( ( ( dsetconstr @ SY2063
@ ^ [SY2066: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY2064 @ SY2063 @ SV170 ) @ SY2066 ) @ SY2064 ) )
!= ( setadjoin @ SY2065 @ emptyset ) )
| ~ ( in @ SY2065
@ ( dsetconstr @ SY2063
@ ^ [SY2067: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY2064 @ SY2063 @ SV170 ) @ SY2067 ) @ SY2064 ) ) ) ) )
| ~ ( subset @ SY2064 @ ( cartprod @ SV170 @ SY2063 ) )
| ! [SY2068: $i] :
( ~ ( in @ SY2068 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY2063
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2068 @ SX4 ) @ SY2064 ) ) )
@ SY2063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(801,plain,
! [SV171: $i] :
( ( ! [SY2070: $i > $o] :
( ~ ( ~ ( in @ ( sK77_Xx @ SY2070 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SY2070 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SY2070 @ ( sK77_Xx @ SY2070 @ SV171 ) )
| ~ ~ ( ~ ( SY2070 @ ( sK78_SY1660 @ SY2070 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SY2070 @ SV171 )
!= ( sK78_SY1660 @ SY2070 @ SV171 ) ) ) ) ) ) )
| ! [SY2071: $i] :
( ~ ( SY2070 @ SY2071 )
| ~ ( in @ SY2071 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SX2: $i] : ( SY2070 @ SX2 ) )
!= ( setadjoin @ ( sK76_SY515 @ SY2070 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SY2070 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SX2: $i] : ( SY2070 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(802,plain,
! [SV172: $i > $o] :
( ( ! [SY2074: $i] :
~ ( ~ ( ( ( sK47_Xy @ SY2074 @ SV172 )
!= SY2074 )
| ~ ( SV172 @ ( sK47_Xy @ SY2074 @ SV172 ) ) )
| ~ ( ( ( sK47_Xy @ SY2074 @ SV172 )
= SY2074 )
| ( SV172 @ ( sK47_Xy @ SY2074 @ SV172 ) ) ) )
| ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(803,plain,
! [SV173: $i > $o] :
( ( ! [SY2076: $i] :
( ~ ( ~ ( SV173 @ ( sK24_SY91 @ SY2076 @ SV173 ) )
| ~ ( ( SY2076
!= ( sK24_SY91 @ SY2076 @ SV173 ) ) ) )
| ~ ( SV173 @ SY2076 ) )
| ( SV173 @ ( sK23_Xx @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(804,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 @ ( sK8_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(805,plain,
! [SV174: $i] :
( ( ! [SY2077: $i > $o] :
( ! [SY2078: $i] :
( ~ ( in @ SY2078 @ SV174 )
| ( SY2077 @ SY2078 ) )
| ~ ( ~ ( in @ ( sK35_Xx @ SY2077 @ SV174 ) @ SV174 )
| ~ ~ ( SY2077 @ ( sK35_Xx @ SY2077 @ SV174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(806,plain,
! [SV175: $i] :
( ( ! [SY2079: $i > $o] :
( ~ ( ~ ( in @ ( sK71_Xx @ SY2079 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SY2079 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SY2079 @ ( sK71_Xx @ SY2079 @ SV175 ) )
| ~ ~ ( ~ ( SY2079 @ ( sK72_SY1655 @ SY2079 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SY2079 @ SV175 )
!= ( sK72_SY1655 @ SY2079 @ SV175 ) ) ) ) ) ) )
| ! [SY2080: $i] :
( ~ ( SY2079 @ SY2080 )
| ~ ( in @ SY2080 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SX2: $i] : ( SY2079 @ SX2 ) )
!= ( setadjoin @ ( sK70_SY484 @ SY2079 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SY2079 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SX2: $i] : ( SY2079 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(807,plain,
! [SV176: $i] :
( ( ~ ( ~ ! [SY2083: $i,SY2084: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2084 @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) ) @ SY2083 ) )
| ! [SY2085: $i] :
( ~ ( in @ SY2085 @ SV176 )
| ~ ( ( ( dsetconstr @ SY2083
@ ^ [SY2086: $i] :
( in @ ( kpair @ SY2085 @ SY2086 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 )
@ ( dsetconstr @ SY2083
@ ^ [SY2089: $i] :
( in @ ( kpair @ SY2085 @ SY2089 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SY2092: $i,SY2093: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2093 @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) ) @ SY2092 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SY2092
@ ^ [SX3: $i,SX4: $i] :
( ( SY2093 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV176 @ SY2092 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(808,plain,
! [SV177: $i] :
( ( ! [SY2096: $i] :
( ~ ( ~ ( in @ ( sK66_Xx @ SY2096 @ SV177 ) @ SV177 )
| ~ ( in @ ( sK66_Xx @ SY2096 @ SV177 ) @ SY2096 ) )
| ( ( binintersect @ SV177 @ SY2096 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(809,plain,
! [SV178: $i] :
( ( ! [SY2097: $i > $o] :
( ~ ( ~ ( in @ ( sK36_Xx @ SY2097 @ SV178 ) @ SV178 )
| ~ ( SY2097 @ ( sK36_Xx @ SY2097 @ SV178 ) ) )
| ! [SY2098: $i] :
( ~ ( SY2097 @ SY2098 )
| ~ ( in @ SY2098 @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(810,plain,
! [SV179: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ~ ( ~ ( in @ ( sK86_SY791 @ SY2100 @ SY2099 @ SV179 ) @ SV179 )
| ~ ! [SY2101: $i] :
( ( ( dsetconstr @ SY2099
@ ^ [SY2102: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY2100 @ SY2099 @ SV179 ) @ SY2102 ) @ SY2100 ) )
!= ( setadjoin @ SY2101 @ emptyset ) )
| ~ ( in @ SY2101
@ ( dsetconstr @ SY2099
@ ^ [SY2103: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY2100 @ SY2099 @ SV179 ) @ SY2103 ) @ SY2100 ) ) ) ) )
| ~ ( subset @ SY2100 @ ( cartprod @ SV179 @ SY2099 ) )
| ( in @ SY2100 @ ( funcSet @ SV179 @ SY2099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(811,plain,
! [SV180: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) )
| ~ ( in @ emptyset @ SV180 )
| ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(812,plain,
! [SV181: $i] :
( ( ! [SY2105: $i,SY2106: $i] :
( ~ ( ~ ( in @ ( sK84_SY716 @ SY2106 @ SY2105 @ SV181 ) @ SV181 )
| ~ ! [SY2107: $i] :
( ( ( dsetconstr @ SY2105
@ ^ [SY2108: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY2106 @ SY2105 @ SV181 ) @ SY2108 ) @ SY2106 ) )
!= ( setadjoin @ SY2107 @ emptyset ) )
| ~ ( in @ SY2107
@ ( dsetconstr @ SY2105
@ ^ [SY2109: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY2106 @ SY2105 @ SV181 ) @ SY2109 ) @ SY2106 ) ) ) ) )
| ~ ( subset @ SY2106 @ ( cartprod @ SV181 @ SY2105 ) )
| ! [SY2110: $i] :
( ~ ( in @ SY2110 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY2105
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2110 @ SX4 ) @ SY2106 ) ) )
@ SY2105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(813,plain,
! [SV182: $i] :
( ( ! [SY2112: $i] :
~ ( in @ SY2112 @ SV182 )
| ~ ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 )
| ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(814,plain,
! [SV183: $i > $o] :
( ( ! [SY2114: $i] :
( ~ ( ~ ( SV183 @ ( sK20_SY62 @ SY2114 @ SV183 ) )
| ~ ( ( SY2114
!= ( sK20_SY62 @ SY2114 @ SV183 ) ) ) )
| ~ ( SV183 @ SY2114 ) )
| ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(815,plain,
! [SV184: $i] :
( ( ! [SY2116: $i,SY2117: $i] :
( ~ ( in @ SY2117 @ ( setadjoin @ SV184 @ SY2116 ) )
| ~ ( ~ ~ ( ~ ( ( SY2117 = SV184 )
| ( in @ SY2117 @ SY2116 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY2117 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY2117 @ SY2116 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(816,plain,
! [SV185: $i] :
( ( ! [SY2122: $i] :
( ~ ( ~ ( in @ ( sK65_Xx @ SY2122 @ SV185 ) @ SV185 )
| ~ ~ ( in @ ( sK65_Xx @ SY2122 @ SV185 ) @ SY2122 ) )
| ( subset @ SV185 @ SY2122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(817,plain,
! [SV186: $i] :
( ( ! [SY2123: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SY2123 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SY2123 @ SV186 ) @ SY2123 ) )
| ~ ( ( in @ ( sK6_Xx @ SY2123 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SY2123 @ SV186 ) @ SY2123 ) ) )
| ( SV186 = SY2123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(818,plain,
! [SV187: $i > $o] :
( ( ! [SY2124: $i > $o] :
( ~ ( ( ( sK60_Xx @ SY2124 @ SV187 )
!= ( sK61_SY1650 @ SY2124 @ SV187 ) )
| ~ ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SY2124 @ SV187 ) )
| ~ ( SY2124 @ ( sK61_SY1650 @ SY2124 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SY2124 @ SV187 ) )
| ( SY2124 @ ( sK61_SY1650 @ SY2124 @ SV187 ) ) ) ) )
| ! [SY2125: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2125 @ SY2124 @ SV187 ) )
| ~ ( ( SY2125
!= ( sK59_SY262 @ SY2125 @ SY2124 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2125 ) )
| ! [SY2126: $i] :
( ~ ( ~ ( SY2124 @ ( sK58_SY265 @ SY2126 @ SY2124 @ SV187 ) )
| ~ ( ( SY2126
!= ( sK58_SY265 @ SY2126 @ SY2124 @ SV187 ) ) ) )
| ~ ( SY2124 @ SY2126 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SX2: $i] : ( SY2124 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(819,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK7_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)],[618]) ).
thf(820,plain,
! [SV188: $i] :
( ( ! [SY2129: $i] :
( ~ ( in @ SY2129 @ ( setunion @ SV188 ) )
| ~ ( ~ ( in @ ( sK69_X @ SY2129 @ SV188 ) @ SV188 )
| ~ ( in @ SY2129 @ ( sK69_X @ SY2129 @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(821,plain,
! [SV189: $i > $o] :
( ( ! [SY2130: $i] :
( ~ ( ~ ( SV189 @ ( sK22_SY79 @ SY2130 @ SV189 ) )
| ~ ( ( SY2130
!= ( sK22_SY79 @ SY2130 @ SV189 ) ) ) )
| ~ ( SV189 @ SY2130 ) )
| ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(822,plain,
! [SV190: $i] :
( ( ~ ( ~ ! [SY2132: $i,SY2133: $i] :
( ~ ( in @ SY2133 @ ( setadjoin @ SV190 @ SY2132 ) )
| ( SY2133 = SV190 )
| ( in @ SY2133 @ SY2132 ) )
| ~ ~ ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) )
| ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(823,plain,
! [SV191: $i,SV1: $i] :
( ( ! [SY2138: $i] :
( ~ ( in @ SY2138 @ ( funcSet @ SV1 @ SV191 ) )
| ! [SY2139: $i] :
( ~ ( in @ SY2139 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY769: $i] : ( in @ ( kpair @ SY2139 @ SY769 ) @ SY2138 ) ) )
@ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(824,plain,
! [SV192: $i,SV2: $i] :
( ( ! [SY2141: $i > $i > $o,SY2142: $i,SY2143: $i] :
( ~ ( in @ ( kpair @ SY2142 @ SY2143 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [Xz: $i,Xu: $i] : ( SY2141 @ Xz @ Xu ) ) )
| ( SY2141 @ SY2142 @ SY2143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(825,plain,
! [SV193: $i,SV3: $i] :
( ( ! [SY2146: $i > $i > $o,SY2147: $i,SY2148: $i] :
( ~ ( in @ ( kpair @ SY2147 @ SY2148 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [Xz: $i,Xu: $i] : ( SY2146 @ Xz @ Xu ) ) )
| ( in @ SY2148 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(826,plain,
! [SV194: $i,SV4: $i] :
( ( ! [SY2151: $i > $i > $o,SY2152: $i] :
( ! [SY2153: $i] :
~ ( in @ ( kpair @ SY2152 @ SY2153 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [Xz: $i,Xu: $i] : ( SY2151 @ Xz @ Xu ) ) )
| ( in @ SY2152 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(827,plain,
! [SV195: $i,SV5: $i] :
( ( ! [SY2156: $i > $i > $o,SY2157: $i] :
( ~ ( in @ SY2157 @ SV5 )
| ! [SY2158: $i] :
( ~ ( in @ SY2158 @ SV195 )
| ~ ( in @ ( kpair @ SY2157 @ SY2158 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [Xz: $i,Xu: $i] : ( SY2156 @ Xz @ Xu ) ) )
| ( SY2156 @ SY2157 @ SY2158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(828,plain,
! [SV196: $i,SV6: $i] :
( ( ! [SY2161: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV6 @ SV196
@ ^ [Xx: $i,Xy: $i] : ( SY2161 @ Xx @ Xy ) )
@ ( cartprod @ SV6 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(829,plain,
! [SV197: $i,SV7: $i] :
( ( ! [SY2164: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV7 @ SV197
@ ^ [Xx: $i,Xy: $i] : ( SY2164 @ Xx @ Xy ) )
@ ( cartprod @ SV7 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(830,plain,
! [SV198: $i,SV8: $i] :
( ( ! [SY2167: $i > $i > $o,SY2168: $i] :
( ~ ( in @ SY2168 @ SV8 )
| ! [SY2169: $i] :
( ~ ( in @ SY2169 @ SV198 )
| ~ ( SY2167 @ SY2168 @ SY2169 )
| ( in @ ( kpair @ SY2168 @ SY2169 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [Xz: $i,Xu: $i] : ( SY2167 @ Xz @ Xu ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(831,plain,
! [SV199: $i,SV9: $i] :
( ( ! [SY2172: $i] :
( ~ ( in @ SY2172 @ ( cartprod @ SV9 @ SV199 ) )
| ( ( kpair @ ( kfst @ SY2172 ) @ ( ksnd @ SY2172 ) )
= SY2172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(832,plain,
! [SV200: $i,SV10: $i] :
( ( ! [SY2173: $i] :
( ~ ( in @ SY2173 @ SV10 )
| ! [SY2174: $i] :
( ~ ( in @ SY2174 @ SV200 )
| ( ( ksnd @ ( kpair @ SY2173 @ SY2174 ) )
= SY2174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(833,plain,
! [SV201: $i,SV11: $i] :
( ( ! [SY2175: $i] :
( ~ ( in @ SY2175 @ SV11 )
| ! [SY2176: $i] :
( ~ ( in @ SY2176 @ SV201 )
| ( ( kfst @ ( kpair @ SY2175 @ SY2176 ) )
= SY2175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(834,plain,
! [SV12: $i] :
( ( ( ! [SY1744: $i] :
~ ( in @ SY1744 @ SV12 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(835,plain,
! [SV202: $i,SV13: $i] :
( ( ! [SY2177: $i,SY2178: $i] :
( ~ ( in @ ( kpair @ SY2177 @ SY2178 ) @ ( cartprod @ SV13 @ SV202 ) )
| ( in @ SY2178 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(836,plain,
! [SV203: $i,SV14: $i] :
( ( ! [SY2179: $i] :
( ! [SY2180: $i] :
~ ( in @ ( kpair @ SY2179 @ SY2180 ) @ ( cartprod @ SV14 @ SV203 ) )
| ( in @ SY2179 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(837,plain,
! [SV204: $i,SV15: $i] :
( ( ! [SY2181: $i] :
( ~ ( in @ SY2181 @ ( cartprod @ SV15 @ SV204 ) )
| ( in @ ( ksnd @ SY2181 ) @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(838,plain,
! [SV16: $i] :
( ( ( ~ ( iskpair @ SV16 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV16 ) @ ( ksnd @ SV16 ) )
= SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(839,plain,
! [SV205: $i,SV17: $i] :
( ( ( ksnd @ ( kpair @ SV17 @ SV205 ) )
= SV205 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(840,plain,
! [SV206: $i,SV18: $i] :
( ( ! [SY2182: $i,SY2183: $i] :
( ( ( kpair @ SV18 @ SV206 )
!= ( kpair @ SY2182 @ SY2183 ) )
| ( SV206 = SY2183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(841,plain,
! [SV207: $i,SV19: $i] :
( ( ! [SY2184: $i,SY2185: $i] :
( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2184 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2184 @ ( setadjoin @ SY2185 @ emptyset ) ) @ emptyset ) ) )
| ( SV207 = SY2185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(842,plain,
! [SV208: $i,SV20: $i] :
( ( ! [SY2186: $i] :
( ( setadjoin @ SV20 @ ( setadjoin @ SV208 @ emptyset ) )
!= ( setadjoin @ SY2186 @ emptyset ) )
| ( SV20 = SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(843,plain,
! [SV209: $i,SV21: $i] :
( ( ! [SY2187: $i,SY2188: $i] :
( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2187 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2187 @ ( setadjoin @ SY2188 @ emptyset ) ) @ emptyset ) ) )
| ( SY2187 != SY2188 )
| ( SV209 = SY2188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(844,plain,
! [SV210: $i,SV22: $i] :
( ( ( SV22 != SV210 )
| ( ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV22 @ ( setadjoin @ SV210 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(845,plain,
! [SV211: $i,SV23: $i] :
( ( ( SV23 != SV211 )
| ( ( setadjoin @ SV23 @ ( setadjoin @ SV211 @ emptyset ) )
= ( setadjoin @ SV23 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(846,plain,
! [SV212: $i,SV24: $i] :
( ( ! [SY2189: $i] :
( ! [SY2190: $i] :
( ( kpair @ SV24 @ SV212 )
!= ( kpair @ SY2189 @ SY2190 ) )
| ( SV24 = SY2189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(847,plain,
! [SV213: $i,SV25: $i] :
( ( ! [SY2191: $i] :
( ! [SY2192: $i] :
( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2191 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2191 @ ( setadjoin @ SY2192 @ emptyset ) ) @ emptyset ) ) )
| ( SV25 = SY2191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(848,plain,
! [SV214: $i,SV26: $i] :
( ( ! [SY2193: $i] :
( ~ ( in @ SY2193 @ ( cartprod @ SV26 @ SV214 ) )
| ( in @ ( kfst @ SY2193 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(849,plain,
! [SV215: $i,SV27: $i] :
( ( ( kfst @ ( kpair @ SV27 @ SV215 ) )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(850,plain,
! [SV28: $i] :
( ( ( ! [SY1778: $i] :
( ( SV28
!= ( setadjoin @ SY1778 @ emptyset ) )
| ~ ( in @ SY1778 @ SV28 ) ) )
= $true )
| ( ( in @ ( setunion @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(851,plain,
! [SV216: $i,SV29: $i] :
( ( ! [SY2194: $i] :
( ~ ( in @ ( setadjoin @ SY2194 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) ) )
| ( SV29 = SY2194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(852,plain,
! [SV217: $i,SV30: $i] :
( ( ( ( setadjoin @ SV30 @ emptyset )
!= ( setadjoin @ SV217 @ emptyset ) )
| ( SV30 = SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(853,plain,
! [SV218: $i,SV34: $i] :
( ( ! [SY2195: $i] :
( ~ ( in @ SY2195 @ ( cartprod @ SV34 @ SV218 ) )
| ( iskpair @ SY2195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(854,plain,
! [SV219: $i,SV35: $i] :
( ( ! [SY2196: $i] :
( ~ ( in @ SY2196 @ SV35 )
| ! [SY2197: $i] :
( ~ ( in @ SY2197 @ SV219 )
| ( in @ ( kpair @ SY2196 @ SY2197 ) @ ( cartprod @ SV35 @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(855,plain,
! [SV220: $i,SV36: $i] :
( ( ! [SY2198: $i] :
( ~ ( in @ SY2198 @ SV36 )
| ! [SY2199: $i] :
( ~ ( in @ SY2199 @ SV220 )
| ( in @ ( kpair @ SY2198 @ SY2199 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(856,plain,
! [SV221: $i,SV37: $i] :
( ( ! [SY2200: $i] :
( ~ ( in @ SY2200 @ SV37 )
| ! [SY2201: $i] :
( ~ ( in @ SY2201 @ SV221 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2200 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2200 @ ( setadjoin @ SY2201 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(857,plain,
! [SV222: $i,SV38: $i] :
( ( ! [SY2202: $i] :
( ~ ( in @ SY2202 @ SV38 )
| ! [SY2203: $i] :
( ~ ( in @ SY2203 @ SV222 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2202 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2202 @ ( setadjoin @ SY2203 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(858,plain,
! [SV223: $i,SV39: $i] :
( ( ! [SY2204: $i] :
( ~ ( in @ SY2204 @ SV39 )
| ! [SY2205: $i] :
( ~ ( in @ SY2205 @ SV223 )
| ( in @ ( setadjoin @ SY2204 @ ( setadjoin @ SY2205 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(859,plain,
! [SV224: $i,SV40: $i] :
( ( ! [SY2206: $i] :
( ~ ( in @ SY2206 @ SV40 )
| ! [SY2207: $i] :
( ~ ( in @ SY2207 @ SV224 )
| ( subset @ ( setadjoin @ SY2206 @ ( setadjoin @ SY2207 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(860,plain,
! [SV225: $i,SV41: $i] :
( ( ! [SY2208: $i] :
( ~ ( in @ SY2208 @ ( setadjoin @ SV41 @ ( setadjoin @ SV225 @ emptyset ) ) )
| ( SY2208 = SV41 )
| ( SY2208 = SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(861,plain,
! [SV226: $i,SV42: $i] :
( ( ! [SY2209: $i] :
( ~ ( in @ SY2209 @ SV42 )
| ( in @ ( setadjoin @ SY2209 @ emptyset ) @ ( powerset @ ( binunion @ SV42 @ SV226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(862,plain,
! [SV43: $i,SV227: $i] :
( ( ~ ( in @ SV227 @ SV43 )
| ( in @ ( setadjoin @ SV227 @ emptyset ) @ ( powerset @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(863,plain,
! [SV44: $i,SV228: $i] :
( ( ~ ( in @ SV228 @ SV44 )
| ( subset @ ( setadjoin @ SV228 @ emptyset ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(864,plain,
! [SV229: $i,SV45: $i] :
( ( iskpair @ ( kpair @ SV45 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(865,plain,
! [SV230: $i,SV46: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV46 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV46 @ ( setadjoin @ SV230 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(866,plain,
! [SV47: $i,SV231: $i] :
( ( in @ SV231 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV47 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV47 @ ( setadjoin @ SV231 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(867,plain,
! [SV232: $i,SV48: $i] :
( ( in @ SV48 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV48 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV48 @ ( setadjoin @ SV232 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(868,plain,
! [SV49: $i,SV233: $i] :
( ( in @ SV233 @ ( setadjoin @ SV49 @ ( setadjoin @ SV233 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(869,plain,
! [SV234: $i,SV50: $i] :
( ( ! [SY2210: $i] :
( ( in @ SY2210 @ SV50 )
| ( in @ SY2210 @ SV234 )
| ~ ( in @ SY2210 @ ( symdiff @ SV50 @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(870,plain,
! [SV235: $i,SV51: $i] :
( ( ! [SY2211: $i] :
( ~ ( in @ SY2211 @ SV51 )
| ~ ( in @ SY2211 @ SV235 )
| ~ ( in @ SY2211 @ ( symdiff @ SV51 @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(871,plain,
! [SV236: $i,SV52: $i] :
( ( ! [SY2212: $i] :
( ( in @ SY2212 @ SV52 )
| ~ ( in @ SY2212 @ SV236 )
| ( in @ SY2212 @ ( symdiff @ SV52 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(872,plain,
! [SV237: $i,SV53: $i] :
( ( ! [SY2213: $i] :
( ~ ( in @ SY2213 @ SV53 )
| ( in @ SY2213 @ SV237 )
| ( in @ SY2213 @ ( symdiff @ SV53 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(873,plain,
! [SV238: $i,SV54: $i] :
( ( ( ( setminus @ SV54 @ SV238 )
!= emptyset )
| ( subset @ SV54 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(874,plain,
! [SV239: $i,SV55: $i] :
( ( subset @ ( setminus @ SV55 @ SV239 ) @ SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(875,plain,
! [SV56: $i,SV240: $i] :
( ( ! [SY2214: $i] :
( ~ ( in @ SY2214 @ SV240 )
| ~ ( in @ SY2214 @ ( setminus @ SV56 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(876,plain,
! [SV241: $i,SV57: $i] :
( ( ! [SY2215: $i] :
( ( in @ SY2215 @ SV57 )
| ~ ( in @ SY2215 @ ( setminus @ SV57 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(877,plain,
! [SV242: $i,SV58: $i] :
( ( ! [SY2216: $i] :
( ( in @ SY2216 @ ( setminus @ SV58 @ SV242 ) )
| ( in @ SY2216 @ SV242 )
| ~ ( in @ SY2216 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(878,plain,
! [SV243: $i,SV59: $i] :
( ( ! [SY2217: $i] :
( ( in @ SY2217 @ ( setminus @ SV59 @ SV243 ) )
| ~ ( in @ SY2217 @ SV59 )
| ( in @ SY2217 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(879,plain,
! [SV244: $i,SV60: $i] :
( ( ~ ( subset @ SV60 @ SV244 )
| ( ( setminus @ SV60 @ SV244 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(880,plain,
! [SV245: $i,SV61: $i] :
( ( ! [SY2218: $i] :
( ~ ( in @ SY2218 @ ( setminus @ SV61 @ SV245 ) )
| ~ ( in @ SY2218 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(881,plain,
! [SV246: $i,SV62: $i] :
( ( ! [SY2219: $i] :
( ~ ( in @ SY2219 @ ( setminus @ SV62 @ SV246 ) )
| ( in @ SY2219 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(882,plain,
! [SV247: $i,SV63: $i] :
( ( ! [SY2220: $i] :
( ~ ( in @ SY2220 @ SV63 )
| ( in @ SY2220 @ SV247 )
| ( in @ SY2220 @ ( setminus @ SV63 @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(883,plain,
! [SV248: $i,SV64: $i] :
( ( ! [SY2221: $i] :
( ( binintersect @ SV64 @ ( binunion @ SV248 @ SY2221 ) )
= ( binunion @ ( binintersect @ SV64 @ SV248 ) @ ( binintersect @ SV64 @ SY2221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(884,plain,
! [SV249: $i,SV65: $i] :
( ( ( ( binintersect @ SV65 @ SV249 )
!= SV65 )
| ( subset @ SV65 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(885,plain,
! [SV66: $i,SV250: $i] :
( ( ~ ( subset @ SV250 @ SV66 )
| ( ( binintersect @ SV66 @ SV250 )
= SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(886,plain,
! [SV251: $i,SV67: $i] :
( ( subset @ ( binintersect @ SV67 @ SV251 ) @ SV251 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(887,plain,
! [SV252: $i,SV68: $i] :
( ( ! [SY2222: $i] :
( ~ ( in @ SY2222 @ ( binintersect @ SV68 @ SV252 ) )
| ( in @ SY2222 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(888,plain,
! [SV253: $i,SV69: $i] :
( ( ( ( binintersect @ SV69 @ SV253 )
!= SV253 )
| ( subset @ SV253 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(889,plain,
! [SV254: $i,SV70: $i] :
( ( ~ ( subset @ SV70 @ SV254 )
| ( ( binintersect @ SV70 @ SV254 )
= SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(890,plain,
! [SV255: $i,SV71: $i] :
( ( subset @ ( binintersect @ SV71 @ SV255 ) @ SV71 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(891,plain,
! [SV256: $i,SV72: $i] :
( ( ! [SY2223: $i] :
( ~ ( in @ SY2223 @ ( binintersect @ SV72 @ SV256 ) )
| ( in @ SY2223 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(892,plain,
! [SV257: $i,SV73: $i] :
( ( ! [SY2224: $i] :
( ~ ( subset @ SY2224 @ SV73 )
| ~ ( subset @ SY2224 @ SV257 )
| ( subset @ SY2224 @ ( binintersect @ SV73 @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(893,plain,
! [SV258: $i,SV74: $i] :
( ( ! [SY2225: $i] :
( ~ ( in @ SY2225 @ SV74 )
| ~ ( in @ SY2225 @ SV258 )
| ( in @ SY2225 @ ( binintersect @ SV74 @ SV258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(894,plain,
! [SV75: $i,SV259: $i] :
( ( subset @ SV259 @ ( binunion @ SV75 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(895,plain,
! [SV260: $i,SV76: $i] :
( ( subset @ SV76 @ ( binunion @ SV76 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(896,plain,
! [SV261: $i,SV77: $i] :
( ( ! [SY2226: $i] :
( ~ ( in @ SY2226 @ ( binunion @ SV77 @ SV261 ) )
| ( in @ SY2226 @ SV77 )
| ( in @ SY2226 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(897,plain,
! [SV78: $i,SV262: $i] :
( ( ! [SY2227: $i] :
( ~ ( in @ SY2227 @ SV262 )
| ( in @ SY2227 @ ( binunion @ SV78 @ SV262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(898,plain,
! [SV79: $i,SV263: $i] :
( ( in @ SV263 @ ( setadjoin @ SV79 @ ( setadjoin @ SV263 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(899,plain,
! [SV264: $i,SV80: $i] :
( ( ! [SY2228: $i] :
( ~ ( in @ SY2228 @ SV80 )
| ( in @ SY2228 @ ( binunion @ SV80 @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(900,plain,
! [SV265: $i > $o,SV81: $i] :
( ( subset
@ ( dsetconstr @ SV81
@ ^ [SY2229: $i] : ( SV265 @ SY2229 ) )
@ SV81 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(901,plain,
! [SV266: $i > $o,SV82: $i] :
( ( in
@ ( dsetconstr @ SV82
@ ^ [SY2230: $i] : ( SV266 @ SY2230 ) )
@ ( powerset @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(902,plain,
! [SV267: $i,SV83: $i] :
( ( ~ ( subset @ SV83 @ SV267 )
| ( subset @ ( powerset @ SV83 ) @ ( powerset @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(903,plain,
! [SV85: $i,SV268: $i] :
( ( ~ ( in @ SV268 @ ( powerset @ SV85 ) )
| ( subset @ SV268 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(904,plain,
! [SV86: $i,SV269: $i] :
( ( ~ ( subset @ SV269 @ SV86 )
| ( in @ SV269 @ ( powerset @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(905,plain,
! [SV87: $i] :
( ( ( ~ ( subset @ SV87 @ emptyset ) )
= $true )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(906,plain,
! [SV270: $i,SV88: $i] :
( ( ~ ( subset @ SV88 @ SV270 )
| ~ ( subset @ SV270 @ SV88 )
| ( SV88 = SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(907,plain,
! [SV271: $i,SV89: $i] :
( ( ~ ( subset @ SV89 @ SV271 )
| ( in @ SV89 @ ( powerset @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(908,plain,
! [SV272: $i,SV90: $i] :
( ( ! [SY2231: $i] :
( ~ ( subset @ SV90 @ SY2231 )
| ( subset @ SV90 @ ( setadjoin @ SV272 @ SY2231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(909,plain,
! [SV91: $i,SV273: $i] :
( ( subset @ SV273 @ ( setadjoin @ SV91 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(910,plain,
! [SV274: $i,SV92: $i] :
( ( ~ ( subset @ SV92 @ SV274 )
| ! [SY2232: $i] :
( ~ ( subset @ SV274 @ SY2232 )
| ( subset @ SV92 @ SY2232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(911,plain,
! [SV275: $i,SV94: $i] :
( ( ! [SY2233: $i] :
( ~ ( in @ SY2233 @ SV94 )
| ( in @ SY2233 @ SV275 )
| ( SV94 != SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(912,plain,
! [SV276: $i,SV95: $i] :
( ( ( subset @ SV95 @ SV276 )
| ( SV95 != SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(913,plain,
! [SV277: $i,SV96: $i] :
( ( ! [SY2234: $i] :
( ~ ( in @ SY2234 @ SV96 )
| ( in @ SY2234 @ SV277 )
| ~ ( subset @ SV96 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(914,plain,
! [SV278: $i,SV97: $i] :
( ( ~ ( subset @ SV97 @ SV278 )
| ! [SY2235: $i] :
( ( in @ SY2235 @ SV278 )
| ~ ( in @ SY2235 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(915,plain,
! [SV279: $i,SV98: $i] :
( ( ~ ( subset @ SV98 @ SV279 )
| ! [SY2236: $i] :
( ~ ( in @ SY2236 @ SV98 )
| ( in @ SY2236 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(916,plain,
! [SV280: $i,SV100: $i] :
( ( ( SV100 != SV280 )
| ( subset @ SV100 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(917,plain,
! [SV281: $i,SV101: $i] :
( ( ( SV101 != SV281 )
| ( subset @ SV281 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(918,plain,
! [SV282: $i,SV102: $i] :
( ( ( SV102 != SV282 )
| ( ( setunion @ SV102 )
= ( setunion @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(919,plain,
! [SV283: $i,SV103: $i] :
( ( ( SV103 != SV283 )
| ( ( powerset @ SV103 )
= ( powerset @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(920,plain,
! [SV284: $i,SV104: $i] :
( ( ( SV104 != SV284 )
| ! [SY2237: $i,SY2238: $i] :
( ( SY2237 != SY2238 )
| ( ( setadjoin @ SV104 @ SY2237 )
= ( setadjoin @ SV284 @ SY2238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(921,plain,
! [SV285: $i,SV105: $i] :
( ( ( SV105 != SV285 )
| ! [SY2239: $i,SY2240: $i] :
( ( SY2239 != SY2240 )
| ~ ( in @ SY2239 @ SV105 )
| ( in @ SY2240 @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(922,plain,
! [SV106: $o] :
( ( ( ~ SV106 ) = $true )
| ( ( set2prop @ ( prop2set @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(923,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(924,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(925,plain,
! [SV107: $o] :
( ( ( ~ SV107 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(926,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(927,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(928,plain,
! [SV108: $i > $o,SV286: $i] :
( ( ~ ( in @ SV286 @ emptyset )
| ( SV108 @ SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(929,plain,
! [SV109: $i,SV287: $i > $o] :
( ( ! [SY2241: $i] :
( ~ ( SV287 @ SY2241 )
| ~ ( in @ SY2241 @ SV109 ) )
| ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(930,plain,
! [SV110: $i,SV288: $i] :
( ( in @ SV288 @ ( setadjoin @ SV110 @ ( setadjoin @ SV288 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(931,plain,
! [SV289: $i,SV111: $i] :
( ( in @ SV111 @ ( setadjoin @ SV111 @ ( setadjoin @ SV289 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(932,plain,
! [SV290: $i,SV112: $i] :
( ( ! [SY2243: $i] :
( ~ ( in @ SY2243 @ ( setadjoin @ SV112 @ ( setadjoin @ SV290 @ emptyset ) ) )
| ( SY2243 = SV112 )
| ( SY2243 = SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(933,plain,
! [SV291: $i,SV113: $i] :
( ( ~ ( in @ SV113 @ ( setadjoin @ SV291 @ emptyset ) )
| ( in @ SV291 @ ( setadjoin @ SV113 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(934,plain,
! [SV292: $i,SV114: $i] :
( ( ( SV114 != SV292 )
| ( in @ SV114 @ ( setadjoin @ SV292 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(935,plain,
! [SV293: $i,SV115: $i] :
( ( ( SV115 = SV293 )
| ~ ( in @ SV293 @ ( setadjoin @ SV115 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(936,plain,
! [SV294: $i,SV116: $i] :
( ( ~ ( in @ SV116 @ ( setadjoin @ SV294 @ emptyset ) )
| ( SV116 = SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(937,plain,
! [SV117: $i] :
( ( ( SV117 = emptyset )
= $true )
| ( ( in @ ( sK34_Xx @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(938,plain,
! [SV118: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ SV118 )
| ( in @ SV295 @ ( powerset @ ( setunion @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(939,plain,
! [SV119: $i,SV296: $i] :
( ( ! [SY2244: $i] :
( ~ ( in @ SV296 @ SY2244 )
| ~ ( in @ SY2244 @ SV119 )
| ( in @ SV296 @ ( setunion @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(940,plain,
! [SV120: $i,SV297: $i] :
( ( ~ ( in @ SV297 @ ( powerset @ SV120 ) )
| ! [SY2245: $i] :
( ~ ( in @ SY2245 @ SV297 )
| ( in @ SY2245 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(941,plain,
! [SV298: $i,SV124: $i] :
( ( ! [SY2246: $i] :
( ~ ( in @ SY2246 @ ( setadjoin @ SV124 @ SV298 ) )
| ( SY2246 = SV124 )
| ( in @ SY2246 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(942,plain,
! [SV125: $i,SV299: $i] :
( ( ! [SY2247: $i] :
( ~ ( in @ SY2247 @ SV299 )
| ( in @ SY2247 @ ( setadjoin @ SV125 @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(943,plain,
! [SV300: $i,SV126: $i] :
( ( in @ SV126 @ ( setadjoin @ SV126 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(944,plain,
! [SV127: $i] :
( ( ( ! [SY1919: $i] :
~ ( in @ SY1919 @ SV127 ) )
= $true )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(945,plain,
! [SV301: $i > $o,SV128: $i] :
( ( ! [SY2248: $i] :
( ~ ( in @ SY2248 @ SV128 )
| ~ ( SV301 @ SY2248 )
| ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(946,plain,
! [SV129: $i] :
( ( ( SV129 = emptyset )
= $true )
| ( ( in @ ( sK29_Xx @ SV129 ) @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(947,plain,
! [SV130: $i] :
( ( ( in @ ( sK28_Xx @ SV130 ) @ SV130 )
= $true )
| ( ( SV130 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(948,plain,
! [SV131: $i] :
( ( ( in @ ( sK27_Xx @ SV131 ) @ SV131 )
= $true )
| ( ( SV131 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(949,plain,
! [SV132: $i] :
( ( in @ SV132 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(950,plain,
! [SV133: $i] :
( ( in @ SV133 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(951,plain,
! [SV302: $i] :
( ( ( ~ ( in @ SV302 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(952,plain,
! [SV134: $o] :
( ( ( ! [SY1923: $i] :
~ ( in @ SY1923 @ ( prop2set @ SV134 ) ) )
= $true )
| ( SV134 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(953,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(954,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(955,plain,
! [SV303: $i > $o,SV135: $i] :
( ( ! [SY2250: $i] :
( ~ ( in @ SY2250
@ ( dsetconstr @ SV135
@ ^ [SY2251: $i] : ( SV303 @ SY2251 ) ) )
| ( SV303 @ SY2250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(956,plain,
! [SV304: $i > $o,SV136: $i] :
( ( ! [SY2252: $i] :
( ~ ( in @ SY2252
@ ( dsetconstr @ SV136
@ ^ [SY2253: $i] : ( SV304 @ SY2253 ) ) )
| ( in @ SY2252 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(957,plain,
! [SV305: $i > $o,SV137: $i] :
( ( ! [SY2254: $i] :
( ~ ( in @ SY2254 @ SV137 )
| ~ ( SV305 @ SY2254 )
| ( in @ SY2254
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(958,plain,
! [SV138: $i] :
( ( ( ~ ( in @ SV138 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV138 @ SV138 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(959,plain,
! [SV139: $i] :
( ( in @ SV139 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(960,plain,
! [SV306: $i > $o,SV140: $i] :
( ( ! [SY2256: $i] :
( ~ ( in @ SY2256 @ SV140 )
| ( SV306 @ SY2256 ) )
| ~ ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(961,plain,
! [SV141: $i > $o] :
( ( ( ! [SY1935: $i] :
( ~ ( ~ ( SV141 @ ( sK33_SY147 @ SY1935 @ SV141 ) )
| ~ ( ( SY1935
!= ( sK33_SY147 @ SY1935 @ SV141 ) ) ) )
| ~ ( SV141 @ SY1935 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(962,plain,
! [SV142: $i,SV307: $i] :
( ( ~ ( ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV307 )
| ~ ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 ) )
| ( in @ SV307 @ ( powerset @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(963,plain,
! [SV143: $i] :
( ( ( ~ ( iskpair @ SV143 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
!= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(964,plain,
! [SV308: $i > $o,SV144: $i] :
( ( ! [SY2257: $i] :
( ~ ( in @ SY2257 @ SV144 )
| ~ ( SV308 @ SY2257 )
| ~ ( ~ ( in @ ( sK75_Xy @ SY2257 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SY2257 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SY2257 @ SV308 @ SV144 )
!= SY2257 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SY2257 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SY2257 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(965,plain,
! [SV309: $i > $o,SV145: $i] :
( ( ! [SY2260: $i] :
( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
!= ( setadjoin @ SY2260 @ emptyset ) )
| ~ ( in @ SY2260
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) ) )
| ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(966,plain,
! [SV146: $i,SV310: $i] :
( ( ! [SY2263: $i > $i] :
( ~ ( ~ ( in @ ( sK93_Xx @ SY2263 @ SV310 @ SV146 ) @ SV146 )
| ~ ~ ( in @ ( SY2263 @ ( sK93_Xx @ SY2263 @ SV310 @ SV146 ) ) @ SV310 ) )
| ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SX3: $i,SX4: $i] :
( ( SY2263 @ SX3 )
= SX4 ) )
@ ( funcSet @ SV146 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(967,plain,
! [SV311: $i,SV147: $i] :
( ( ( SV147 != SV311 )
| ~ ( ~ ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) )
| ~ ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(968,plain,
! [SV148: $i] :
( ( ( ~ ( iskpair @ SV148 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
| ~ ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(969,plain,
! [SV312: $i,SV149: $i] :
( ( ! [SY2270: $i] :
( ~ ( in @ SY2270 @ ( cartprod @ SV149 @ SV312 ) )
| ~ ( ~ ~ ( ( SY2270
!= ( kpair @ ( sK67_Xx @ SY2270 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SY2270 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SY2270 @ SV312 @ SV149 ) @ SV312 ) )
| ~ ( in @ ( sK67_Xx @ SY2270 @ SV312 @ SV149 ) @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(970,plain,
! [SV313: $i > $o,SV150: $i] :
( ( ! [SY2271: $i] :
( ~ ( in @ SY2271 @ SV150 )
| ( SV313 @ SY2271 ) )
| ~ ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(971,plain,
! [SV151: $i] :
( ( ~ ! [SY1964: $i > $o,SY1965: $i] :
( ~ ( in @ SY1965 @ SV151 )
| ~ ( SY1964 @ SY1965 )
| ( in @ SY1965
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1964 @ SX3 ) ) ) )
| ~ ! [SY1967: $i > $o,SY1968: $i] :
( ~ ( in @ SY1968 @ SV151 )
| ~ ( in @ SY1968
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1967 @ SX3 ) ) )
| ( SY1967 @ SY1968 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(972,plain,
! [SV152: $i > $o] :
( ( ( ! [SY1970: $i] :
~ ( SV152 @ SY1970 ) )
= $true )
| ( ( ~ ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
| ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(973,plain,
! [SV153: $i,SV314: $i] :
( ( ~ ( ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
| ~ ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 ) )
| ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(974,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) )
| ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(975,plain,
! [SV316: $i,SV155: $i] :
( ( ! [SY2280: $i] :
( ~ ( subset @ SY2280 @ ( cartprod @ SV155 @ SV316 ) )
| ! [SY2281: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SY2281 @ SY2280 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SY2281 @ SY2280 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SY2281 @ SY2280 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2281 @ SY2280 @ SV316 @ SV155 ) ) @ SY2280 )
| ~ ~ ( SY2281 @ ( kpair @ ( sK94_Xx @ SY2281 @ SY2280 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2281 @ SY2280 @ SV316 @ SV155 ) ) ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2280 )
| ( SY2281 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(976,plain,
! [SV156: $i > $o] :
( ( ( ! [SY1986: $i] :
( ~ ( ~ ( SV156 @ ( sK42_Xy @ SY1986 @ SV156 ) )
| ~ ( ( SY1986
!= ( sK42_Xy @ SY1986 @ SV156 ) ) ) )
| ~ ( SV156 @ SY1986 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(977,plain,
! [SV157: $i] :
( ( ~ ! [SY1988: $i,SY1989: $i] :
( ~ ( in @ SY1989 @ ( funcSet @ SV157 @ SY1988 ) )
| ! [SY1990: $i] :
( ~ ( in @ SY1990 @ SV157 )
| ~ ( ( ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 )
@ ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) ) ) ) ) )
| ~ ! [SY1993: $i,SY1994: $i] :
( ~ ( in @ SY1994 @ ( funcSet @ SV157 @ SY1993 ) )
| ( subset @ SY1994 @ ( cartprod @ SV157 @ SY1993 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(978,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ~ ( ~ ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
| ~ ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 ) )
| ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(979,plain,
! [SV318: $i,SV159: $i] :
( ( ( SV159 != SV318 )
| ! [SY2284: $i > $o,SY2285: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) )
| ~ ( ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SX4: $i] : ( SY2284 @ SX4 ) )
= ( dsetconstr @ SV318
@ ^ [SX4: $i] : ( SY2285 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(980,plain,
! [SV160: $i] :
( ( ~ ! [SY2002: $i,SY2003: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2003 @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) ) @ SY2002 ) )
| ! [SY2004: $i] :
( ~ ( in @ SY2004 @ SV160 )
| ~ ( ( ( dsetconstr @ SY2002
@ ^ [SY2005: $i] :
( in @ ( kpair @ SY2004 @ SY2005 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 )
@ ( dsetconstr @ SY2002
@ ^ [SY2008: $i] :
( in @ ( kpair @ SY2004 @ SY2008 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SY2011: $i,SY2012: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2012 @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) ) @ SY2011 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SY2011
@ ^ [SX3: $i,SX4: $i] :
( ( SY2012 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV160 @ SY2011 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(981,plain,
! [SV161: $i,SV319: $i] :
( ( ~ ( ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV161 )
| ~ ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 ) )
| ( subset @ SV161 @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(982,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ~ ( ~ ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
| ~ ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 ) )
| ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(983,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
!= ( sK56_SY1649 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK53_SY240 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK53_SY240 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(984,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
!= ( sK52_SY1647 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK49_SY237 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK49_SY237 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(985,plain,
! [SV163: $i] :
( ( ~ ! [SY2018: $i] :
( ~ ( ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SY2018 )
| ~ ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SV163 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2018 )
| ~ ( ~ ! [SY2020: $i] :
( ~ ( in @ SY2020 @ ( sK15_B @ SV163 ) )
| ! [SY2021: $i] :
( ~ ( in @ SY2021 @ SY2020 )
| ( in @ SY2021 @ ( sK17_SY1618 @ SY2018 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2020 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SY2018 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2018 ) )
| ~ ! [SY2022: $i] :
( ~ ( in @ SY2022 @ ( sK17_SY1618 @ SY2018 @ SV163 ) )
| ~ ( in @ SY2022 @ SY2018 ) ) ) ) )
| ~ ~ ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) )
| ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(986,plain,
! [SV164: $i,SV321: $i] :
( ( ! [SY2289: $i] :
( ~ ( ~ ( in @ ( sK82_SY661 @ SY2289 @ SV321 @ SV164 ) @ SV164 )
| ~ ! [SY2290: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2291: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY2289 @ SV321 @ SV164 ) @ SY2291 ) @ SY2289 ) )
!= ( setadjoin @ SY2290 @ emptyset ) )
| ~ ( in @ SY2290
@ ( dsetconstr @ SV321
@ ^ [SY2292: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SY2289 @ SV321 @ SV164 ) @ SY2292 ) @ SY2289 ) ) ) ) )
| ~ ( subset @ SY2289 @ ( cartprod @ SV164 @ SV321 ) )
| ! [SY2293: $i] :
( ~ ( in @ SY2293 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2293 @ SX4 ) @ SY2289 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2293 @ SY2289 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2293 @ SY2289 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2293 @ SX4 ) @ SY2289 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(987,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ~ ( ~ ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
| ~ ! [SY2296: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) )
| ~ ( ( SY2296
!= ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SY2296 ) ) )
| ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(988,plain,
! [SV323: $i,SV166: $i] :
( ( ! [SY2300: $i] :
( ~ ( in @ SY2300 @ ( symdiff @ SV166 @ SV323 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY2300 @ SV166 )
| ~ ( in @ SY2300 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY2300 @ SV166 )
| ( in @ SY2300 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY2300 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY2300 @ SV323 )
| ~ ( in @ SY2300 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY2300 @ SV323 )
| ( in @ SY2300 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY2300 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2052: $o] :
( ~ SY2052
| ~ ( in @ SY2300 @ SV166 )
| SY2052 )
| ~ ~ ( ~ ! [SY2308: $o] :
( ~ SY2308
| ( in @ SY2300 @ SV323 )
| SY2308 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(989,plain,
! [SV167: $i > $o] :
( ( ( ! [SY2055: $i] :
( ~ ( ~ ( SV167 @ ( sK48_SY229 @ SY2055 @ SV167 ) )
| ~ ( ( SY2055
!= ( sK48_SY229 @ SY2055 @ SV167 ) ) ) )
| ~ ( SV167 @ SY2055 ) ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(990,plain,
! [SV168: $i,SV324: $i] :
( ( ~ ( in @ SV324 @ ( setunion @ SV168 ) )
| ! [SY2310: $o] :
( ~ ( ~ ( in @ SV324 @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SY2310 ) )
| SY2310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(991,plain,
( ( ~ ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(992,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(993,plain,
! [SV169: $i > $o] :
( ( ( ! [SY2060: $i] :
( ~ ( ~ ( SV169 @ ( sK57_SY253 @ SY2060 @ SV169 ) )
| ~ ( ( SY2060
!= ( sK57_SY253 @ SY2060 @ SV169 ) ) ) )
| ~ ( SV169 @ SY2060 ) ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(994,plain,
! [SV170: $i,SV325: $i] :
( ( ! [SY2311: $i] :
( ~ ( ~ ( in @ ( sK83_SY689 @ SY2311 @ SV325 @ SV170 ) @ SV170 )
| ~ ! [SY2312: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2313: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY2311 @ SV325 @ SV170 ) @ SY2313 ) @ SY2311 ) )
!= ( setadjoin @ SY2312 @ emptyset ) )
| ~ ( in @ SY2312
@ ( dsetconstr @ SV325
@ ^ [SY2314: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SY2311 @ SV325 @ SV170 ) @ SY2314 ) @ SY2311 ) ) ) ) )
| ~ ( subset @ SY2311 @ ( cartprod @ SV170 @ SV325 ) )
| ! [SY2315: $i] :
( ~ ( in @ SY2315 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2315 @ SX4 ) @ SY2311 ) ) )
@ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(995,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ~ ( ~ ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) ) )
| ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(996,plain,
! [SV172: $i > $o] :
( ( ( ! [SY2074: $i] :
~ ( ~ ( ( ( sK47_Xy @ SY2074 @ SV172 )
!= SY2074 )
| ~ ( SV172 @ ( sK47_Xy @ SY2074 @ SV172 ) ) )
| ~ ( ( ( sK47_Xy @ SY2074 @ SV172 )
= SY2074 )
| ( SV172 @ ( sK47_Xy @ SY2074 @ SV172 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(997,plain,
! [SV173: $i > $o] :
( ( ( ! [SY2076: $i] :
( ~ ( ~ ( SV173 @ ( sK24_SY91 @ SY2076 @ SV173 ) )
| ~ ( ( SY2076
!= ( sK24_SY91 @ SY2076 @ SV173 ) ) ) )
| ~ ( SV173 @ SY2076 ) ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(998,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(999,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(1000,plain,
! [SV327: $i > $o,SV174: $i] :
( ( ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV174 )
| ( SV327 @ SY2320 ) )
| ~ ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1001,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ~ ( ~ ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) ) )
| ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1002,plain,
! [SV176: $i] :
( ( ~ ! [SY2083: $i,SY2084: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2084 @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) ) @ SY2083 ) )
| ! [SY2085: $i] :
( ~ ( in @ SY2085 @ SV176 )
| ~ ( ( ( dsetconstr @ SY2083
@ ^ [SY2086: $i] :
( in @ ( kpair @ SY2085 @ SY2086 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 )
@ ( dsetconstr @ SY2083
@ ^ [SY2089: $i] :
( in @ ( kpair @ SY2085 @ SY2089 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) ) ) ) ) )
| ~ ! [SY2092: $i,SY2093: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2093 @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) ) @ SY2092 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SY2092
@ ^ [SX3: $i,SX4: $i] :
( ( SY2093 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV176 @ SY2092 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(1003,plain,
! [SV177: $i,SV329: $i] :
( ( ~ ( ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV177 )
| ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV329 ) )
| ( ( binintersect @ SV177 @ SV329 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1004,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ~ ( ~ ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
| ~ ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) ) )
| ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1005,plain,
! [SV179: $i,SV331: $i] :
( ( ! [SY2325: $i] :
( ~ ( ~ ( in @ ( sK86_SY791 @ SY2325 @ SV331 @ SV179 ) @ SV179 )
| ~ ! [SY2326: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2327: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY2325 @ SV331 @ SV179 ) @ SY2327 ) @ SY2325 ) )
!= ( setadjoin @ SY2326 @ emptyset ) )
| ~ ( in @ SY2326
@ ( dsetconstr @ SV331
@ ^ [SY2328: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SY2325 @ SV331 @ SV179 ) @ SY2328 ) @ SY2325 ) ) ) ) )
| ~ ( subset @ SY2325 @ ( cartprod @ SV179 @ SV331 ) )
| ( in @ SY2325 @ ( funcSet @ SV179 @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1006,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) )
| ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(1007,plain,
! [SV181: $i,SV332: $i] :
( ( ! [SY2329: $i] :
( ~ ( ~ ( in @ ( sK84_SY716 @ SY2329 @ SV332 @ SV181 ) @ SV181 )
| ~ ! [SY2330: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2331: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY2329 @ SV332 @ SV181 ) @ SY2331 ) @ SY2329 ) )
!= ( setadjoin @ SY2330 @ emptyset ) )
| ~ ( in @ SY2330
@ ( dsetconstr @ SV332
@ ^ [SY2332: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SY2329 @ SV332 @ SV181 ) @ SY2332 ) @ SY2329 ) ) ) ) )
| ~ ( subset @ SY2329 @ ( cartprod @ SV181 @ SV332 ) )
| ! [SY2333: $i] :
( ~ ( in @ SY2333 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2333 @ SX4 ) @ SY2329 ) ) )
@ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1008,plain,
! [SV182: $i] :
( ( ( ! [SY2112: $i] :
~ ( in @ SY2112 @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 )
| ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(1009,plain,
! [SV183: $i > $o] :
( ( ( ! [SY2114: $i] :
( ~ ( ~ ( SV183 @ ( sK20_SY62 @ SY2114 @ SV183 ) )
| ~ ( ( SY2114
!= ( sK20_SY62 @ SY2114 @ SV183 ) ) ) )
| ~ ( SV183 @ SY2114 ) ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(1010,plain,
! [SV333: $i,SV184: $i] :
( ( ! [SY2335: $i] :
( ~ ( in @ SY2335 @ ( setadjoin @ SV184 @ SV333 ) )
| ~ ( ~ ~ ( ~ ( ( SY2335 = SV184 )
| ( in @ SY2335 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY2335 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2338: $o] :
( ~ SY2338
| ( in @ SY2335 @ SV333 )
| SY2338 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1011,plain,
! [SV185: $i,SV334: $i] :
( ( ~ ( ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV185 )
| ~ ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 ) )
| ( subset @ SV185 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1012,plain,
! [SV186: $i,SV335: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
| ~ ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) ) )
| ( SV186 = SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1013,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ~ ( ( ( sK60_Xx @ SV336 @ SV187 )
!= ( sK61_SY1650 @ SV336 @ SV187 ) )
| ~ ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) ) )
| ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1014,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(1015,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(1016,plain,
! [SV188: $i,SV337: $i] :
( ( ~ ( in @ SV337 @ ( setunion @ SV188 ) )
| ~ ( ~ ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 )
| ~ ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1017,plain,
! [SV189: $i > $o] :
( ( ( ! [SY2130: $i] :
( ~ ( ~ ( SV189 @ ( sK22_SY79 @ SY2130 @ SV189 ) )
| ~ ( ( SY2130
!= ( sK22_SY79 @ SY2130 @ SV189 ) ) ) )
| ~ ( SV189 @ SY2130 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(1018,plain,
! [SV190: $i] :
( ( ~ ! [SY2132: $i,SY2133: $i] :
( ~ ( in @ SY2133 @ ( setadjoin @ SV190 @ SY2132 ) )
| ( SY2133 = SV190 )
| ( in @ SY2133 @ SY2132 ) )
| ~ ~ ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) )
| ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(1019,plain,
! [SV191: $i,SV1: $i,SV338: $i] :
( ( ~ ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) )
| ! [SY2344: $i] :
( ~ ( in @ SY2344 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2345: $i] : ( in @ ( kpair @ SY2344 @ SY2345 ) @ SV338 ) ) )
@ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1020,plain,
! [SV339: $i > $i > $o,SV192: $i,SV2: $i] :
( ( ! [SY2346: $i,SY2347: $i] :
( ~ ( in @ ( kpair @ SY2346 @ SY2347 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [SY2348: $i,SY2349: $i] : ( SV339 @ SY2348 @ SY2349 ) ) )
| ( SV339 @ SY2346 @ SY2347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1021,plain,
! [SV340: $i > $i > $o,SV193: $i,SV3: $i] :
( ( ! [SY2350: $i,SY2351: $i] :
( ~ ( in @ ( kpair @ SY2350 @ SY2351 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [SY2352: $i,SY2353: $i] : ( SV340 @ SY2352 @ SY2353 ) ) )
| ( in @ SY2351 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1022,plain,
! [SV341: $i > $i > $o,SV194: $i,SV4: $i] :
( ( ! [SY2354: $i] :
( ! [SY2355: $i] :
~ ( in @ ( kpair @ SY2354 @ SY2355 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [SY2356: $i,SY2357: $i] : ( SV341 @ SY2356 @ SY2357 ) ) )
| ( in @ SY2354 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1023,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i] :
( ( ! [SY2358: $i] :
( ~ ( in @ SY2358 @ SV5 )
| ! [SY2359: $i] :
( ~ ( in @ SY2359 @ SV195 )
| ~ ( in @ ( kpair @ SY2358 @ SY2359 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SY2358 @ SY2359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1024,plain,
! [SV343: $i > $i > $o,SV196: $i,SV6: $i] :
( ( subset
@ ( dpsetconstr @ SV6 @ SV196
@ ^ [SY2362: $i,SY2363: $i] : ( SV343 @ SY2362 @ SY2363 ) )
@ ( cartprod @ SV6 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1025,plain,
! [SV344: $i > $i > $o,SV197: $i,SV7: $i] :
( ( subset
@ ( dpsetconstr @ SV7 @ SV197
@ ^ [SY2364: $i,SY2365: $i] : ( SV344 @ SY2364 @ SY2365 ) )
@ ( cartprod @ SV7 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1026,plain,
! [SV345: $i > $i > $o,SV198: $i,SV8: $i] :
( ( ! [SY2366: $i] :
( ~ ( in @ SY2366 @ SV8 )
| ! [SY2367: $i] :
( ~ ( in @ SY2367 @ SV198 )
| ~ ( SV345 @ SY2366 @ SY2367 )
| ( in @ ( kpair @ SY2366 @ SY2367 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1027,plain,
! [SV199: $i,SV9: $i,SV346: $i] :
( ( ~ ( in @ SV346 @ ( cartprod @ SV9 @ SV199 ) )
| ( ( kpair @ ( kfst @ SV346 ) @ ( ksnd @ SV346 ) )
= SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1028,plain,
! [SV200: $i,SV10: $i,SV347: $i] :
( ( ~ ( in @ SV347 @ SV10 )
| ! [SY2370: $i] :
( ~ ( in @ SY2370 @ SV200 )
| ( ( ksnd @ ( kpair @ SV347 @ SY2370 ) )
= SY2370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1029,plain,
! [SV201: $i,SV11: $i,SV348: $i] :
( ( ~ ( in @ SV348 @ SV11 )
| ! [SY2371: $i] :
( ~ ( in @ SY2371 @ SV201 )
| ( ( kfst @ ( kpair @ SV348 @ SY2371 ) )
= SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1030,plain,
! [SV12: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ SV12 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1031,plain,
! [SV202: $i,SV13: $i,SV350: $i] :
( ( ! [SY2372: $i] :
( ~ ( in @ ( kpair @ SV350 @ SY2372 ) @ ( cartprod @ SV13 @ SV202 ) )
| ( in @ SY2372 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1032,plain,
! [SV203: $i,SV14: $i,SV351: $i] :
( ( ! [SY2373: $i] :
~ ( in @ ( kpair @ SV351 @ SY2373 ) @ ( cartprod @ SV14 @ SV203 ) )
| ( in @ SV351 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1033,plain,
! [SV204: $i,SV15: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ ( cartprod @ SV15 @ SV204 ) )
| ( in @ ( ksnd @ SV352 ) @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1034,plain,
! [SV16: $i] :
( ( ( iskpair @ SV16 )
= $false )
| ( ( ( kpair @ ( kfst @ SV16 ) @ ( ksnd @ SV16 ) )
= SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(1035,plain,
! [SV353: $i,SV206: $i,SV18: $i] :
( ( ! [SY2374: $i] :
( ( ( kpair @ SV18 @ SV206 )
!= ( kpair @ SV353 @ SY2374 ) )
| ( SV206 = SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1036,plain,
! [SV354: $i,SV207: $i,SV19: $i] :
( ( ! [SY2375: $i] :
( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV354 @ ( setadjoin @ SY2375 @ emptyset ) ) @ emptyset ) ) )
| ( SV207 = SY2375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1037,plain,
! [SV208: $i,SV20: $i] :
( ( ( ! [SY2186: $i] :
( ( setadjoin @ SV20 @ ( setadjoin @ SV208 @ emptyset ) )
!= ( setadjoin @ SY2186 @ emptyset ) ) )
= $true )
| ( ( SV20 = SV208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(1038,plain,
! [SV355: $i,SV209: $i,SV21: $i] :
( ( ! [SY2376: $i] :
( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SY2376 @ emptyset ) ) @ emptyset ) ) )
| ( SV355 != SY2376 )
| ( SV209 = SY2376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1039,plain,
! [SV210: $i,SV22: $i] :
( ( ( SV22 != SV210 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV22 @ ( setadjoin @ SV210 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(1040,plain,
! [SV211: $i,SV23: $i] :
( ( ( SV23 != SV211 )
= $true )
| ( ( ( setadjoin @ SV23 @ ( setadjoin @ SV211 @ emptyset ) )
= ( setadjoin @ SV23 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(1041,plain,
! [SV356: $i,SV212: $i,SV24: $i] :
( ( ! [SY2377: $i] :
( ( kpair @ SV24 @ SV212 )
!= ( kpair @ SV356 @ SY2377 ) )
| ( SV24 = SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1042,plain,
! [SV357: $i,SV213: $i,SV25: $i] :
( ( ! [SY2378: $i] :
( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV357 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV357 @ ( setadjoin @ SY2378 @ emptyset ) ) @ emptyset ) ) )
| ( SV25 = SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1043,plain,
! [SV214: $i,SV26: $i,SV358: $i] :
( ( ~ ( in @ SV358 @ ( cartprod @ SV26 @ SV214 ) )
| ( in @ ( kfst @ SV358 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1044,plain,
! [SV359: $i,SV28: $i] :
( ( ( ( SV28
!= ( setadjoin @ SV359 @ emptyset ) )
| ~ ( in @ SV359 @ SV28 ) )
= $true )
| ( ( in @ ( setunion @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1045,plain,
! [SV216: $i,SV29: $i,SV360: $i] :
( ( ~ ( in @ ( setadjoin @ SV360 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) ) )
| ( SV29 = SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1046,plain,
! [SV217: $i,SV30: $i] :
( ( ( ( setadjoin @ SV30 @ emptyset )
!= ( setadjoin @ SV217 @ emptyset ) )
= $true )
| ( ( SV30 = SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(1047,plain,
! [SV218: $i,SV34: $i,SV361: $i] :
( ( ~ ( in @ SV361 @ ( cartprod @ SV34 @ SV218 ) )
| ( iskpair @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1048,plain,
! [SV219: $i,SV35: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ SV35 )
| ! [SY2379: $i] :
( ~ ( in @ SY2379 @ SV219 )
| ( in @ ( kpair @ SV362 @ SY2379 ) @ ( cartprod @ SV35 @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1049,plain,
! [SV220: $i,SV36: $i,SV363: $i] :
( ( ~ ( in @ SV363 @ SV36 )
| ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV220 )
| ( in @ ( kpair @ SV363 @ SY2380 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1050,plain,
! [SV221: $i,SV37: $i,SV364: $i] :
( ( ~ ( in @ SV364 @ SV37 )
| ! [SY2381: $i] :
( ~ ( in @ SY2381 @ SV221 )
| ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SY2381 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1051,plain,
! [SV222: $i,SV38: $i,SV365: $i] :
( ( ~ ( in @ SV365 @ SV38 )
| ! [SY2382: $i] :
( ~ ( in @ SY2382 @ SV222 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SY2382 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1052,plain,
! [SV223: $i,SV39: $i,SV366: $i] :
( ( ~ ( in @ SV366 @ SV39 )
| ! [SY2383: $i] :
( ~ ( in @ SY2383 @ SV223 )
| ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SY2383 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1053,plain,
! [SV224: $i,SV40: $i,SV367: $i] :
( ( ~ ( in @ SV367 @ SV40 )
| ! [SY2384: $i] :
( ~ ( in @ SY2384 @ SV224 )
| ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SY2384 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1054,plain,
! [SV225: $i,SV41: $i,SV368: $i] :
( ( ~ ( in @ SV368 @ ( setadjoin @ SV41 @ ( setadjoin @ SV225 @ emptyset ) ) )
| ( SV368 = SV41 )
| ( SV368 = SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1055,plain,
! [SV226: $i,SV42: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ SV42 )
| ( in @ ( setadjoin @ SV369 @ emptyset ) @ ( powerset @ ( binunion @ SV42 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1056,plain,
! [SV43: $i,SV227: $i] :
( ( ( ~ ( in @ SV227 @ SV43 ) )
= $true )
| ( ( in @ ( setadjoin @ SV227 @ emptyset ) @ ( powerset @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(1057,plain,
! [SV44: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV44 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV228 @ emptyset ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(1058,plain,
! [SV234: $i,SV50: $i,SV370: $i] :
( ( ( in @ SV370 @ SV50 )
| ( in @ SV370 @ SV234 )
| ~ ( in @ SV370 @ ( symdiff @ SV50 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1059,plain,
! [SV235: $i,SV51: $i,SV371: $i] :
( ( ~ ( in @ SV371 @ SV51 )
| ~ ( in @ SV371 @ SV235 )
| ~ ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1060,plain,
! [SV236: $i,SV52: $i,SV372: $i] :
( ( ( in @ SV372 @ SV52 )
| ~ ( in @ SV372 @ SV236 )
| ( in @ SV372 @ ( symdiff @ SV52 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1061,plain,
! [SV237: $i,SV53: $i,SV373: $i] :
( ( ~ ( in @ SV373 @ SV53 )
| ( in @ SV373 @ SV237 )
| ( in @ SV373 @ ( symdiff @ SV53 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1062,plain,
! [SV238: $i,SV54: $i] :
( ( ( ( setminus @ SV54 @ SV238 )
!= emptyset )
= $true )
| ( ( subset @ SV54 @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1063,plain,
! [SV56: $i,SV240: $i,SV374: $i] :
( ( ~ ( in @ SV374 @ SV240 )
| ~ ( in @ SV374 @ ( setminus @ SV56 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1064,plain,
! [SV241: $i,SV57: $i,SV375: $i] :
( ( ( in @ SV375 @ SV57 )
| ~ ( in @ SV375 @ ( setminus @ SV57 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1065,plain,
! [SV242: $i,SV58: $i,SV376: $i] :
( ( ( in @ SV376 @ ( setminus @ SV58 @ SV242 ) )
| ( in @ SV376 @ SV242 )
| ~ ( in @ SV376 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1066,plain,
! [SV243: $i,SV59: $i,SV377: $i] :
( ( ( in @ SV377 @ ( setminus @ SV59 @ SV243 ) )
| ~ ( in @ SV377 @ SV59 )
| ( in @ SV377 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1067,plain,
! [SV244: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV244 ) )
= $true )
| ( ( ( setminus @ SV60 @ SV244 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1068,plain,
! [SV245: $i,SV61: $i,SV378: $i] :
( ( ~ ( in @ SV378 @ ( setminus @ SV61 @ SV245 ) )
| ~ ( in @ SV378 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1069,plain,
! [SV246: $i,SV62: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ ( setminus @ SV62 @ SV246 ) )
| ( in @ SV379 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1070,plain,
! [SV247: $i,SV63: $i,SV380: $i] :
( ( ~ ( in @ SV380 @ SV63 )
| ( in @ SV380 @ SV247 )
| ( in @ SV380 @ ( setminus @ SV63 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1071,plain,
! [SV381: $i,SV248: $i,SV64: $i] :
( ( ( binintersect @ SV64 @ ( binunion @ SV248 @ SV381 ) )
= ( binunion @ ( binintersect @ SV64 @ SV248 ) @ ( binintersect @ SV64 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1072,plain,
! [SV249: $i,SV65: $i] :
( ( ( ( binintersect @ SV65 @ SV249 )
!= SV65 )
= $true )
| ( ( subset @ SV65 @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1073,plain,
! [SV66: $i,SV250: $i] :
( ( ( ~ ( subset @ SV250 @ SV66 ) )
= $true )
| ( ( ( binintersect @ SV66 @ SV250 )
= SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(1074,plain,
! [SV252: $i,SV68: $i,SV382: $i] :
( ( ~ ( in @ SV382 @ ( binintersect @ SV68 @ SV252 ) )
| ( in @ SV382 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1075,plain,
! [SV253: $i,SV69: $i] :
( ( ( ( binintersect @ SV69 @ SV253 )
!= SV253 )
= $true )
| ( ( subset @ SV253 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1076,plain,
! [SV254: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ SV254 ) )
= $true )
| ( ( ( binintersect @ SV70 @ SV254 )
= SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1077,plain,
! [SV256: $i,SV72: $i,SV383: $i] :
( ( ~ ( in @ SV383 @ ( binintersect @ SV72 @ SV256 ) )
| ( in @ SV383 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1078,plain,
! [SV257: $i,SV73: $i,SV384: $i] :
( ( ~ ( subset @ SV384 @ SV73 )
| ~ ( subset @ SV384 @ SV257 )
| ( subset @ SV384 @ ( binintersect @ SV73 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1079,plain,
! [SV258: $i,SV74: $i,SV385: $i] :
( ( ~ ( in @ SV385 @ SV74 )
| ~ ( in @ SV385 @ SV258 )
| ( in @ SV385 @ ( binintersect @ SV74 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1080,plain,
! [SV261: $i,SV77: $i,SV386: $i] :
( ( ~ ( in @ SV386 @ ( binunion @ SV77 @ SV261 ) )
| ( in @ SV386 @ SV77 )
| ( in @ SV386 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1081,plain,
! [SV78: $i,SV262: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ SV262 )
| ( in @ SV387 @ ( binunion @ SV78 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1082,plain,
! [SV264: $i,SV80: $i,SV388: $i] :
( ( ~ ( in @ SV388 @ SV80 )
| ( in @ SV388 @ ( binunion @ SV80 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1083,plain,
! [SV267: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV267 ) )
= $true )
| ( ( subset @ ( powerset @ SV83 ) @ ( powerset @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1084,plain,
! [SV85: $i,SV268: $i] :
( ( ( ~ ( in @ SV268 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( subset @ SV268 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(1085,plain,
! [SV86: $i,SV269: $i] :
( ( ( ~ ( subset @ SV269 @ SV86 ) )
= $true )
| ( ( in @ SV269 @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(1086,plain,
! [SV87: $i] :
( ( ( subset @ SV87 @ emptyset )
= $false )
| ( ( SV87 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(1087,plain,
! [SV270: $i,SV88: $i] :
( ( ( ~ ( subset @ SV88 @ SV270 ) )
= $true )
| ( ( ~ ( subset @ SV270 @ SV88 )
| ( SV88 = SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1088,plain,
! [SV271: $i,SV89: $i] :
( ( ( ~ ( subset @ SV89 @ SV271 ) )
= $true )
| ( ( in @ SV89 @ ( powerset @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1089,plain,
! [SV272: $i,SV389: $i,SV90: $i] :
( ( ~ ( subset @ SV90 @ SV389 )
| ( subset @ SV90 @ ( setadjoin @ SV272 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1090,plain,
! [SV274: $i,SV92: $i] :
( ( ( ~ ( subset @ SV92 @ SV274 ) )
= $true )
| ( ( ! [SY2232: $i] :
( ~ ( subset @ SV274 @ SY2232 )
| ( subset @ SV92 @ SY2232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1091,plain,
! [SV275: $i,SV94: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ SV94 )
| ( in @ SV390 @ SV275 )
| ( SV94 != SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1092,plain,
! [SV276: $i,SV95: $i] :
( ( ( subset @ SV95 @ SV276 )
= $true )
| ( ( SV95 != SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1093,plain,
! [SV277: $i,SV96: $i,SV391: $i] :
( ( ~ ( in @ SV391 @ SV96 )
| ( in @ SV391 @ SV277 )
| ~ ( subset @ SV96 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1094,plain,
! [SV278: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV278 ) )
= $true )
| ( ( ! [SY2235: $i] :
( ( in @ SY2235 @ SV278 )
| ~ ( in @ SY2235 @ SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1095,plain,
! [SV279: $i,SV98: $i] :
( ( ( ~ ( subset @ SV98 @ SV279 ) )
= $true )
| ( ( ! [SY2236: $i] :
( ~ ( in @ SY2236 @ SV98 )
| ( in @ SY2236 @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1096,plain,
! [SV280: $i,SV100: $i] :
( ( ( SV100 != SV280 )
= $true )
| ( ( subset @ SV100 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1097,plain,
! [SV281: $i,SV101: $i] :
( ( ( SV101 != SV281 )
= $true )
| ( ( subset @ SV281 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1098,plain,
! [SV282: $i,SV102: $i] :
( ( ( SV102 != SV282 )
= $true )
| ( ( ( setunion @ SV102 )
= ( setunion @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1099,plain,
! [SV283: $i,SV103: $i] :
( ( ( SV103 != SV283 )
= $true )
| ( ( ( powerset @ SV103 )
= ( powerset @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1100,plain,
! [SV284: $i,SV104: $i] :
( ( ( SV104 != SV284 )
= $true )
| ( ( ! [SY2237: $i,SY2238: $i] :
( ( SY2237 != SY2238 )
| ( ( setadjoin @ SV104 @ SY2237 )
= ( setadjoin @ SV284 @ SY2238 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1101,plain,
! [SV285: $i,SV105: $i] :
( ( ( SV105 != SV285 )
= $true )
| ( ( ! [SY2239: $i,SY2240: $i] :
( ( SY2239 != SY2240 )
| ~ ( in @ SY2239 @ SV105 )
| ( in @ SY2240 @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1102,plain,
! [SV106: $o] :
( ( SV106 = $false )
| ( ( set2prop @ ( prop2set @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1103,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1104,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1105,plain,
! [SV107: $o] :
( ( SV107 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1106,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1107,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1108,plain,
! [SV108: $i > $o,SV286: $i] :
( ( ( ~ ( in @ SV286 @ emptyset ) )
= $true )
| ( ( SV108 @ SV286 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1109,plain,
! [SV109: $i,SV287: $i > $o] :
( ( ( ! [SY2241: $i] :
( ~ ( SV287 @ SY2241 )
| ~ ( in @ SY2241 @ SV109 ) ) )
= $true )
| ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1110,plain,
! [SV290: $i,SV112: $i,SV392: $i] :
( ( ~ ( in @ SV392 @ ( setadjoin @ SV112 @ ( setadjoin @ SV290 @ emptyset ) ) )
| ( SV392 = SV112 )
| ( SV392 = SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1111,plain,
! [SV291: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ ( setadjoin @ SV291 @ emptyset ) ) )
= $true )
| ( ( in @ SV291 @ ( setadjoin @ SV113 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1112,plain,
! [SV292: $i,SV114: $i] :
( ( ( SV114 != SV292 )
= $true )
| ( ( in @ SV114 @ ( setadjoin @ SV292 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1113,plain,
! [SV293: $i,SV115: $i] :
( ( ( SV115 = SV293 )
= $true )
| ( ( ~ ( in @ SV293 @ ( setadjoin @ SV115 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1114,plain,
! [SV294: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ ( setadjoin @ SV294 @ emptyset ) ) )
= $true )
| ( ( SV116 = SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1115,plain,
! [SV118: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV118 ) )
= $true )
| ( ( in @ SV295 @ ( powerset @ ( setunion @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1116,plain,
! [SV119: $i,SV393: $i,SV296: $i] :
( ( ~ ( in @ SV296 @ SV393 )
| ~ ( in @ SV393 @ SV119 )
| ( in @ SV296 @ ( setunion @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1117,plain,
! [SV120: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ! [SY2245: $i] :
( ~ ( in @ SY2245 @ SV297 )
| ( in @ SY2245 @ SV120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1118,plain,
! [SV298: $i,SV124: $i,SV394: $i] :
( ( ~ ( in @ SV394 @ ( setadjoin @ SV124 @ SV298 ) )
| ( SV394 = SV124 )
| ( in @ SV394 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1119,plain,
! [SV125: $i,SV299: $i,SV395: $i] :
( ( ~ ( in @ SV395 @ SV299 )
| ( in @ SV395 @ ( setadjoin @ SV125 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1120,plain,
! [SV127: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV127 ) )
= $true )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1121,plain,
! [SV301: $i > $o,SV128: $i,SV397: $i] :
( ( ~ ( in @ SV397 @ SV128 )
| ~ ( SV301 @ SV397 )
| ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1122,plain,
! [SV302: $i] :
( ( ( in @ SV302 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1123,plain,
! [SV134: $o,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( prop2set @ SV134 ) ) )
= $true )
| ( SV134 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1124,plain,
! [SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1125,plain,
! [SV400: $i] :
( ( ( ~ ( in @ SV400 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1126,plain,
! [SV303: $i > $o,SV135: $i,SV401: $i] :
( ( ~ ( in @ SV401
@ ( dsetconstr @ SV135
@ ^ [SY2251: $i] : ( SV303 @ SY2251 ) ) )
| ( SV303 @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1127,plain,
! [SV304: $i > $o,SV136: $i,SV402: $i] :
( ( ~ ( in @ SV402
@ ( dsetconstr @ SV136
@ ^ [SY2253: $i] : ( SV304 @ SY2253 ) ) )
| ( in @ SV402 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1128,plain,
! [SV305: $i > $o,SV137: $i,SV403: $i] :
( ( ~ ( in @ SV403 @ SV137 )
| ~ ( SV305 @ SV403 )
| ( in @ SV403
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1129,plain,
! [SV138: $i] :
( ( ( in @ SV138 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV138 @ SV138 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1130,plain,
! [SV306: $i > $o,SV140: $i] :
( ( ( ! [SY2256: $i] :
( ~ ( in @ SY2256 @ SV140 )
| ( SV306 @ SY2256 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1131,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
| ~ ( ( SV404
!= ( sK33_SY147 @ SV404 @ SV141 ) ) ) )
| ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1132,plain,
! [SV142: $i,SV307: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV307 )
| ~ ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 ) ) )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1133,plain,
! [SV143: $i] :
( ( ( iskpair @ SV143 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
!= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1134,plain,
! [SV308: $i > $o,SV144: $i,SV405: $i] :
( ( ~ ( in @ SV405 @ SV144 )
| ~ ( SV308 @ SV405 )
| ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1135,plain,
! [SV309: $i > $o,SV145: $i] :
( ( ( ! [SY2260: $i] :
( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
!= ( setadjoin @ SY2260 @ emptyset ) )
| ~ ( in @ SY2260
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1136,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ~ ( ~ ( in @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) @ SV146 )
| ~ ~ ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 ) )
| ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1137,plain,
! [SV311: $i,SV147: $i] :
( ( ( SV147 != SV311 )
= $true )
| ( ( ~ ( ~ ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) )
| ~ ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1138,plain,
! [SV148: $i] :
( ( ( iskpair @ SV148 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
| ~ ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1139,plain,
! [SV312: $i,SV149: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
| ~ ( ~ ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
| ~ ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1140,plain,
! [SV313: $i > $o,SV150: $i] :
( ( ( ! [SY2271: $i] :
( ~ ( in @ SY2271 @ SV150 )
| ( SV313 @ SY2271 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1141,plain,
! [SV151: $i] :
( ( ~ ! [SY1964: $i > $o,SY1965: $i] :
( ~ ( in @ SY1965 @ SV151 )
| ~ ( SY1964 @ SY1965 )
| ( in @ SY1965
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1964 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1142,plain,
! [SV151: $i] :
( ( ~ ! [SY1967: $i > $o,SY1968: $i] :
( ~ ( in @ SY1968 @ SV151 )
| ~ ( in @ SY1968
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1967 @ SX3 ) ) )
| ( SY1967 @ SY1968 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1143,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV408 ) )
= $true )
| ( ( ~ ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
| ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1144,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
| ~ ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1145,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) )
| ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1146,plain,
! [SV316: $i,SV155: $i,SV409: $i] :
( ( ~ ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
| ! [SY2393: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SY2393 @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
| ! [SY2394: $i] :
( ~ ( in @ SY2394 @ SV409 )
| ( SY2393 @ SY2394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1147,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( ~ ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
| ~ ( ( SV410
!= ( sK42_Xy @ SV410 @ SV156 ) ) ) )
| ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1148,plain,
! [SV157: $i] :
( ( ~ ! [SY1988: $i,SY1989: $i] :
( ~ ( in @ SY1989 @ ( funcSet @ SV157 @ SY1988 ) )
| ! [SY1990: $i] :
( ~ ( in @ SY1990 @ SV157 )
| ~ ( ( ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 )
@ ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1149,plain,
! [SV157: $i] :
( ( ~ ! [SY1993: $i,SY1994: $i] :
( ~ ( in @ SY1994 @ ( funcSet @ SV157 @ SY1993 ) )
| ( subset @ SY1994 @ ( cartprod @ SV157 @ SY1993 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1150,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( ~ ( ~ ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
| ~ ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 ) ) )
= $true )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1151,plain,
! [SV318: $i,SV159: $i] :
( ( ( SV159 != SV318 )
= $true )
| ( ( ! [SY2284: $i > $o,SY2285: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) )
| ~ ( ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SX4: $i] : ( SY2284 @ SX4 ) )
= ( dsetconstr @ SV318
@ ^ [SX4: $i] : ( SY2285 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1152,plain,
! [SV160: $i] :
( ( ~ ! [SY2002: $i,SY2003: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2003 @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) ) @ SY2002 ) )
| ! [SY2004: $i] :
( ~ ( in @ SY2004 @ SV160 )
| ~ ( ( ( dsetconstr @ SY2002
@ ^ [SY2005: $i] :
( in @ ( kpair @ SY2004 @ SY2005 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 )
@ ( dsetconstr @ SY2002
@ ^ [SY2008: $i] :
( in @ ( kpair @ SY2004 @ SY2008 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1153,plain,
! [SV160: $i] :
( ( ~ ! [SY2011: $i,SY2012: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2012 @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) ) @ SY2011 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SY2011
@ ^ [SX3: $i,SX4: $i] :
( ( SY2012 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV160 @ SY2011 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1154,plain,
! [SV161: $i,SV319: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV161 )
| ~ ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 ) ) )
= $true )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1155,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( ~ ( ~ ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
| ~ ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 ) ) )
= $true )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1156,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
!= ( sK56_SY1649 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK56_SY1649 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK54_SY238 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK53_SY240 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK53_SY240 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1157,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
!= ( sK52_SY1647 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK52_SY1647 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK50_SY241 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK49_SY237 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK49_SY237 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1158,plain,
! [SV163: $i] :
( ( ~ ! [SY2018: $i] :
( ~ ( ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SY2018 )
| ~ ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SV163 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2018 )
| ~ ( ~ ! [SY2020: $i] :
( ~ ( in @ SY2020 @ ( sK15_B @ SV163 ) )
| ! [SY2021: $i] :
( ~ ( in @ SY2021 @ SY2020 )
| ( in @ SY2021 @ ( sK17_SY1618 @ SY2018 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2020 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SY2018 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2018 ) )
| ~ ! [SY2022: $i] :
( ~ ( in @ SY2022 @ ( sK17_SY1618 @ SY2018 @ SV163 ) )
| ~ ( in @ SY2022 @ SY2018 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1159,plain,
! [SV163: $i] :
( ( ~ ~ ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) )
| ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1160,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ~ ( ~ ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
| ~ ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) )
| ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
| ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1161,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
| ~ ! [SY2296: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) )
| ~ ( ( SY2296
!= ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SY2296 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1162,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ~ ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1163,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
| ~ ( ( SV413
!= ( sK48_SY229 @ SV413 @ SV167 ) ) ) )
| ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1164,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( setunion @ SV168 ) ) )
= $true )
| ( ( ! [SY2310: $o] :
( ~ ( ~ ( in @ SV324 @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SY2310 ) )
| SY2310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1165,plain,
( ( subset @ sK3_SY1596 @ ( cartprod @ sK1_SY0 @ sK2_SY1590 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1166,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1167,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( ~ ( ~ ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
| ~ ( ( SV414
!= ( sK57_SY253 @ SV414 @ SV169 ) ) ) )
| ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1168,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ~ ( ~ ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
| ~ ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) )
| ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
| ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1169,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1170,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ~ ( ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
!= SV416 )
| ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
| ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
| ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1171,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( ~ ( ~ ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) )
| ~ ( ( SV417
!= ( sK24_SY91 @ SV417 @ SV173 ) ) ) )
| ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1174,plain,
! [SV327: $i > $o,SV174: $i] :
( ( ( ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV174 )
| ( SV327 @ SY2320 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1175,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1176,plain,
! [SV176: $i] :
( ( ~ ! [SY2083: $i,SY2084: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2084 @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) ) @ SY2083 ) )
| ! [SY2085: $i] :
( ~ ( in @ SY2085 @ SV176 )
| ~ ( ( ( dsetconstr @ SY2083
@ ^ [SY2086: $i] :
( in @ ( kpair @ SY2085 @ SY2086 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 )
@ ( dsetconstr @ SY2083
@ ^ [SY2089: $i] :
( in @ ( kpair @ SY2085 @ SY2089 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1177,plain,
! [SV176: $i] :
( ( ~ ! [SY2092: $i,SY2093: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2093 @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) ) @ SY2092 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SY2092
@ ^ [SX3: $i,SX4: $i] :
( ( SY2093 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV176 @ SY2092 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1178,plain,
! [SV177: $i,SV329: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV177 )
| ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV329 ) ) )
= $true )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1179,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
| ~ ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) ) ) )
= $true )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1180,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ~ ( ~ ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
| ~ ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) )
| ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) )
| ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1181,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1182,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ~ ( ~ ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
| ~ ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) )
| ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
| ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1183,plain,
! [SV182: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 )
| ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1184,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) )
| ~ ( ( SV421
!= ( sK20_SY62 @ SV421 @ SV183 ) ) ) )
| ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1185,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ~ ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
| ~ ( ~ ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1186,plain,
! [SV185: $i,SV334: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV185 )
| ~ ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 ) ) )
= $true )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1187,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
| ~ ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) ) ) )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1188,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ( ~ ( ( ( sK60_Xx @ SV336 @ SV187 )
!= ( sK61_SY1650 @ SV336 @ SV187 ) )
| ~ ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1191,plain,
! [SV188: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ ( setunion @ SV188 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 )
| ~ ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1192,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( ~ ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
| ~ ( ( SV423
!= ( sK22_SY79 @ SV423 @ SV189 ) ) ) )
| ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1193,plain,
! [SV190: $i] :
( ( ~ ! [SY2132: $i,SY2133: $i] :
( ~ ( in @ SY2133 @ ( setadjoin @ SV190 @ SY2132 ) )
| ( SY2133 = SV190 )
| ( in @ SY2133 @ SY2132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1194,plain,
! [SV190: $i] :
( ( ~ ~ ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) )
| ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1195,plain,
! [SV191: $i,SV1: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) ) )
= $true )
| ( ( ! [SY2344: $i] :
( ~ ( in @ SY2344 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2345: $i] : ( in @ ( kpair @ SY2344 @ SY2345 ) @ SV338 ) ) )
@ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1196,plain,
! [SV339: $i > $i > $o,SV192: $i,SV2: $i,SV424: $i] :
( ( ! [SY2427: $i] :
( ~ ( in @ ( kpair @ SV424 @ SY2427 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [SY2348: $i,SY2349: $i] : ( SV339 @ SY2348 @ SY2349 ) ) )
| ( SV339 @ SV424 @ SY2427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1197,plain,
! [SV340: $i > $i > $o,SV193: $i,SV3: $i,SV425: $i] :
( ( ! [SY2430: $i] :
( ~ ( in @ ( kpair @ SV425 @ SY2430 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [SY2352: $i,SY2353: $i] : ( SV340 @ SY2352 @ SY2353 ) ) )
| ( in @ SY2430 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1198,plain,
! [SV341: $i > $i > $o,SV194: $i,SV4: $i,SV426: $i] :
( ( ! [SY2433: $i] :
~ ( in @ ( kpair @ SV426 @ SY2433 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [SY2356: $i,SY2357: $i] : ( SV341 @ SY2356 @ SY2357 ) ) )
| ( in @ SV426 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1199,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i,SV427: $i] :
( ( ~ ( in @ SV427 @ SV5 )
| ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV195 )
| ~ ( in @ ( kpair @ SV427 @ SY2436 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SY2436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1200,plain,
! [SV345: $i > $i > $o,SV198: $i,SV8: $i,SV428: $i] :
( ( ~ ( in @ SV428 @ SV8 )
| ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV198 )
| ~ ( SV345 @ SV428 @ SY2439 )
| ( in @ ( kpair @ SV428 @ SY2439 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1201,plain,
! [SV199: $i,SV9: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ ( cartprod @ SV9 @ SV199 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV346 ) @ ( ksnd @ SV346 ) )
= SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1202,plain,
! [SV200: $i,SV10: $i,SV347: $i] :
( ( ( ~ ( in @ SV347 @ SV10 ) )
= $true )
| ( ( ! [SY2370: $i] :
( ~ ( in @ SY2370 @ SV200 )
| ( ( ksnd @ ( kpair @ SV347 @ SY2370 ) )
= SY2370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1203,plain,
! [SV201: $i,SV11: $i,SV348: $i] :
( ( ( ~ ( in @ SV348 @ SV11 ) )
= $true )
| ( ( ! [SY2371: $i] :
( ~ ( in @ SY2371 @ SV201 )
| ( ( kfst @ ( kpair @ SV348 @ SY2371 ) )
= SV348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1204,plain,
! [SV12: $i,SV349: $i] :
( ( ( in @ SV349 @ SV12 )
= $false )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1205,plain,
! [SV202: $i,SV13: $i,SV429: $i,SV350: $i] :
( ( ~ ( in @ ( kpair @ SV350 @ SV429 ) @ ( cartprod @ SV13 @ SV202 ) )
| ( in @ SV429 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1206,plain,
! [SV203: $i,SV14: $i,SV351: $i] :
( ( ( ! [SY2373: $i] :
~ ( in @ ( kpair @ SV351 @ SY2373 ) @ ( cartprod @ SV14 @ SV203 ) ) )
= $true )
| ( ( in @ SV351 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1207,plain,
! [SV204: $i,SV15: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( cartprod @ SV15 @ SV204 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV352 ) @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1208,plain,
! [SV430: $i,SV353: $i,SV206: $i,SV18: $i] :
( ( ( ( kpair @ SV18 @ SV206 )
!= ( kpair @ SV353 @ SV430 ) )
| ( SV206 = SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1209,plain,
! [SV431: $i,SV354: $i,SV207: $i,SV19: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV354 @ ( setadjoin @ SV431 @ emptyset ) ) @ emptyset ) ) )
| ( SV207 = SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1210,plain,
! [SV432: $i,SV208: $i,SV20: $i] :
( ( ( ( setadjoin @ SV20 @ ( setadjoin @ SV208 @ emptyset ) )
!= ( setadjoin @ SV432 @ emptyset ) )
= $true )
| ( ( SV20 = SV208 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1211,plain,
! [SV433: $i,SV355: $i,SV209: $i,SV21: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV433 @ emptyset ) ) @ emptyset ) ) )
| ( SV355 != SV433 )
| ( SV209 = SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1212,plain,
! [SV210: $i,SV22: $i] :
( ( ( SV22 = SV210 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV22 @ ( setadjoin @ SV210 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV22 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1213,plain,
! [SV211: $i,SV23: $i] :
( ( ( SV23 = SV211 )
= $false )
| ( ( ( setadjoin @ SV23 @ ( setadjoin @ SV211 @ emptyset ) )
= ( setadjoin @ SV23 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1214,plain,
! [SV356: $i,SV212: $i,SV24: $i] :
( ( ( ! [SY2377: $i] :
( ( kpair @ SV24 @ SV212 )
!= ( kpair @ SV356 @ SY2377 ) ) )
= $true )
| ( ( SV24 = SV356 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1215,plain,
! [SV357: $i,SV213: $i,SV25: $i] :
( ( ( ! [SY2378: $i] :
( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV357 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV357 @ ( setadjoin @ SY2378 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV25 = SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1216,plain,
! [SV214: $i,SV26: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ ( cartprod @ SV26 @ SV214 ) ) )
= $true )
| ( ( in @ ( kfst @ SV358 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1217,plain,
! [SV359: $i,SV28: $i] :
( ( ( SV28
!= ( setadjoin @ SV359 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV359 @ SV28 ) )
= $true )
| ( ( in @ ( setunion @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1218,plain,
! [SV216: $i,SV29: $i,SV360: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV360 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV29 = SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1219,plain,
! [SV217: $i,SV30: $i] :
( ( ( ( setadjoin @ SV30 @ emptyset )
= ( setadjoin @ SV217 @ emptyset ) )
= $false )
| ( ( SV30 = SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1220,plain,
! [SV218: $i,SV34: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( cartprod @ SV34 @ SV218 ) ) )
= $true )
| ( ( iskpair @ SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1221,plain,
! [SV219: $i,SV35: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV35 ) )
= $true )
| ( ( ! [SY2379: $i] :
( ~ ( in @ SY2379 @ SV219 )
| ( in @ ( kpair @ SV362 @ SY2379 ) @ ( cartprod @ SV35 @ SV219 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1222,plain,
! [SV220: $i,SV36: $i,SV363: $i] :
( ( ( ~ ( in @ SV363 @ SV36 ) )
= $true )
| ( ( ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV220 )
| ( in @ ( kpair @ SV363 @ SY2380 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1223,plain,
! [SV221: $i,SV37: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV37 ) )
= $true )
| ( ( ! [SY2381: $i] :
( ~ ( in @ SY2381 @ SV221 )
| ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SY2381 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1224,plain,
! [SV222: $i,SV38: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ SV38 ) )
= $true )
| ( ( ! [SY2382: $i] :
( ~ ( in @ SY2382 @ SV222 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SY2382 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1225,plain,
! [SV223: $i,SV39: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV39 ) )
= $true )
| ( ( ! [SY2383: $i] :
( ~ ( in @ SY2383 @ SV223 )
| ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SY2383 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1226,plain,
! [SV224: $i,SV40: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV40 ) )
= $true )
| ( ( ! [SY2384: $i] :
( ~ ( in @ SY2384 @ SV224 )
| ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SY2384 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1227,plain,
! [SV225: $i,SV41: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( setadjoin @ SV41 @ ( setadjoin @ SV225 @ emptyset ) ) ) )
= $true )
| ( ( ( SV368 = SV41 )
| ( SV368 = SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1228,plain,
! [SV226: $i,SV42: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV42 ) )
= $true )
| ( ( in @ ( setadjoin @ SV369 @ emptyset ) @ ( powerset @ ( binunion @ SV42 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1229,plain,
! [SV43: $i,SV227: $i] :
( ( ( in @ SV227 @ SV43 )
= $false )
| ( ( in @ ( setadjoin @ SV227 @ emptyset ) @ ( powerset @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1230,plain,
! [SV44: $i,SV228: $i] :
( ( ( in @ SV228 @ SV44 )
= $false )
| ( ( subset @ ( setadjoin @ SV228 @ emptyset ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1231,plain,
! [SV234: $i,SV50: $i,SV370: $i] :
( ( ( in @ SV370 @ SV50 )
= $true )
| ( ( ( in @ SV370 @ SV234 )
| ~ ( in @ SV370 @ ( symdiff @ SV50 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1232,plain,
! [SV235: $i,SV51: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV51 ) )
= $true )
| ( ( ~ ( in @ SV371 @ SV235 )
| ~ ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1233,plain,
! [SV236: $i,SV52: $i,SV372: $i] :
( ( ( in @ SV372 @ SV52 )
= $true )
| ( ( ~ ( in @ SV372 @ SV236 )
| ( in @ SV372 @ ( symdiff @ SV52 @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1234,plain,
! [SV237: $i,SV53: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV53 ) )
= $true )
| ( ( ( in @ SV373 @ SV237 )
| ( in @ SV373 @ ( symdiff @ SV53 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1235,plain,
! [SV238: $i,SV54: $i] :
( ( ( ( setminus @ SV54 @ SV238 )
= emptyset )
= $false )
| ( ( subset @ SV54 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1236,plain,
! [SV56: $i,SV240: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV240 ) )
= $true )
| ( ( ~ ( in @ SV374 @ ( setminus @ SV56 @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1237,plain,
! [SV241: $i,SV57: $i,SV375: $i] :
( ( ( in @ SV375 @ SV57 )
= $true )
| ( ( ~ ( in @ SV375 @ ( setminus @ SV57 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1238,plain,
! [SV242: $i,SV58: $i,SV376: $i] :
( ( ( in @ SV376 @ ( setminus @ SV58 @ SV242 ) )
= $true )
| ( ( ( in @ SV376 @ SV242 )
| ~ ( in @ SV376 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1239,plain,
! [SV243: $i,SV59: $i,SV377: $i] :
( ( ( in @ SV377 @ ( setminus @ SV59 @ SV243 ) )
= $true )
| ( ( ~ ( in @ SV377 @ SV59 )
| ( in @ SV377 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1240,plain,
! [SV244: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV244 )
= $false )
| ( ( ( setminus @ SV60 @ SV244 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1241,plain,
! [SV245: $i,SV61: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ ( setminus @ SV61 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ SV378 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1242,plain,
! [SV246: $i,SV62: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ ( setminus @ SV62 @ SV246 ) ) )
= $true )
| ( ( in @ SV379 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1243,plain,
! [SV247: $i,SV63: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV63 ) )
= $true )
| ( ( ( in @ SV380 @ SV247 )
| ( in @ SV380 @ ( setminus @ SV63 @ SV247 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1244,plain,
! [SV249: $i,SV65: $i] :
( ( ( ( binintersect @ SV65 @ SV249 )
= SV65 )
= $false )
| ( ( subset @ SV65 @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1245,plain,
! [SV66: $i,SV250: $i] :
( ( ( subset @ SV250 @ SV66 )
= $false )
| ( ( ( binintersect @ SV66 @ SV250 )
= SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1246,plain,
! [SV252: $i,SV68: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ ( binintersect @ SV68 @ SV252 ) ) )
= $true )
| ( ( in @ SV382 @ SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1247,plain,
! [SV253: $i,SV69: $i] :
( ( ( ( binintersect @ SV69 @ SV253 )
= SV253 )
= $false )
| ( ( subset @ SV253 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1248,plain,
! [SV254: $i,SV70: $i] :
( ( ( subset @ SV70 @ SV254 )
= $false )
| ( ( ( binintersect @ SV70 @ SV254 )
= SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1249,plain,
! [SV256: $i,SV72: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( binintersect @ SV72 @ SV256 ) ) )
= $true )
| ( ( in @ SV383 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1250,plain,
! [SV257: $i,SV73: $i,SV384: $i] :
( ( ( ~ ( subset @ SV384 @ SV73 ) )
= $true )
| ( ( ~ ( subset @ SV384 @ SV257 )
| ( subset @ SV384 @ ( binintersect @ SV73 @ SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1251,plain,
! [SV258: $i,SV74: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV74 ) )
= $true )
| ( ( ~ ( in @ SV385 @ SV258 )
| ( in @ SV385 @ ( binintersect @ SV74 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1252,plain,
! [SV261: $i,SV77: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( binunion @ SV77 @ SV261 ) ) )
= $true )
| ( ( ( in @ SV386 @ SV77 )
| ( in @ SV386 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1253,plain,
! [SV78: $i,SV262: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV262 ) )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV78 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1254,plain,
! [SV264: $i,SV80: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV80 ) )
= $true )
| ( ( in @ SV388 @ ( binunion @ SV80 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1255,plain,
! [SV267: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV267 )
= $false )
| ( ( subset @ ( powerset @ SV83 ) @ ( powerset @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1256,plain,
! [SV85: $i,SV268: $i] :
( ( ( in @ SV268 @ ( powerset @ SV85 ) )
= $false )
| ( ( subset @ SV268 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1257,plain,
! [SV86: $i,SV269: $i] :
( ( ( subset @ SV269 @ SV86 )
= $false )
| ( ( in @ SV269 @ ( powerset @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1258,plain,
! [SV270: $i,SV88: $i] :
( ( ( subset @ SV88 @ SV270 )
= $false )
| ( ( ~ ( subset @ SV270 @ SV88 )
| ( SV88 = SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1259,plain,
! [SV271: $i,SV89: $i] :
( ( ( subset @ SV89 @ SV271 )
= $false )
| ( ( in @ SV89 @ ( powerset @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1260,plain,
! [SV272: $i,SV389: $i,SV90: $i] :
( ( ( ~ ( subset @ SV90 @ SV389 ) )
= $true )
| ( ( subset @ SV90 @ ( setadjoin @ SV272 @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1261,plain,
! [SV274: $i,SV92: $i] :
( ( ( subset @ SV92 @ SV274 )
= $false )
| ( ( ! [SY2232: $i] :
( ~ ( subset @ SV274 @ SY2232 )
| ( subset @ SV92 @ SY2232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1262,plain,
! [SV275: $i,SV94: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV94 ) )
= $true )
| ( ( ( in @ SV390 @ SV275 )
| ( SV94 != SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1263,plain,
! [SV276: $i,SV95: $i] :
( ( ( SV95 = SV276 )
= $false )
| ( ( subset @ SV95 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1264,plain,
! [SV277: $i,SV96: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV96 ) )
= $true )
| ( ( ( in @ SV391 @ SV277 )
| ~ ( subset @ SV96 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1265,plain,
! [SV278: $i,SV97: $i] :
( ( ( subset @ SV97 @ SV278 )
= $false )
| ( ( ! [SY2235: $i] :
( ( in @ SY2235 @ SV278 )
| ~ ( in @ SY2235 @ SV97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1266,plain,
! [SV279: $i,SV98: $i] :
( ( ( subset @ SV98 @ SV279 )
= $false )
| ( ( ! [SY2236: $i] :
( ~ ( in @ SY2236 @ SV98 )
| ( in @ SY2236 @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1267,plain,
! [SV280: $i,SV100: $i] :
( ( ( SV100 = SV280 )
= $false )
| ( ( subset @ SV100 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1268,plain,
! [SV281: $i,SV101: $i] :
( ( ( SV101 = SV281 )
= $false )
| ( ( subset @ SV281 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1269,plain,
! [SV282: $i,SV102: $i] :
( ( ( SV102 = SV282 )
= $false )
| ( ( ( setunion @ SV102 )
= ( setunion @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1270,plain,
! [SV283: $i,SV103: $i] :
( ( ( SV103 = SV283 )
= $false )
| ( ( ( powerset @ SV103 )
= ( powerset @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1271,plain,
! [SV284: $i,SV104: $i] :
( ( ( SV104 = SV284 )
= $false )
| ( ( ! [SY2237: $i,SY2238: $i] :
( ( SY2237 != SY2238 )
| ( ( setadjoin @ SV104 @ SY2237 )
= ( setadjoin @ SV284 @ SY2238 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1272,plain,
! [SV285: $i,SV105: $i] :
( ( ( SV105 = SV285 )
= $false )
| ( ( ! [SY2239: $i,SY2240: $i] :
( ( SY2239 != SY2240 )
| ~ ( in @ SY2239 @ SV105 )
| ( in @ SY2240 @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1273,plain,
! [SV108: $i > $o,SV286: $i] :
( ( ( in @ SV286 @ emptyset )
= $false )
| ( ( SV108 @ SV286 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1274,plain,
! [SV109: $i,SV434: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ SV434 )
| ~ ( in @ SV434 @ SV109 ) )
= $true )
| ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1275,plain,
! [SV290: $i,SV112: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( setadjoin @ SV112 @ ( setadjoin @ SV290 @ emptyset ) ) ) )
= $true )
| ( ( ( SV392 = SV112 )
| ( SV392 = SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1276,plain,
! [SV291: $i,SV113: $i] :
( ( ( in @ SV113 @ ( setadjoin @ SV291 @ emptyset ) )
= $false )
| ( ( in @ SV291 @ ( setadjoin @ SV113 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1277,plain,
! [SV292: $i,SV114: $i] :
( ( ( SV114 = SV292 )
= $false )
| ( ( in @ SV114 @ ( setadjoin @ SV292 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1278,plain,
! [SV115: $i,SV293: $i] :
( ( ( in @ SV293 @ ( setadjoin @ SV115 @ emptyset ) )
= $false )
| ( ( SV115 = SV293 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1279,plain,
! [SV294: $i,SV116: $i] :
( ( ( in @ SV116 @ ( setadjoin @ SV294 @ emptyset ) )
= $false )
| ( ( SV116 = SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1280,plain,
! [SV118: $i,SV295: $i] :
( ( ( in @ SV295 @ SV118 )
= $false )
| ( ( in @ SV295 @ ( powerset @ ( setunion @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1281,plain,
! [SV119: $i,SV393: $i,SV296: $i] :
( ( ( ~ ( in @ SV296 @ SV393 ) )
= $true )
| ( ( ~ ( in @ SV393 @ SV119 )
| ( in @ SV296 @ ( setunion @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1282,plain,
! [SV120: $i,SV297: $i] :
( ( ( in @ SV297 @ ( powerset @ SV120 ) )
= $false )
| ( ( ! [SY2245: $i] :
( ~ ( in @ SY2245 @ SV297 )
| ( in @ SY2245 @ SV120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1283,plain,
! [SV298: $i,SV124: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ ( setadjoin @ SV124 @ SV298 ) ) )
= $true )
| ( ( ( SV394 = SV124 )
| ( in @ SV394 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1284,plain,
! [SV125: $i,SV299: $i,SV395: $i] :
( ( ( ~ ( in @ SV395 @ SV299 ) )
= $true )
| ( ( in @ SV395 @ ( setadjoin @ SV125 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1285,plain,
! [SV127: $i,SV396: $i] :
( ( ( in @ SV396 @ SV127 )
= $false )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1286,plain,
! [SV301: $i > $o,SV128: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV128 ) )
= $true )
| ( ( ~ ( SV301 @ SV397 )
| ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1287,plain,
! [SV302: $i,SV435: $o] :
( ( SV435 = $true )
| ( ( in @ SV302 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1122]) ).
thf(1288,plain,
! [SV302: $i] :
( ( $true = $true )
| ( ( in @ SV302 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1122]) ).
thf(1289,plain,
! [SV302: $i] :
( ( $false = $true )
| ( ( in @ SV302 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1122]) ).
thf(1290,plain,
! [SV134: $o,SV398: $i] :
( ( ( in @ SV398 @ ( prop2set @ SV134 ) )
= $false )
| ( SV134 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1291,plain,
! [SV399: $i] :
( ( ( in @ SV399 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1292,plain,
! [SV400: $i] :
( ( ( in @ SV400 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1293,plain,
! [SV303: $i > $o,SV135: $i,SV401: $i] :
( ( ( ~ ( in @ SV401
@ ( dsetconstr @ SV135
@ ^ [SY2251: $i] : ( SV303 @ SY2251 ) ) ) )
= $true )
| ( ( SV303 @ SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1294,plain,
! [SV304: $i > $o,SV136: $i,SV402: $i] :
( ( ( ~ ( in @ SV402
@ ( dsetconstr @ SV136
@ ^ [SY2253: $i] : ( SV304 @ SY2253 ) ) ) )
= $true )
| ( ( in @ SV402 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1295,plain,
! [SV305: $i > $o,SV137: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV137 ) )
= $true )
| ( ( ~ ( SV305 @ SV403 )
| ( in @ SV403
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1296,plain,
! [SV306: $i > $o,SV140: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV140 )
| ( SV306 @ SV436 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1297,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
| ~ ( ( SV404
!= ( sK33_SY147 @ SV404 @ SV141 ) ) ) ) )
= $true )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1298,plain,
! [SV142: $i,SV307: $i] :
( ( ( ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV307 )
| ~ ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1299,plain,
! [SV143: $i] :
( ( ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
!= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) ) )
= $false )
| ( ( iskpair @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1300,plain,
! [SV308: $i > $o,SV144: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV144 ) )
= $true )
| ( ( ~ ( SV308 @ SV405 )
| ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1301,plain,
! [SV437: $i,SV309: $i > $o,SV145: $i] :
( ( ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
!= ( setadjoin @ SV437 @ emptyset ) )
| ~ ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1302,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) @ SV146 )
| ~ ~ ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 ) ) )
= $true )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1303,plain,
! [SV311: $i,SV147: $i] :
( ( ( SV147 = SV311 )
= $false )
| ( ( ~ ( ~ ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) )
| ~ ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1304,plain,
! [SV148: $i] :
( ( ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
| ~ ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) ) )
= $false )
| ( ( iskpair @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1305,plain,
! [SV312: $i,SV149: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
| ~ ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1306,plain,
! [SV313: $i > $o,SV150: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV150 )
| ( SV313 @ SV438 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1307,plain,
! [SV151: $i] :
( ( ! [SY1964: $i > $o,SY1965: $i] :
( ~ ( in @ SY1965 @ SV151 )
| ~ ( SY1964 @ SY1965 )
| ( in @ SY1965
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1964 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1308,plain,
! [SV151: $i] :
( ( ! [SY1967: $i > $o,SY1968: $i] :
( ~ ( in @ SY1968 @ SV151 )
| ~ ( in @ SY1968
@ ( dsetconstr @ SV151
@ ^ [SX3: $i] : ( SY1967 @ SX3 ) ) )
| ( SY1967 @ SY1968 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1309,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ SV408 )
= $false )
| ( ( ~ ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
| ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1310,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
| ~ ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1311,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1312,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ~ ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) )
| ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1145]) ).
thf(1313,plain,
! [SV316: $i,SV155: $i,SV409: $i] :
( ( ( ~ ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) ) )
= $true )
| ( ( ! [SY2393: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SY2393 @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
| ! [SY2394: $i] :
( ~ ( in @ SY2394 @ SV409 )
| ( SY2393 @ SY2394 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1314,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( ~ ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
| ~ ( ( SV410
!= ( sK42_Xy @ SV410 @ SV156 ) ) ) ) )
= $true )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1315,plain,
! [SV157: $i] :
( ( ! [SY1988: $i,SY1989: $i] :
( ~ ( in @ SY1989 @ ( funcSet @ SV157 @ SY1988 ) )
| ! [SY1990: $i] :
( ~ ( in @ SY1990 @ SV157 )
| ~ ( ( ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY1990 @ SY1989 @ SY1988 @ SV157 )
@ ( dsetconstr @ SY1988
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1990 @ SX4 ) @ SY1989 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1316,plain,
! [SV157: $i] :
( ( ! [SY1993: $i,SY1994: $i] :
( ~ ( in @ SY1994 @ ( funcSet @ SV157 @ SY1993 ) )
| ( subset @ SY1994 @ ( cartprod @ SV157 @ SY1993 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1317,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( ~ ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
| ~ ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 ) )
= $false )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1318,plain,
! [SV318: $i,SV159: $i] :
( ( ( SV159 = SV318 )
= $false )
| ( ( ! [SY2284: $i > $o,SY2285: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ~ ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) )
| ~ ( ( SY2284 @ ( sK62_Xx @ SY2285 @ SY2284 @ SV318 @ SV159 ) )
| ( SY2285 @ ( sK63_SY1651 @ SY2285 @ SY2284 @ SV318 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SX4: $i] : ( SY2284 @ SX4 ) )
= ( dsetconstr @ SV318
@ ^ [SX4: $i] : ( SY2285 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1319,plain,
! [SV160: $i] :
( ( ! [SY2002: $i,SY2003: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2003 @ ( sK89_Xx @ SY2003 @ SY2002 @ SV160 ) ) @ SY2002 ) )
| ! [SY2004: $i] :
( ~ ( in @ SY2004 @ SV160 )
| ~ ( ( ( dsetconstr @ SY2002
@ ^ [SY2005: $i] :
( in @ ( kpair @ SY2004 @ SY2005 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2004 @ SY2003 @ SY2002 @ SV160 )
@ ( dsetconstr @ SY2002
@ ^ [SY2008: $i] :
( in @ ( kpair @ SY2004 @ SY2008 )
@ ( dpsetconstr @ SV160 @ SY2002
@ ^ [SX5: $i,SX6: $i] :
( ( SY2003 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1320,plain,
! [SV160: $i] :
( ( ! [SY2011: $i,SY2012: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2012 @ ( sK87_Xx @ SY2012 @ SY2011 @ SV160 ) ) @ SY2011 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SY2011
@ ^ [SX3: $i,SX4: $i] :
( ( SY2012 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV160 @ SY2011 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1321,plain,
! [SV161: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV161 )
| ~ ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 ) )
= $false )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1322,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
| ~ ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 ) )
= $false )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1323,plain,
! [SV439: $i > $o] :
( ( ! [SY2444: $i > $o] :
( ~ ( ( ( sK55_Xx @ SY2444 @ SV439 )
!= ( sK56_SY1649 @ SY2444 @ SV439 ) )
| ~ ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SY2444 @ SV439 ) )
| ~ ( SY2444 @ ( sK56_SY1649 @ SY2444 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SY2444 @ SV439 ) )
| ( SY2444 @ ( sK56_SY1649 @ SY2444 @ SV439 ) ) ) ) )
| ! [SY2445: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2445 @ SY2444 @ SV439 ) )
| ~ ( ( SY2445
!= ( sK54_SY238 @ SY2445 @ SY2444 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2445 ) )
| ~ ( ~ ! [SY2446: $i] :
( ~ ( SY2444 @ SY2446 )
| ( ( sK53_SY240 @ SY2444 @ SV439 )
= SY2446 ) )
| ~ ( SY2444 @ ( sK53_SY240 @ SY2444 @ SV439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1324,plain,
! [SV440: $i > $o] :
( ( ! [SY2447: $i > $o] :
( ~ ( ( ( sK51_Xx @ SY2447 @ SV440 )
!= ( sK52_SY1647 @ SY2447 @ SV440 ) )
| ~ ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SY2447 @ SV440 ) )
| ~ ( SY2447 @ ( sK52_SY1647 @ SY2447 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SY2447 @ SV440 ) )
| ( SY2447 @ ( sK52_SY1647 @ SY2447 @ SV440 ) ) ) ) )
| ! [SY2448: $i] :
( ~ ( ~ ( SY2447 @ ( sK50_SY241 @ SY2448 @ SY2447 @ SV440 ) )
| ~ ( ( SY2448
!= ( sK50_SY241 @ SY2448 @ SY2447 @ SV440 ) ) ) )
| ~ ( SY2447 @ SY2448 ) )
| ~ ( ~ ! [SY2449: $i] :
( ~ ( SV440 @ SY2449 )
| ( ( sK49_SY237 @ SY2447 @ SV440 )
= SY2449 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SY2447 @ SV440 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1325,plain,
! [SV163: $i] :
( ( ! [SY2018: $i] :
( ~ ( ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SY2018 )
| ~ ~ ( in @ ( sK19_Xx @ SY2018 @ SV163 ) @ SV163 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY2018 )
| ~ ( ~ ! [SY2020: $i] :
( ~ ( in @ SY2020 @ ( sK15_B @ SV163 ) )
| ! [SY2021: $i] :
( ~ ( in @ SY2021 @ SY2020 )
| ( in @ SY2021 @ ( sK17_SY1618 @ SY2018 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2020 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SY2018 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SY2018 @ SV163 ) @ SY2018 ) )
| ~ ! [SY2022: $i] :
( ~ ( in @ SY2022 @ ( sK17_SY1618 @ SY2018 @ SV163 ) )
| ~ ( in @ SY2022 @ SY2018 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1326,plain,
! [SV163: $i] :
( ( ~ ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) )
| ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1327,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
| ~ ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) )
| ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1328,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
| ~ ! [SY2296: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) )
| ~ ( ( SY2296
!= ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SY2296 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1329,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1330,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
| ~ ( ( SV413
!= ( sK48_SY229 @ SV413 @ SV167 ) ) ) ) )
= $true )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1331,plain,
! [SV168: $i,SV324: $i] :
( ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false )
| ( ( ! [SY2310: $o] :
( ~ ( ~ ( in @ SV324 @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SY2310 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SY2310 ) )
| SY2310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1332,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) )
| ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1333,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( ~ ( ~ ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
| ~ ( ( SV414
!= ( sK57_SY253 @ SV414 @ SV169 ) ) ) ) )
= $true )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1334,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
| ~ ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) )
| ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1335,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1336,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
!= SV416 )
| ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
| ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
| ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1337,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( ~ ( ~ ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) )
| ~ ( ( SV417
!= ( sK24_SY91 @ SV417 @ SV173 ) ) ) ) )
= $true )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1338,plain,
! [SV441: $i] :
( ( ! [SY2450: $i] :
( ! [SY2451: $i] :
( ~ ( in @ SY2450 @ SY2451 )
| ~ ( in @ SY2451 @ SV441 ) )
| ( in @ SY2450 @ ( setunion @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1339,plain,
! [SV442: $i] :
( ( ! [SY2452: $i] :
( ~ ( in @ SY2452 @ ( setunion @ SV442 ) )
| ~ ( ~ ( in @ SY2452 @ ( sK8_B @ SY2452 @ SV442 ) )
| ~ ( in @ ( sK8_B @ SY2452 @ SV442 ) @ SV442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1340,plain,
! [SV327: $i > $o,SV174: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV174 )
| ( SV327 @ SV443 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1341,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1342,plain,
! [SV176: $i] :
( ( ! [SY2083: $i,SY2084: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2084 @ ( sK92_Xx @ SY2084 @ SY2083 @ SV176 ) ) @ SY2083 ) )
| ! [SY2085: $i] :
( ~ ( in @ SY2085 @ SV176 )
| ~ ( ( ( dsetconstr @ SY2083
@ ^ [SY2086: $i] :
( in @ ( kpair @ SY2085 @ SY2086 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2085 @ SY2084 @ SY2083 @ SV176 )
@ ( dsetconstr @ SY2083
@ ^ [SY2089: $i] :
( in @ ( kpair @ SY2085 @ SY2089 )
@ ( dpsetconstr @ SV176 @ SY2083
@ ^ [SX5: $i,SX6: $i] :
( ( SY2084 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1343,plain,
! [SV176: $i] :
( ( ! [SY2092: $i,SY2093: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2093 @ ( sK90_Xx @ SY2093 @ SY2092 @ SV176 ) ) @ SY2092 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SY2092
@ ^ [SX3: $i,SX4: $i] :
( ( SY2093 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV176 @ SY2092 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1344,plain,
! [SV177: $i,SV329: $i] :
( ( ( ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV177 )
| ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV329 ) )
= $false )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1345,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( ~ ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
| ~ ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) ) )
= $false )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1346,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
| ~ ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) )
| ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1347,plain,
! [SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1348,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
| ~ ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) )
| ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1349,plain,
! [SV182: $i,SV420: $i] :
( ( ( in @ SV420 @ SV182 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 )
| ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1350,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( ~ ( ~ ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) )
| ~ ( ( SV421
!= ( sK20_SY62 @ SV421 @ SV183 ) ) ) ) )
= $true )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1351,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1352,plain,
! [SV185: $i,SV334: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV185 )
| ~ ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 ) )
= $false )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1353,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
| ~ ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) ) )
= $false )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1354,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ( ( ( sK60_Xx @ SV336 @ SV187 )
!= ( sK61_SY1650 @ SV336 @ SV187 ) )
| ~ ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1355,plain,
! [SV444: $i] :
( ( ! [SY2453: $i] :
( ~ ( ~ ( in @ ( sK7_Xx @ SY2453 @ SV444 ) @ SY2453 )
| ~ ~ ( in @ ( sK7_Xx @ SY2453 @ SV444 ) @ SV444 ) )
| ( in @ SY2453 @ ( powerset @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1356,plain,
! [SV445: $i] :
( ( ! [SY2454: $i] :
( ~ ( in @ SY2454 @ ( powerset @ SV445 ) )
| ! [SY2455: $i] :
( ~ ( in @ SY2455 @ SY2454 )
| ( in @ SY2455 @ SV445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1357,plain,
! [SV188: $i,SV337: $i] :
( ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 )
| ~ ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1358,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( ~ ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
| ~ ( ( SV423
!= ( sK22_SY79 @ SV423 @ SV189 ) ) ) ) )
= $true )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1359,plain,
! [SV190: $i] :
( ( ! [SY2132: $i,SY2133: $i] :
( ~ ( in @ SY2133 @ ( setadjoin @ SV190 @ SY2132 ) )
| ( SY2133 = SV190 )
| ( in @ SY2133 @ SY2132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1360,plain,
! [SV190: $i] :
( ( ~ ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) )
| ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1194]) ).
thf(1361,plain,
! [SV191: $i,SV1: $i,SV338: $i] :
( ( ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) )
= $false )
| ( ( ! [SY2344: $i] :
( ~ ( in @ SY2344 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2345: $i] : ( in @ ( kpair @ SY2344 @ SY2345 ) @ SV338 ) ) )
@ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1362,plain,
! [SV339: $i > $i > $o,SV192: $i,SV2: $i,SV446: $i,SV424: $i] :
( ( ~ ( in @ ( kpair @ SV424 @ SV446 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [SY2348: $i,SY2349: $i] : ( SV339 @ SY2348 @ SY2349 ) ) )
| ( SV339 @ SV424 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1363,plain,
! [SV340: $i > $i > $o,SV193: $i,SV3: $i,SV447: $i,SV425: $i] :
( ( ~ ( in @ ( kpair @ SV425 @ SV447 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [SY2352: $i,SY2353: $i] : ( SV340 @ SY2352 @ SY2353 ) ) )
| ( in @ SV447 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1364,plain,
! [SV341: $i > $i > $o,SV194: $i,SV4: $i,SV426: $i] :
( ( ( ! [SY2433: $i] :
~ ( in @ ( kpair @ SV426 @ SY2433 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [SY2356: $i,SY2357: $i] : ( SV341 @ SY2356 @ SY2357 ) ) ) )
= $true )
| ( ( in @ SV426 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1365,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV5 ) )
= $true )
| ( ( ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV195 )
| ~ ( in @ ( kpair @ SV427 @ SY2436 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SY2436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1366,plain,
! [SV345: $i > $i > $o,SV198: $i,SV8: $i,SV428: $i] :
( ( ( ~ ( in @ SV428 @ SV8 ) )
= $true )
| ( ( ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV198 )
| ~ ( SV345 @ SV428 @ SY2439 )
| ( in @ ( kpair @ SV428 @ SY2439 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1367,plain,
! [SV199: $i,SV9: $i,SV346: $i] :
( ( ( in @ SV346 @ ( cartprod @ SV9 @ SV199 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV346 ) @ ( ksnd @ SV346 ) )
= SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1368,plain,
! [SV200: $i,SV10: $i,SV347: $i] :
( ( ( in @ SV347 @ SV10 )
= $false )
| ( ( ! [SY2370: $i] :
( ~ ( in @ SY2370 @ SV200 )
| ( ( ksnd @ ( kpair @ SV347 @ SY2370 ) )
= SY2370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1369,plain,
! [SV201: $i,SV11: $i,SV348: $i] :
( ( ( in @ SV348 @ SV11 )
= $false )
| ( ( ! [SY2371: $i] :
( ~ ( in @ SY2371 @ SV201 )
| ( ( kfst @ ( kpair @ SV348 @ SY2371 ) )
= SV348 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1370,plain,
! [SV12: $i,SV349: $i] :
( ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B ) )
= $true )
| ( $true = $true )
| ( ( in @ SV349 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1371,plain,
! [SV202: $i,SV13: $i,SV429: $i,SV350: $i] :
( ( ( ~ ( in @ ( kpair @ SV350 @ SV429 ) @ ( cartprod @ SV13 @ SV202 ) ) )
= $true )
| ( ( in @ SV429 @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1372,plain,
! [SV203: $i,SV14: $i,SV448: $i,SV351: $i] :
( ( ( ~ ( in @ ( kpair @ SV351 @ SV448 ) @ ( cartprod @ SV14 @ SV203 ) ) )
= $true )
| ( ( in @ SV351 @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1373,plain,
! [SV204: $i,SV15: $i,SV352: $i] :
( ( ( in @ SV352 @ ( cartprod @ SV15 @ SV204 ) )
= $false )
| ( ( in @ ( ksnd @ SV352 ) @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1374,plain,
! [SV430: $i,SV353: $i,SV206: $i,SV18: $i] :
( ( ( ( kpair @ SV18 @ SV206 )
!= ( kpair @ SV353 @ SV430 ) )
= $true )
| ( ( SV206 = SV430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1375,plain,
! [SV431: $i,SV354: $i,SV207: $i,SV19: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV354 @ ( setadjoin @ SV431 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV207 = SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1376,plain,
! [SV432: $i,SV208: $i,SV20: $i] :
( ( ( ( setadjoin @ SV20 @ ( setadjoin @ SV208 @ emptyset ) )
= ( setadjoin @ SV432 @ emptyset ) )
= $false )
| ( ( SV20 = SV208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1377,plain,
! [SV433: $i,SV355: $i,SV209: $i,SV21: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV433 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV355 != SV433 )
| ( SV209 = SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1378,plain,
! [SV449: $i,SV356: $i,SV212: $i,SV24: $i] :
( ( ( ( kpair @ SV24 @ SV212 )
!= ( kpair @ SV356 @ SV449 ) )
= $true )
| ( ( SV24 = SV356 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1379,plain,
! [SV450: $i,SV357: $i,SV213: $i,SV25: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV357 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV357 @ ( setadjoin @ SV450 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV25 = SV357 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1380,plain,
! [SV214: $i,SV26: $i,SV358: $i] :
( ( ( in @ SV358 @ ( cartprod @ SV26 @ SV214 ) )
= $false )
| ( ( in @ ( kfst @ SV358 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1381,plain,
! [SV359: $i,SV28: $i] :
( ( ( SV28
= ( setadjoin @ SV359 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV359 @ SV28 ) )
= $true )
| ( ( in @ ( setunion @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1382,plain,
! [SV216: $i,SV29: $i,SV360: $i] :
( ( ( in @ ( setadjoin @ SV360 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV29 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV29 = SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1383,plain,
! [SV218: $i,SV34: $i,SV361: $i] :
( ( ( in @ SV361 @ ( cartprod @ SV34 @ SV218 ) )
= $false )
| ( ( iskpair @ SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1384,plain,
! [SV219: $i,SV35: $i,SV362: $i] :
( ( ( in @ SV362 @ SV35 )
= $false )
| ( ( ! [SY2379: $i] :
( ~ ( in @ SY2379 @ SV219 )
| ( in @ ( kpair @ SV362 @ SY2379 ) @ ( cartprod @ SV35 @ SV219 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1385,plain,
! [SV220: $i,SV36: $i,SV363: $i] :
( ( ( in @ SV363 @ SV36 )
= $false )
| ( ( ! [SY2380: $i] :
( ~ ( in @ SY2380 @ SV220 )
| ( in @ ( kpair @ SV363 @ SY2380 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1386,plain,
! [SV221: $i,SV37: $i,SV364: $i] :
( ( ( in @ SV364 @ SV37 )
= $false )
| ( ( ! [SY2381: $i] :
( ~ ( in @ SY2381 @ SV221 )
| ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SY2381 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1387,plain,
! [SV222: $i,SV38: $i,SV365: $i] :
( ( ( in @ SV365 @ SV38 )
= $false )
| ( ( ! [SY2382: $i] :
( ~ ( in @ SY2382 @ SV222 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SY2382 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1388,plain,
! [SV223: $i,SV39: $i,SV366: $i] :
( ( ( in @ SV366 @ SV39 )
= $false )
| ( ( ! [SY2383: $i] :
( ~ ( in @ SY2383 @ SV223 )
| ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SY2383 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1389,plain,
! [SV224: $i,SV40: $i,SV367: $i] :
( ( ( in @ SV367 @ SV40 )
= $false )
| ( ( ! [SY2384: $i] :
( ~ ( in @ SY2384 @ SV224 )
| ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SY2384 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1390,plain,
! [SV225: $i,SV41: $i,SV368: $i] :
( ( ( in @ SV368 @ ( setadjoin @ SV41 @ ( setadjoin @ SV225 @ emptyset ) ) )
= $false )
| ( ( ( SV368 = SV41 )
| ( SV368 = SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1391,plain,
! [SV226: $i,SV42: $i,SV369: $i] :
( ( ( in @ SV369 @ SV42 )
= $false )
| ( ( in @ ( setadjoin @ SV369 @ emptyset ) @ ( powerset @ ( binunion @ SV42 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1392,plain,
! [SV50: $i,SV234: $i,SV370: $i] :
( ( ( in @ SV370 @ SV234 )
= $true )
| ( ( ~ ( in @ SV370 @ ( symdiff @ SV50 @ SV234 ) ) )
= $true )
| ( ( in @ SV370 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1393,plain,
! [SV235: $i,SV51: $i,SV371: $i] :
( ( ( in @ SV371 @ SV51 )
= $false )
| ( ( ~ ( in @ SV371 @ SV235 )
| ~ ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1394,plain,
! [SV52: $i,SV236: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ SV236 ) )
= $true )
| ( ( in @ SV372 @ ( symdiff @ SV52 @ SV236 ) )
= $true )
| ( ( in @ SV372 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1395,plain,
! [SV237: $i,SV53: $i,SV373: $i] :
( ( ( in @ SV373 @ SV53 )
= $false )
| ( ( ( in @ SV373 @ SV237 )
| ( in @ SV373 @ ( symdiff @ SV53 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1396,plain,
! [SV56: $i,SV240: $i,SV374: $i] :
( ( ( in @ SV374 @ SV240 )
= $false )
| ( ( ~ ( in @ SV374 @ ( setminus @ SV56 @ SV240 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1397,plain,
! [SV241: $i,SV57: $i,SV375: $i] :
( ( ( in @ SV375 @ ( setminus @ SV57 @ SV241 ) )
= $false )
| ( ( in @ SV375 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1398,plain,
! [SV58: $i,SV242: $i,SV376: $i] :
( ( ( in @ SV376 @ SV242 )
= $true )
| ( ( ~ ( in @ SV376 @ SV58 ) )
= $true )
| ( ( in @ SV376 @ ( setminus @ SV58 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1399,plain,
! [SV243: $i,SV59: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV59 ) )
= $true )
| ( ( in @ SV377 @ SV243 )
= $true )
| ( ( in @ SV377 @ ( setminus @ SV59 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1400,plain,
! [SV245: $i,SV61: $i,SV378: $i] :
( ( ( in @ SV378 @ ( setminus @ SV61 @ SV245 ) )
= $false )
| ( ( ~ ( in @ SV378 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1401,plain,
! [SV246: $i,SV62: $i,SV379: $i] :
( ( ( in @ SV379 @ ( setminus @ SV62 @ SV246 ) )
= $false )
| ( ( in @ SV379 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1402,plain,
! [SV247: $i,SV63: $i,SV380: $i] :
( ( ( in @ SV380 @ SV63 )
= $false )
| ( ( ( in @ SV380 @ SV247 )
| ( in @ SV380 @ ( setminus @ SV63 @ SV247 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1403,plain,
! [SV252: $i,SV68: $i,SV382: $i] :
( ( ( in @ SV382 @ ( binintersect @ SV68 @ SV252 ) )
= $false )
| ( ( in @ SV382 @ SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1404,plain,
! [SV256: $i,SV72: $i,SV383: $i] :
( ( ( in @ SV383 @ ( binintersect @ SV72 @ SV256 ) )
= $false )
| ( ( in @ SV383 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1405,plain,
! [SV257: $i,SV73: $i,SV384: $i] :
( ( ( subset @ SV384 @ SV73 )
= $false )
| ( ( ~ ( subset @ SV384 @ SV257 )
| ( subset @ SV384 @ ( binintersect @ SV73 @ SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1406,plain,
! [SV258: $i,SV74: $i,SV385: $i] :
( ( ( in @ SV385 @ SV74 )
= $false )
| ( ( ~ ( in @ SV385 @ SV258 )
| ( in @ SV385 @ ( binintersect @ SV74 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1407,plain,
! [SV261: $i,SV77: $i,SV386: $i] :
( ( ( in @ SV386 @ ( binunion @ SV77 @ SV261 ) )
= $false )
| ( ( ( in @ SV386 @ SV77 )
| ( in @ SV386 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1408,plain,
! [SV78: $i,SV262: $i,SV387: $i] :
( ( ( in @ SV387 @ SV262 )
= $false )
| ( ( in @ SV387 @ ( binunion @ SV78 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1409,plain,
! [SV264: $i,SV80: $i,SV388: $i] :
( ( ( in @ SV388 @ SV80 )
= $false )
| ( ( in @ SV388 @ ( binunion @ SV80 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1410,plain,
! [SV88: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV88 ) )
= $true )
| ( ( SV88 = SV270 )
= $true )
| ( ( subset @ SV88 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1411,plain,
! [SV272: $i,SV389: $i,SV90: $i] :
( ( ( subset @ SV90 @ SV389 )
= $false )
| ( ( subset @ SV90 @ ( setadjoin @ SV272 @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1412,plain,
! [SV92: $i,SV451: $i,SV274: $i] :
( ( ( ~ ( subset @ SV274 @ SV451 )
| ( subset @ SV92 @ SV451 ) )
= $true )
| ( ( subset @ SV92 @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1413,plain,
! [SV275: $i,SV94: $i,SV390: $i] :
( ( ( in @ SV390 @ SV94 )
= $false )
| ( ( ( in @ SV390 @ SV275 )
| ( SV94 != SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1414,plain,
! [SV277: $i,SV96: $i,SV391: $i] :
( ( ( in @ SV391 @ SV96 )
= $false )
| ( ( ( in @ SV391 @ SV277 )
| ~ ( subset @ SV96 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1415,plain,
! [SV97: $i,SV278: $i,SV452: $i] :
( ( ( ( in @ SV452 @ SV278 )
| ~ ( in @ SV452 @ SV97 ) )
= $true )
| ( ( subset @ SV97 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1416,plain,
! [SV279: $i,SV98: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV98 )
| ( in @ SV453 @ SV279 ) )
= $true )
| ( ( subset @ SV98 @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1417,plain,
! [SV284: $i,SV104: $i,SV454: $i] :
( ( ( ! [SY2460: $i] :
( ( SV454 != SY2460 )
| ( ( setadjoin @ SV104 @ SV454 )
= ( setadjoin @ SV284 @ SY2460 ) ) ) )
= $true )
| ( ( SV104 = SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1418,plain,
! [SV285: $i,SV105: $i,SV455: $i] :
( ( ( ! [SY2461: $i] :
( ( SV455 != SY2461 )
| ~ ( in @ SV455 @ SV105 )
| ( in @ SY2461 @ SV285 ) ) )
= $true )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1419,plain,
! [SV109: $i,SV434: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ SV434 ) )
= $true )
| ( ( ~ ( in @ SV434 @ SV109 ) )
= $true )
| ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1420,plain,
! [SV290: $i,SV112: $i,SV392: $i] :
( ( ( in @ SV392 @ ( setadjoin @ SV112 @ ( setadjoin @ SV290 @ emptyset ) ) )
= $false )
| ( ( ( SV392 = SV112 )
| ( SV392 = SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1421,plain,
! [SV119: $i,SV393: $i,SV296: $i] :
( ( ( in @ SV296 @ SV393 )
= $false )
| ( ( ~ ( in @ SV393 @ SV119 )
| ( in @ SV296 @ ( setunion @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1422,plain,
! [SV120: $i,SV297: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV297 )
| ( in @ SV456 @ SV120 ) )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1423,plain,
! [SV298: $i,SV124: $i,SV394: $i] :
( ( ( in @ SV394 @ ( setadjoin @ SV124 @ SV298 ) )
= $false )
| ( ( ( SV394 = SV124 )
| ( in @ SV394 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1424,plain,
! [SV125: $i,SV299: $i,SV395: $i] :
( ( ( in @ SV395 @ SV299 )
= $false )
| ( ( in @ SV395 @ ( setadjoin @ SV125 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1425,plain,
! [SV396: $i,SV127: $i] :
( ( ( SV127 = emptyset )
= $false )
| ( ( in @ SV396 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1426,plain,
! [SV301: $i > $o,SV128: $i,SV397: $i] :
( ( ( in @ SV397 @ SV128 )
= $false )
| ( ( ~ ( SV301 @ SV397 )
| ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1427,plain,
! [SV303: $i > $o,SV135: $i,SV401: $i] :
( ( ( in @ SV401
@ ( dsetconstr @ SV135
@ ^ [SY2251: $i] : ( SV303 @ SY2251 ) ) )
= $false )
| ( ( SV303 @ SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1428,plain,
! [SV304: $i > $o,SV136: $i,SV402: $i] :
( ( ( in @ SV402
@ ( dsetconstr @ SV136
@ ^ [SY2253: $i] : ( SV304 @ SY2253 ) ) )
= $false )
| ( ( in @ SV402 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1429,plain,
! [SV305: $i > $o,SV137: $i,SV403: $i] :
( ( ( in @ SV403 @ SV137 )
= $false )
| ( ( ~ ( SV305 @ SV403 )
| ( in @ SV403
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1430,plain,
! [SV306: $i > $o,SV140: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ SV140 ) )
= $true )
| ( ( SV306 @ SV436 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1431,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
| ~ ( ( SV404
!= ( sK33_SY147 @ SV404 @ SV141 ) ) ) )
= $false )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1432,plain,
! [SV142: $i,SV307: $i] :
( ( ( ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV307 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1433,plain,
! [SV142: $i,SV307: $i] :
( ( ( ~ ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1434,plain,
! [SV143: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
!= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1435,plain,
! [SV143: $i] :
( ( ( ~ ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) ) )
= $false )
| ( ( iskpair @ SV143 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1299]) ).
thf(1436,plain,
! [SV308: $i > $o,SV144: $i,SV405: $i] :
( ( ( in @ SV405 @ SV144 )
= $false )
| ( ( ~ ( SV308 @ SV405 )
| ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1437,plain,
! [SV437: $i,SV309: $i > $o,SV145: $i] :
( ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
!= ( setadjoin @ SV437 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1438,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( ~ ( in @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) @ SV146 )
| ~ ~ ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1439,plain,
! [SV311: $i,SV147: $i] :
( ( ( ~ ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) )
| ~ ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1440,plain,
! [SV148: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
!= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1441,plain,
! [SV148: $i] :
( ( ( ~ ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) ) )
= $false )
| ( ( iskpair @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1442,plain,
! [SV312: $i,SV149: $i,SV407: $i] :
( ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
| ~ ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1443,plain,
! [SV313: $i > $o,SV150: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV150 ) )
= $true )
| ( ( SV313 @ SV438 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1444,plain,
! [SV457: $i > $o,SV151: $i] :
( ( ! [SY2462: $i] :
( ~ ( in @ SY2462 @ SV151 )
| ~ ( SV457 @ SY2462 )
| ( in @ SY2462
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1445,plain,
! [SV458: $i > $o,SV151: $i] :
( ( ! [SY2464: $i] :
( ~ ( in @ SY2464 @ SV151 )
| ~ ( in @ SY2464
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) )
| ( SV458 @ SY2464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1446,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1447,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1448,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1310]) ).
thf(1449,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1450,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) )
| ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1451,plain,
! [SV316: $i,SV155: $i,SV409: $i] :
( ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false )
| ( ( ! [SY2393: $i > $o] :
( ~ ( ~ ( in @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SY2393 @ ( kpair @ ( sK94_Xx @ SY2393 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SY2393 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
| ! [SY2394: $i] :
( ~ ( in @ SY2394 @ SV409 )
| ( SY2393 @ SY2394 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1452,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
| ~ ( ( SV410
!= ( sK42_Xy @ SV410 @ SV156 ) ) ) )
= $false )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1453,plain,
! [SV459: $i,SV157: $i] :
( ( ! [SY2466: $i] :
( ~ ( in @ SY2466 @ ( funcSet @ SV157 @ SV459 ) )
| ! [SY2467: $i] :
( ~ ( in @ SY2467 @ SV157 )
| ~ ( ( ( dsetconstr @ SV459
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2467 @ SX4 ) @ SY2466 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY2467 @ SY2466 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY2467 @ SY2466 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2467 @ SX4 ) @ SY2466 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1454,plain,
! [SV460: $i,SV157: $i] :
( ( ! [SY2470: $i] :
( ~ ( in @ SY2470 @ ( funcSet @ SV157 @ SV460 ) )
| ( subset @ SY2470 @ ( cartprod @ SV157 @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1455,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( ~ ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) ) )
= $false )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1456,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( ~ ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 ) )
= $false )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1317]) ).
thf(1457,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o] :
( ( ( ! [SY2471: $i > $o] :
( ~ ( ~ ( in @ ( sK62_Xx @ SY2471 @ SV461 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SY2471 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SY2471 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SY2471 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SY2471 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SY2471 @ ( sK63_SY1651 @ SY2471 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SY2471 @ SV461 @ SV318 @ SV159 ) )
| ( SY2471 @ ( sK63_SY1651 @ SY2471 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SX4: $i] : ( SY2471 @ SX4 ) ) ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1458,plain,
! [SV160: $i,SV462: $i] :
( ( ! [SY2474: $i > $i] :
( ~ ( ~ ( in @ ( sK89_Xx @ SY2474 @ SV462 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2474 @ ( sK89_Xx @ SY2474 @ SV462 @ SV160 ) ) @ SV462 ) )
| ! [SY2475: $i] :
( ~ ( in @ SY2475 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2476: $i] :
( in @ ( kpair @ SY2475 @ SY2476 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SX5: $i,SX6: $i] :
( ( SY2474 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2475 @ SY2474 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2475 @ SY2474 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2479: $i] :
( in @ ( kpair @ SY2475 @ SY2479 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SX5: $i,SX6: $i] :
( ( SY2474 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1459,plain,
! [SV160: $i,SV463: $i] :
( ( ! [SY2482: $i > $i] :
( ~ ( ~ ( in @ ( sK87_Xx @ SY2482 @ SV463 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SY2482 @ ( sK87_Xx @ SY2482 @ SV463 @ SV160 ) ) @ SV463 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SX3: $i,SX4: $i] :
( ( SY2482 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV160 @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1460,plain,
! [SV161: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV161 ) )
= $false )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1461,plain,
! [SV161: $i,SV319: $i] :
( ( ( ~ ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 ) )
= $false )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1321]) ).
thf(1462,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) ) )
= $false )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1463,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( ~ ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 ) )
= $false )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1464,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ~ ( ( ( sK55_Xx @ SV464 @ SV439 )
!= ( sK56_SY1649 @ SV464 @ SV439 ) )
| ~ ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) ) )
| ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1465,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ~ ( ( ( sK51_Xx @ SV465 @ SV440 )
!= ( sK52_SY1647 @ SV465 @ SV440 ) )
| ~ ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) ) )
| ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1466,plain,
! [SV163: $i,SV466: $i] :
( ( ~ ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
| ~ ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) )
| ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 )
| ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1467,plain,
! [SV163: $i] :
( ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) )
| ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1468,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
| ~ ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1469,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1470,plain,
! [SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2296: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) )
| ~ ( ( SY2296
!= ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SY2296 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1471,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1472,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
| ~ ( ( SV413
!= ( sK48_SY229 @ SV413 @ SV167 ) ) ) )
= $false )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1473,plain,
! [SV168: $i,SV467: $o,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ SV467 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 ) )
| SV467 )
= $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1331]) ).
thf(1474,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ $true @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true ) )
| $true )
= $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1331]) ).
thf(1475,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ $false @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false ) )
| $false )
= $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1331]) ).
thf(1476,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1477,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1478,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
| ~ ( ( SV414
!= ( sK57_SY253 @ SV414 @ SV169 ) ) ) )
= $false )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1479,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
| ~ ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1480,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1335]) ).
thf(1481,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1335]) ).
thf(1482,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
!= SV416 )
| ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1483,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ~ ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
| ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1484,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( ~ ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) )
| ~ ( ( SV417
!= ( sK24_SY91 @ SV417 @ SV173 ) ) ) )
= $false )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1485,plain,
! [SV441: $i,SV468: $i] :
( ( ! [SY2493: $i] :
( ~ ( in @ SV468 @ SY2493 )
| ~ ( in @ SY2493 @ SV441 ) )
| ( in @ SV468 @ ( setunion @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1486,plain,
! [SV442: $i,SV469: $i] :
( ( ~ ( in @ SV469 @ ( setunion @ SV442 ) )
| ~ ( ~ ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) )
| ~ ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1487,plain,
! [SV327: $i > $o,SV174: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV174 ) )
= $true )
| ( ( SV327 @ SV443 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1488,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1489,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1490,plain,
! [SV176: $i,SV470: $i] :
( ( ! [SY2494: $i > $i] :
( ~ ( ~ ( in @ ( sK92_Xx @ SY2494 @ SV470 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2494 @ ( sK92_Xx @ SY2494 @ SV470 @ SV176 ) ) @ SV470 ) )
| ! [SY2495: $i] :
( ~ ( in @ SY2495 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2496: $i] :
( in @ ( kpair @ SY2495 @ SY2496 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SX5: $i,SX6: $i] :
( ( SY2494 @ SX5 )
= SX6 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2495 @ SY2494 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2495 @ SY2494 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2499: $i] :
( in @ ( kpair @ SY2495 @ SY2499 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SX5: $i,SX6: $i] :
( ( SY2494 @ SX5 )
= SX6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1491,plain,
! [SV176: $i,SV471: $i] :
( ( ! [SY2502: $i > $i] :
( ~ ( ~ ( in @ ( sK90_Xx @ SY2502 @ SV471 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SY2502 @ ( sK90_Xx @ SY2502 @ SV471 @ SV176 ) ) @ SV471 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SX3: $i,SX4: $i] :
( ( SY2502 @ SX3 )
= SX4 ) )
@ ( cartprod @ SV176 @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1492,plain,
! [SV177: $i,SV329: $i] :
( ( ( ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV177 ) )
= $false )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1493,plain,
! [SV177: $i,SV329: $i] :
( ( ( ~ ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV329 ) )
= $false )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1494,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( ~ ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 ) )
= $false )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1495,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( ~ ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) ) )
= $false )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1496,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
| ~ ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1497,plain,
! [SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1498,plain,
! [SV180: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1499,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
| ~ ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1500,plain,
! [SV420: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 )
| ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) )
= $false )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1501,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) )
| ~ ( ( SV421
!= ( sK20_SY62 @ SV421 @ SV183 ) ) ) )
= $false )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1502,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1503,plain,
! [SV185: $i,SV334: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV185 ) )
= $false )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1504,plain,
! [SV185: $i,SV334: $i] :
( ( ( ~ ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 ) )
= $false )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1352]) ).
thf(1505,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) ) )
= $false )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1506,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) ) )
= $false )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1507,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ( ( sK60_Xx @ SV336 @ SV187 )
!= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1508,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1509,plain,
! [SV444: $i,SV472: $i] :
( ( ~ ( ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV472 )
| ~ ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 ) )
| ( in @ SV472 @ ( powerset @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1510,plain,
! [SV445: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ ( powerset @ SV445 ) )
| ! [SY2505: $i] :
( ~ ( in @ SY2505 @ SV473 )
| ( in @ SY2505 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1511,plain,
! [SV188: $i,SV337: $i] :
( ( ( ~ ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 )
| ~ ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) ) )
= $false )
| ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1512,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
| ~ ( ( SV423
!= ( sK22_SY79 @ SV423 @ SV189 ) ) ) )
= $false )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1513,plain,
! [SV474: $i,SV190: $i] :
( ( ! [SY2506: $i] :
( ~ ( in @ SY2506 @ ( setadjoin @ SV190 @ SV474 ) )
| ( SY2506 = SV190 )
| ( in @ SY2506 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1514,plain,
! [SV190: $i] :
( ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) )
| ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1515,plain,
! [SV338: $i,SV191: $i,SV1: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV1 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2507: $i] : ( in @ ( kpair @ SV475 @ SY2507 ) @ SV338 ) ) )
@ SV191 ) )
= $true )
| ( ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1516,plain,
! [SV339: $i > $i > $o,SV192: $i,SV2: $i,SV446: $i,SV424: $i] :
( ( ( ~ ( in @ ( kpair @ SV424 @ SV446 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [SY2348: $i,SY2349: $i] : ( SV339 @ SY2348 @ SY2349 ) ) ) )
= $true )
| ( ( SV339 @ SV424 @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1517,plain,
! [SV340: $i > $i > $o,SV193: $i,SV3: $i,SV447: $i,SV425: $i] :
( ( ( ~ ( in @ ( kpair @ SV425 @ SV447 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [SY2352: $i,SY2353: $i] : ( SV340 @ SY2352 @ SY2353 ) ) ) )
= $true )
| ( ( in @ SV447 @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1518,plain,
! [SV341: $i > $i > $o,SV194: $i,SV4: $i,SV476: $i,SV426: $i] :
( ( ( ~ ( in @ ( kpair @ SV426 @ SV476 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [SY2356: $i,SY2357: $i] : ( SV341 @ SY2356 @ SY2357 ) ) ) )
= $true )
| ( ( in @ SV426 @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1519,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i,SV427: $i] :
( ( ( in @ SV427 @ SV5 )
= $false )
| ( ( ! [SY2436: $i] :
( ~ ( in @ SY2436 @ SV195 )
| ~ ( in @ ( kpair @ SV427 @ SY2436 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SY2436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1520,plain,
! [SV345: $i > $i > $o,SV198: $i,SV8: $i,SV428: $i] :
( ( ( in @ SV428 @ SV8 )
= $false )
| ( ( ! [SY2439: $i] :
( ~ ( in @ SY2439 @ SV198 )
| ~ ( SV345 @ SV428 @ SY2439 )
| ( in @ ( kpair @ SV428 @ SY2439 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1521,plain,
! [SV10: $i,SV347: $i,SV200: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV200 )
| ( ( ksnd @ ( kpair @ SV347 @ SV477 ) )
= SV477 ) )
= $true )
| ( ( in @ SV347 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1522,plain,
! [SV11: $i,SV348: $i,SV201: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV201 )
| ( ( kfst @ ( kpair @ SV348 @ SV478 ) )
= SV348 ) )
= $true )
| ( ( in @ SV348 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1523,plain,
! [SV12: $i,SV349: $i,SV479: $i] :
( ( ( ! [SY2510: $i] :
~ ( in @ SY2510 @ SV479 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV349 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1524,plain,
! [SV202: $i,SV13: $i,SV429: $i,SV350: $i] :
( ( ( in @ ( kpair @ SV350 @ SV429 ) @ ( cartprod @ SV13 @ SV202 ) )
= $false )
| ( ( in @ SV429 @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1525,plain,
! [SV203: $i,SV14: $i,SV448: $i,SV351: $i] :
( ( ( in @ ( kpair @ SV351 @ SV448 ) @ ( cartprod @ SV14 @ SV203 ) )
= $false )
| ( ( in @ SV351 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1526,plain,
! [SV430: $i,SV353: $i,SV206: $i,SV18: $i] :
( ( ( ( kpair @ SV18 @ SV206 )
= ( kpair @ SV353 @ SV430 ) )
= $false )
| ( ( SV206 = SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1527,plain,
! [SV431: $i,SV354: $i,SV207: $i,SV19: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV354 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV354 @ ( setadjoin @ SV431 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV207 = SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1528,plain,
! [SV433: $i,SV355: $i,SV209: $i,SV21: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV433 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV355 != SV433 )
| ( SV209 = SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1529,plain,
! [SV449: $i,SV356: $i,SV212: $i,SV24: $i] :
( ( ( ( kpair @ SV24 @ SV212 )
= ( kpair @ SV356 @ SV449 ) )
= $false )
| ( ( SV24 = SV356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1530,plain,
! [SV450: $i,SV357: $i,SV213: $i,SV25: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV25 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV357 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV357 @ ( setadjoin @ SV450 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV25 = SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1531,plain,
! [SV28: $i,SV359: $i] :
( ( ( in @ SV359 @ SV28 )
= $false )
| ( ( SV28
= ( setadjoin @ SV359 @ emptyset ) )
= $false )
| ( ( in @ ( setunion @ SV28 ) @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1532,plain,
! [SV35: $i,SV362: $i,SV219: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV219 )
| ( in @ ( kpair @ SV362 @ SV480 ) @ ( cartprod @ SV35 @ SV219 ) ) )
= $true )
| ( ( in @ SV362 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1533,plain,
! [SV36: $i,SV363: $i,SV220: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV220 )
| ( in @ ( kpair @ SV363 @ SV481 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) ) )
= $true )
| ( ( in @ SV363 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1534,plain,
! [SV37: $i,SV364: $i,SV221: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV221 )
| ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SV482 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) ) )
= $true )
| ( ( in @ SV364 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1535,plain,
! [SV38: $i,SV365: $i,SV222: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV222 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SV483 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) ) )
= $true )
| ( ( in @ SV365 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1536,plain,
! [SV39: $i,SV366: $i,SV223: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ SV223 )
| ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SV484 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) ) )
= $true )
| ( ( in @ SV366 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1537,plain,
! [SV40: $i,SV367: $i,SV224: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV224 )
| ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SV485 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) ) )
= $true )
| ( ( in @ SV367 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1538,plain,
! [SV225: $i,SV41: $i,SV368: $i] :
( ( ( SV368 = SV41 )
= $true )
| ( ( SV368 = SV225 )
= $true )
| ( ( in @ SV368 @ ( setadjoin @ SV41 @ ( setadjoin @ SV225 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1539,plain,
! [SV234: $i,SV50: $i,SV370: $i] :
( ( ( in @ SV370 @ ( symdiff @ SV50 @ SV234 ) )
= $false )
| ( ( in @ SV370 @ SV234 )
= $true )
| ( ( in @ SV370 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1540,plain,
! [SV51: $i,SV235: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV235 ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) ) )
= $true )
| ( ( in @ SV371 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1541,plain,
! [SV52: $i,SV236: $i,SV372: $i] :
( ( ( in @ SV372 @ SV236 )
= $false )
| ( ( in @ SV372 @ ( symdiff @ SV52 @ SV236 ) )
= $true )
| ( ( in @ SV372 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1542,plain,
! [SV53: $i,SV237: $i,SV373: $i] :
( ( ( in @ SV373 @ SV237 )
= $true )
| ( ( in @ SV373 @ ( symdiff @ SV53 @ SV237 ) )
= $true )
| ( ( in @ SV373 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1543,plain,
! [SV240: $i,SV56: $i,SV374: $i] :
( ( ( in @ SV374 @ ( setminus @ SV56 @ SV240 ) )
= $false )
| ( ( in @ SV374 @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1544,plain,
! [SV242: $i,SV58: $i,SV376: $i] :
( ( ( in @ SV376 @ SV58 )
= $false )
| ( ( in @ SV376 @ SV242 )
= $true )
| ( ( in @ SV376 @ ( setminus @ SV58 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1545,plain,
! [SV243: $i,SV59: $i,SV377: $i] :
( ( ( in @ SV377 @ SV59 )
= $false )
| ( ( in @ SV377 @ SV243 )
= $true )
| ( ( in @ SV377 @ ( setminus @ SV59 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1546,plain,
! [SV61: $i,SV245: $i,SV378: $i] :
( ( ( in @ SV378 @ SV245 )
= $false )
| ( ( in @ SV378 @ ( setminus @ SV61 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1547,plain,
! [SV63: $i,SV247: $i,SV380: $i] :
( ( ( in @ SV380 @ SV247 )
= $true )
| ( ( in @ SV380 @ ( setminus @ SV63 @ SV247 ) )
= $true )
| ( ( in @ SV380 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1548,plain,
! [SV73: $i,SV257: $i,SV384: $i] :
( ( ( ~ ( subset @ SV384 @ SV257 ) )
= $true )
| ( ( subset @ SV384 @ ( binintersect @ SV73 @ SV257 ) )
= $true )
| ( ( subset @ SV384 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1549,plain,
! [SV74: $i,SV258: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV258 ) )
= $true )
| ( ( in @ SV385 @ ( binintersect @ SV74 @ SV258 ) )
= $true )
| ( ( in @ SV385 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1550,plain,
! [SV261: $i,SV77: $i,SV386: $i] :
( ( ( in @ SV386 @ SV77 )
= $true )
| ( ( in @ SV386 @ SV261 )
= $true )
| ( ( in @ SV386 @ ( binunion @ SV77 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1551,plain,
! [SV88: $i,SV270: $i] :
( ( ( subset @ SV270 @ SV88 )
= $false )
| ( ( SV88 = SV270 )
= $true )
| ( ( subset @ SV88 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1552,plain,
! [SV92: $i,SV451: $i,SV274: $i] :
( ( ( ~ ( subset @ SV274 @ SV451 ) )
= $true )
| ( ( subset @ SV92 @ SV451 )
= $true )
| ( ( subset @ SV92 @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1553,plain,
! [SV94: $i,SV275: $i,SV390: $i] :
( ( ( in @ SV390 @ SV275 )
= $true )
| ( ( SV94 != SV275 )
= $true )
| ( ( in @ SV390 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1554,plain,
! [SV96: $i,SV277: $i,SV391: $i] :
( ( ( in @ SV391 @ SV277 )
= $true )
| ( ( ~ ( subset @ SV96 @ SV277 ) )
= $true )
| ( ( in @ SV391 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1555,plain,
! [SV97: $i,SV278: $i,SV452: $i] :
( ( ( in @ SV452 @ SV278 )
= $true )
| ( ( ~ ( in @ SV452 @ SV97 ) )
= $true )
| ( ( subset @ SV97 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1556,plain,
! [SV279: $i,SV98: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV98 ) )
= $true )
| ( ( in @ SV453 @ SV279 )
= $true )
| ( ( subset @ SV98 @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1557,plain,
! [SV284: $i,SV104: $i,SV486: $i,SV454: $i] :
( ( ( ( SV454 != SV486 )
| ( ( setadjoin @ SV104 @ SV454 )
= ( setadjoin @ SV284 @ SV486 ) ) )
= $true )
| ( ( SV104 = SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1558,plain,
! [SV285: $i,SV105: $i,SV487: $i,SV455: $i] :
( ( ( ( SV455 != SV487 )
| ~ ( in @ SV455 @ SV105 )
| ( in @ SV487 @ SV285 ) )
= $true )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1559,plain,
! [SV109: $i,SV434: $i,SV287: $i > $o] :
( ( ( SV287 @ SV434 )
= $false )
| ( ( ~ ( in @ SV434 @ SV109 ) )
= $true )
| ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1560,plain,
! [SV290: $i,SV112: $i,SV392: $i] :
( ( ( SV392 = SV112 )
= $true )
| ( ( SV392 = SV290 )
= $true )
| ( ( in @ SV392 @ ( setadjoin @ SV112 @ ( setadjoin @ SV290 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1561,plain,
! [SV296: $i,SV119: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV119 ) )
= $true )
| ( ( in @ SV296 @ ( setunion @ SV119 ) )
= $true )
| ( ( in @ SV296 @ SV393 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1562,plain,
! [SV120: $i,SV297: $i,SV456: $i] :
( ( ( ~ ( in @ SV456 @ SV297 ) )
= $true )
| ( ( in @ SV456 @ SV120 )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1563,plain,
! [SV298: $i,SV124: $i,SV394: $i] :
( ( ( SV394 = SV124 )
= $true )
| ( ( in @ SV394 @ SV298 )
= $true )
| ( ( in @ SV394 @ ( setadjoin @ SV124 @ SV298 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1564,plain,
! [SV128: $i,SV397: $i,SV301: $i > $o] :
( ( ( ~ ( SV301 @ SV397 ) )
= $true )
| ( ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset )
= $true )
| ( ( in @ SV397 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1565,plain,
! [SV137: $i,SV403: $i,SV305: $i > $o] :
( ( ( ~ ( SV305 @ SV403 ) )
= $true )
| ( ( in @ SV403
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) )
= $true )
| ( ( in @ SV403 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1566,plain,
! [SV306: $i > $o,SV140: $i,SV436: $i] :
( ( ( in @ SV436 @ SV140 )
= $false )
| ( ( SV306 @ SV436 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1567,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) ) )
= $false )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1568,plain,
! [SV141: $i > $o,SV404: $i] :
( ( ( ~ ( ( SV404
!= ( sK33_SY147 @ SV404 @ SV141 ) ) ) )
= $false )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1569,plain,
! [SV142: $i,SV307: $i] :
( ( ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV307 )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1570,plain,
! [SV142: $i,SV307: $i] :
( ( ( ~ ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 ) )
= $true )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1571,plain,
! [SV143: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1939: $i] : ( in @ ( setadjoin @ SY1939 @ emptyset ) @ SV143 ) )
= ( setadjoin @ ( sK79_SY525 @ SV143 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1572,plain,
! [SV143: $i] :
( ( ( in @ ( sK79_SY525 @ SV143 )
@ ( dsetconstr @ ( setunion @ SV143 )
@ ^ [SY1940: $i] : ( in @ ( setadjoin @ SY1940 @ emptyset ) @ SV143 ) ) )
= $true )
| ( ( iskpair @ SV143 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1573,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( ~ ( SV308 @ SV405 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1574,plain,
! [SV437: $i,SV309: $i > $o,SV145: $i] :
( ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1575,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( ~ ( in @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) @ SV146 ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1576,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( ~ ~ ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1577,plain,
! [SV311: $i,SV147: $i] :
( ( ( ~ ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) ) )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1578,plain,
! [SV147: $i,SV311: $i] :
( ( ( ~ ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1579,plain,
! [SV148: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1958: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1958 ) ) )
= ( setadjoin @ ( sK80_SY562 @ SV148 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1580,plain,
! [SV148: $i] :
( ( ( in @ ( sK80_SY562 @ SV148 )
@ ( dsetconstr @ ( setunion @ SV148 )
@ ^ [SY1959: $i] :
( SV148
= ( kpair @ ( kfst @ SV148 ) @ SY1959 ) ) ) )
= $true )
| ( ( iskpair @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1441]) ).
thf(1581,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ~ ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
| ~ ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1582,plain,
! [SV313: $i > $o,SV150: $i,SV438: $i] :
( ( ( in @ SV438 @ SV150 )
= $false )
| ( ( SV313 @ SV438 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1583,plain,
! [SV457: $i > $o,SV151: $i,SV488: $i] :
( ( ~ ( in @ SV488 @ SV151 )
| ~ ( SV457 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1584,plain,
! [SV458: $i > $o,SV151: $i,SV489: $i] :
( ( ~ ( in @ SV489 @ SV151 )
| ~ ( in @ SV489
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) )
| ( SV458 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1585,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) )
| ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1586,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1447]) ).
thf(1587,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1588,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1589,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) )
| ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1590,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
| ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1591,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) ) )
= $false )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1592,plain,
! [SV156: $i > $o,SV410: $i] :
( ( ( ~ ( ( SV410
!= ( sK42_Xy @ SV410 @ SV156 ) ) ) )
= $false )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1593,plain,
! [SV459: $i,SV157: $i,SV491: $i] :
( ( ~ ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
| ! [SY2514: $i] :
( ~ ( in @ SY2514 @ SV157 )
| ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2515: $i] : ( in @ ( kpair @ SY2514 @ SY2515 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2516: $i] : ( in @ ( kpair @ SY2514 @ SY2516 ) @ SV491 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1594,plain,
! [SV460: $i,SV157: $i,SV492: $i] :
( ( ~ ( in @ SV492 @ ( funcSet @ SV157 @ SV460 ) )
| ( subset @ SV492 @ ( cartprod @ SV157 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1595,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
= $true )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1596,plain,
! [SV158: $i,SV317: $i > $o] :
( ( ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 )
= $true )
| ( ( ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV158 )
| ~ ( SV317 @ SY2283 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1597,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1598,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ~ ( ~ ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 ) )
| ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1599,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ~ ( ~ ( in @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 ) )
| ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1600,plain,
! [SV161: $i,SV319: $i] :
( ( ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV161 )
= $true )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1601,plain,
! [SV161: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 ) )
= $true )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1602,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
= $true )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1603,plain,
! [SV162: $i,SV320: $i > $o] :
( ( ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 )
= $true )
| ( ( ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV162 )
| ~ ( SV320 @ SY2288 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1463]) ).
thf(1604,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( ( ( sK55_Xx @ SV464 @ SV439 )
!= ( sK56_SY1649 @ SV464 @ SV439 ) )
| ~ ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1605,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ~ ( ( ( sK51_Xx @ SV465 @ SV440 )
!= ( sK52_SY1647 @ SV465 @ SV440 ) )
| ~ ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1606,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
| ~ ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) )
| ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1607,plain,
! [SV163: $i] :
( ( ~ ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1608,plain,
! [SV163: $i] :
( ( ~ ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1609,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
| ~ ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1610,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1611,plain,
! [SV322: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2296: $i] :
( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) )
| ~ ( ( SY2296
!= ( sK13_SY1613 @ SY2296 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SY2296 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1612,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1613,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) ) )
= $false )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1614,plain,
! [SV167: $i > $o,SV413: $i] :
( ( ( ~ ( ( SV413
!= ( sK48_SY229 @ SV413 @ SV167 ) ) ) )
= $false )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1615,plain,
! [SV168: $i,SV467: $o,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ SV467 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 ) ) )
= $true )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1616,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ $true @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true ) ) )
= $true )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1617,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ SV324 @ ( sK31_B @ $false @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false ) ) )
= $true )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1618,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1619,plain,
( ( ~ ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1620,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) ) )
= $false )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1621,plain,
! [SV169: $i > $o,SV414: $i] :
( ( ( ~ ( ( SV414
!= ( sK57_SY253 @ SV414 @ SV169 ) ) ) )
= $false )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1622,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
| ~ ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1623,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1480]) ).
thf(1624,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1625,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ( ( sK47_Xy @ SV416 @ SV172 )
!= SV416 )
| ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1626,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
| ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1627,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( ~ ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) ) )
= $false )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1628,plain,
! [SV173: $i > $o,SV417: $i] :
( ( ( ~ ( ( SV417
!= ( sK24_SY91 @ SV417 @ SV173 ) ) ) )
= $false )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1629,plain,
! [SV441: $i,SV468: $i] :
( ( ( ! [SY2493: $i] :
( ~ ( in @ SV468 @ SY2493 )
| ~ ( in @ SY2493 @ SV441 ) ) )
= $true )
| ( ( in @ SV468 @ ( setunion @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1630,plain,
! [SV442: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( setunion @ SV442 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) )
| ~ ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1631,plain,
! [SV327: $i > $o,SV174: $i,SV443: $i] :
( ( ( in @ SV443 @ SV174 )
= $false )
| ( ( SV327 @ SV443 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1632,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1633,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1489]) ).
thf(1634,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ~ ( ~ ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 ) )
| ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1635,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ~ ( ~ ( in @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 ) )
| ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1636,plain,
! [SV177: $i,SV329: $i] :
( ( ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV177 )
= $true )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1492]) ).
thf(1637,plain,
! [SV177: $i,SV329: $i] :
( ( ( in @ ( sK66_Xx @ SV329 @ SV177 ) @ SV329 )
= $true )
| ( ( ( binintersect @ SV177 @ SV329 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1638,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
= $true )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1639,plain,
! [SV178: $i,SV330: $i > $o] :
( ( ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) )
= $true )
| ( ( ! [SY2324: $i] :
( ~ ( SV330 @ SY2324 )
| ~ ( in @ SY2324 @ SV178 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1640,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
| ~ ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1641,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1642,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1643,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
| ~ ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1644,plain,
! [SV420: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK14_B @ SV182 ) @ SV182 ) )
= $false )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1645,plain,
! [SV420: $i,SV182: $i] :
( ( ( ~ ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) )
= $false )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1646,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( ~ ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) ) )
= $false )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1647,plain,
! [SV183: $i > $o,SV421: $i] :
( ( ( ~ ( ( SV421
!= ( sK20_SY62 @ SV421 @ SV183 ) ) ) )
= $false )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1648,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1649,plain,
! [SV185: $i,SV334: $i] :
( ( ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV185 )
= $true )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1650,plain,
! [SV185: $i,SV334: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 ) )
= $true )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1651,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1652,plain,
! [SV186: $i,SV335: $i] :
( ( ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
| ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1653,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1654,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1655,plain,
! [SV444: $i,SV472: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV472 )
| ~ ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 ) ) )
= $true )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1656,plain,
! [SV445: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ ( powerset @ SV445 ) ) )
= $true )
| ( ( ! [SY2505: $i] :
( ~ ( in @ SY2505 @ SV473 )
| ( in @ SY2505 @ SV445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1657,plain,
! [SV188: $i,SV337: $i] :
( ( ( ~ ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 ) )
= $false )
| ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1658,plain,
! [SV188: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) ) )
= $false )
| ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1659,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) ) )
= $false )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1660,plain,
! [SV189: $i > $o,SV423: $i] :
( ( ( ~ ( ( SV423
!= ( sK22_SY79 @ SV423 @ SV189 ) ) ) )
= $false )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1512]) ).
thf(1661,plain,
! [SV474: $i,SV190: $i,SV498: $i] :
( ( ~ ( in @ SV498 @ ( setadjoin @ SV190 @ SV474 ) )
| ( SV498 = SV190 )
| ( in @ SV498 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1662,plain,
! [SV190: $i] :
( ( ~ ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1663,plain,
! [SV190: $i] :
( ( ~ ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1664,plain,
! [SV338: $i,SV191: $i,SV1: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV1 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2507: $i] : ( in @ ( kpair @ SV475 @ SY2507 ) @ SV338 ) ) )
@ SV191 )
= $true )
| ( ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1665,plain,
! [SV339: $i > $i > $o,SV192: $i,SV2: $i,SV446: $i,SV424: $i] :
( ( ( in @ ( kpair @ SV424 @ SV446 )
@ ( dpsetconstr @ SV2 @ SV192
@ ^ [SY2348: $i,SY2349: $i] : ( SV339 @ SY2348 @ SY2349 ) ) )
= $false )
| ( ( SV339 @ SV424 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1666,plain,
! [SV340: $i > $i > $o,SV193: $i,SV3: $i,SV447: $i,SV425: $i] :
( ( ( in @ ( kpair @ SV425 @ SV447 )
@ ( dpsetconstr @ SV3 @ SV193
@ ^ [SY2352: $i,SY2353: $i] : ( SV340 @ SY2352 @ SY2353 ) ) )
= $false )
| ( ( in @ SV447 @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1667,plain,
! [SV341: $i > $i > $o,SV194: $i,SV4: $i,SV476: $i,SV426: $i] :
( ( ( in @ ( kpair @ SV426 @ SV476 )
@ ( dpsetconstr @ SV4 @ SV194
@ ^ [SY2356: $i,SY2357: $i] : ( SV341 @ SY2356 @ SY2357 ) ) )
= $false )
| ( ( in @ SV426 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1668,plain,
! [SV342: $i > $i > $o,SV5: $i,SV427: $i,SV195: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ SV195 )
| ~ ( in @ ( kpair @ SV427 @ SV499 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SV499 ) )
= $true )
| ( ( in @ SV427 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1669,plain,
! [SV8: $i,SV428: $i,SV345: $i > $i > $o,SV198: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV198 )
| ~ ( SV345 @ SV428 @ SV500 )
| ( in @ ( kpair @ SV428 @ SV500 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) )
= $true )
| ( ( in @ SV428 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1670,plain,
! [SV10: $i,SV347: $i,SV200: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV200 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV347 @ SV477 ) )
= SV477 )
= $true )
| ( ( in @ SV347 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1671,plain,
! [SV11: $i,SV348: $i,SV201: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV201 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV348 @ SV478 ) )
= SV348 )
= $true )
| ( ( in @ SV348 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1672,plain,
! [SV12: $i,SV349: $i,SV479: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV479 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV349 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1673,plain,
! [SV21: $i,SV209: $i,SV433: $i,SV355: $i] :
( ( ( SV355 != SV433 )
= $true )
| ( ( SV209 = SV433 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV433 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1674,plain,
! [SV35: $i,SV362: $i,SV219: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV219 ) )
= $true )
| ( ( in @ ( kpair @ SV362 @ SV480 ) @ ( cartprod @ SV35 @ SV219 ) )
= $true )
| ( ( in @ SV362 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1675,plain,
! [SV36: $i,SV363: $i,SV220: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV220 ) )
= $true )
| ( ( in @ ( kpair @ SV363 @ SV481 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) )
= $true )
| ( ( in @ SV363 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1676,plain,
! [SV37: $i,SV364: $i,SV221: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV221 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SV482 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) )
= $true )
| ( ( in @ SV364 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1677,plain,
! [SV38: $i,SV365: $i,SV222: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV222 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SV483 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) )
= $true )
| ( ( in @ SV365 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1678,plain,
! [SV39: $i,SV366: $i,SV223: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ SV223 ) )
= $true )
| ( ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SV484 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) )
= $true )
| ( ( in @ SV366 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1679,plain,
! [SV40: $i,SV367: $i,SV224: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV224 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SV485 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) )
= $true )
| ( ( in @ SV367 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1680,plain,
! [SV51: $i,SV235: $i,SV371: $i] :
( ( ( in @ SV371 @ SV235 )
= $false )
| ( ( ~ ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) ) )
= $true )
| ( ( in @ SV371 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1681,plain,
! [SV73: $i,SV257: $i,SV384: $i] :
( ( ( subset @ SV384 @ SV257 )
= $false )
| ( ( subset @ SV384 @ ( binintersect @ SV73 @ SV257 ) )
= $true )
| ( ( subset @ SV384 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1682,plain,
! [SV74: $i,SV258: $i,SV385: $i] :
( ( ( in @ SV385 @ SV258 )
= $false )
| ( ( in @ SV385 @ ( binintersect @ SV74 @ SV258 ) )
= $true )
| ( ( in @ SV385 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1683,plain,
! [SV92: $i,SV451: $i,SV274: $i] :
( ( ( subset @ SV274 @ SV451 )
= $false )
| ( ( subset @ SV92 @ SV451 )
= $true )
| ( ( subset @ SV92 @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1684,plain,
! [SV390: $i,SV275: $i,SV94: $i] :
( ( ( SV94 = SV275 )
= $false )
| ( ( in @ SV390 @ SV275 )
= $true )
| ( ( in @ SV390 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1685,plain,
! [SV391: $i,SV277: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV277 )
= $false )
| ( ( in @ SV391 @ SV277 )
= $true )
| ( ( in @ SV391 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1686,plain,
! [SV278: $i,SV97: $i,SV452: $i] :
( ( ( in @ SV452 @ SV97 )
= $false )
| ( ( in @ SV452 @ SV278 )
= $true )
| ( ( subset @ SV97 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1687,plain,
! [SV279: $i,SV98: $i,SV453: $i] :
( ( ( in @ SV453 @ SV98 )
= $false )
| ( ( in @ SV453 @ SV279 )
= $true )
| ( ( subset @ SV98 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1688,plain,
! [SV284: $i,SV104: $i,SV486: $i,SV454: $i] :
( ( ( SV454 != SV486 )
= $true )
| ( ( ( setadjoin @ SV104 @ SV454 )
= ( setadjoin @ SV284 @ SV486 ) )
= $true )
| ( ( SV104 = SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1689,plain,
! [SV285: $i,SV105: $i,SV487: $i,SV455: $i] :
( ( ( SV455 != SV487 )
= $true )
| ( ( ~ ( in @ SV455 @ SV105 )
| ( in @ SV487 @ SV285 ) )
= $true )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1690,plain,
! [SV287: $i > $o,SV109: $i,SV434: $i] :
( ( ( in @ SV434 @ SV109 )
= $false )
| ( ( SV287 @ SV434 )
= $false )
| ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1691,plain,
! [SV296: $i,SV119: $i,SV393: $i] :
( ( ( in @ SV393 @ SV119 )
= $false )
| ( ( in @ SV296 @ ( setunion @ SV119 ) )
= $true )
| ( ( in @ SV296 @ SV393 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1692,plain,
! [SV120: $i,SV297: $i,SV456: $i] :
( ( ( in @ SV456 @ SV297 )
= $false )
| ( ( in @ SV456 @ SV120 )
= $true )
| ( ( in @ SV297 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1693,plain,
! [SV128: $i,SV397: $i,SV301: $i > $o] :
( ( ( SV301 @ SV397 )
= $false )
| ( ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
!= emptyset )
= $true )
| ( ( in @ SV397 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1694,plain,
! [SV137: $i,SV403: $i,SV305: $i > $o] :
( ( ( SV305 @ SV403 )
= $false )
| ( ( in @ SV403
@ ( dsetconstr @ SV137
@ ^ [SY2255: $i] : ( SV305 @ SY2255 ) ) )
= $true )
| ( ( in @ SV403 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1695,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
| ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) )
= $false )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1696,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1567]) ).
thf(1697,plain,
! [SV141: $i > $o,SV404: $i] :
( ( ( SV404
!= ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1698,plain,
! [SV142: $i,SV307: $i] :
( ( ( in @ ( sK30_Xx @ SV307 @ SV142 ) @ SV142 )
= $false )
| ( ( in @ SV307 @ ( powerset @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1699,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( SV308 @ SV405 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
| ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1700,plain,
! [SV309: $i > $o,SV145: $i,SV437: $i] :
( ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( ~ ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1701,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( in @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) @ SV146 )
= $true )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1702,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( ~ ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 ) )
= $true )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1703,plain,
! [SV311: $i,SV147: $i] :
( ( ( ! [SY2266: $i,SY2267: $i] :
( ( SY2266 != SY2267 )
| ~ ( in @ SY2266 @ SV147 )
| ( in @ SY2267 @ SV311 ) ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1704,plain,
! [SV147: $i,SV311: $i] :
( ( ( ! [SY2268: $i,SY2269: $i] :
( ( SY2268 != SY2269 )
| ~ ( in @ SY2269 @ SV311 )
| ( in @ SY2268 @ SV147 ) ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1705,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ~ ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1706,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1581]) ).
thf(1707,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
| ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) )
= $false )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1708,plain,
! [SV457: $i > $o,SV151: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV151 ) )
= $true )
| ( ( ~ ( SV457 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1709,plain,
! [SV458: $i > $o,SV151: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ SV151 ) )
= $true )
| ( ( ~ ( in @ SV489
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) )
| ( SV458 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1710,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK44_Xx @ SV152 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1711,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1585]) ).
thf(1712,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1713,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
| ( SV153 = SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1714,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1715,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1716,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1717,plain,
! [SV315: $i,SV154: $i] :
( ( ~ ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1718,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1719,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1720,plain,
! [SV156: $i > $o,SV410: $i] :
( ( ( SV410
!= ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1721,plain,
! [SV459: $i,SV157: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) ) )
= $true )
| ( ( ! [SY2514: $i] :
( ~ ( in @ SY2514 @ SV157 )
| ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2515: $i] : ( in @ ( kpair @ SY2514 @ SY2515 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2516: $i] : ( in @ ( kpair @ SY2514 @ SY2516 ) @ SV491 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1722,plain,
! [SV460: $i,SV157: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ ( funcSet @ SV157 @ SV460 ) ) )
= $true )
| ( ( subset @ SV492 @ ( cartprod @ SV157 @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1723,plain,
! [SV317: $i > $o,SV158: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV158 )
| ~ ( SV317 @ SV502 ) )
= $true )
| ( ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1724,plain,
! [SV317: $i > $o,SV158: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV158 )
| ~ ( SV317 @ SV503 ) )
= $true )
| ( ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1725,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1726,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 ) ) )
= $true )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1727,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 ) ) )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1728,plain,
! [SV161: $i,SV319: $i] :
( ( ( in @ ( sK64_Xx @ SV319 @ SV161 ) @ SV319 )
= $false )
| ( ( subset @ SV161 @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1729,plain,
! [SV320: $i > $o,SV162: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV162 )
| ~ ( SV320 @ SV504 ) )
= $true )
| ( ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1730,plain,
! [SV320: $i > $o,SV162: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV162 )
| ~ ( SV320 @ SV505 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1731,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ( ( ( sK55_Xx @ SV464 @ SV439 )
!= ( sK56_SY1649 @ SV464 @ SV439 ) )
| ~ ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1732,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ( ( sK51_Xx @ SV465 @ SV440 )
!= ( sK52_SY1647 @ SV465 @ SV440 ) )
| ~ ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1733,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
| ~ ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) ) )
= $true )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1734,plain,
! [SV163: $i] :
( ( ! [SY2023: $i,SY2024: $i] :
( ~ ( in @ SY2023 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2024 @ ( sK15_B @ SV163 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2023 )
| ( in @ SX3 @ SY2024 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2024 )
| ( in @ SX3 @ SY2023 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1735,plain,
! [SV163: $i] :
( ( ~ ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1736,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 ) )
= $false )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1737,plain,
! [SV164: $i,SV411: $i,SV321: $i] :
( ( ( ~ ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1738,plain,
! [SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1739,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
| ~ ( ( SV506
!= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) ) ) )
| ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1740,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1741,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1742,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1743,plain,
! [SV167: $i > $o,SV413: $i] :
( ( ( SV413
!= ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1744,plain,
! [SV168: $i,SV467: $o,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ SV467 @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 ) )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1745,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ $true @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1746,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ $false @ SV324 @ SV168 ) )
| ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1747,plain,
! [SV507: $i] :
( ( ~ ( in @ SV507 @ sK1_SY0 )
| ! [SY2541: $i] :
( ~ ( in @ SY2541 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SV507 @ SY2541 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SY2541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1748,plain,
( ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 )
| ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1749,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1750,plain,
! [SV169: $i > $o,SV414: $i] :
( ( ( SV414
!= ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1751,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ( ~ ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 ) )
= $false )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1752,plain,
! [SV170: $i,SV415: $i,SV325: $i] :
( ( ( ~ ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1753,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1754,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
| ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1755,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ( sK47_Xy @ SV416 @ SV172 )
!= SV416 )
= $true )
| ( ( ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1756,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1757,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) )
= $true )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1758,plain,
! [SV173: $i > $o,SV417: $i] :
( ( ( SV417
!= ( sK24_SY91 @ SV417 @ SV173 ) )
= $true )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1759,plain,
! [SV441: $i,SV508: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV508 )
| ~ ( in @ SV508 @ SV441 ) )
= $true )
| ( ( in @ SV468 @ ( setunion @ SV441 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1760,plain,
! [SV442: $i,SV469: $i] :
( ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) )
| ~ ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1761,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
| ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) )
= $false )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1762,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1763,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
| ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1764,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 ) ) )
= $true )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1765,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 ) ) )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1766,plain,
! [SV178: $i,SV509: $i,SV330: $i > $o] :
( ( ( ~ ( SV330 @ SV509 )
| ~ ( in @ SV509 @ SV178 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1767,plain,
! [SV178: $i,SV510: $i,SV330: $i > $o] :
( ( ( ~ ( SV330 @ SV510 )
| ~ ( in @ SV510 @ SV178 ) )
= $true )
| ( ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1768,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1769,plain,
! [SV179: $i,SV418: $i,SV331: $i] :
( ( ( ~ ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1770,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega )
| ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1771,plain,
! [SV180: $i] :
( ( ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1772,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ( ~ ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 ) )
= $false )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1773,plain,
! [SV181: $i,SV419: $i,SV332: $i] :
( ( ( ~ ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) )
= $false )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1643]) ).
thf(1774,plain,
! [SV420: $i,SV182: $i] :
( ( ( in @ ( sK14_B @ SV182 ) @ SV182 )
= $true )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1775,plain,
! [SV420: $i,SV182: $i] :
( ( ( ! [SY2113: $i] :
( ~ ( in @ SY2113 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SY2113 @ SV182 ) ) )
= $true )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1776,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) )
= $true )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1777,plain,
! [SV183: $i > $o,SV421: $i] :
( ( ( SV421
!= ( sK20_SY62 @ SV421 @ SV183 ) )
= $true )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1778,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1779,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1780,plain,
! [SV185: $i,SV334: $i] :
( ( ( in @ ( sK65_Xx @ SV334 @ SV185 ) @ SV334 )
= $false )
| ( ( subset @ SV185 @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1781,plain,
! [SV186: $i,SV335: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1782,plain,
! [SV186: $i,SV335: $i] :
( ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
= $true )
| ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1783,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1784,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
| ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1785,plain,
! [SV444: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV472 )
| ~ ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 ) )
= $false )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1786,plain,
! [SV445: $i,SV473: $i] :
( ( ( in @ SV473 @ ( powerset @ SV445 ) )
= $false )
| ( ( ! [SY2505: $i] :
( ~ ( in @ SY2505 @ SV473 )
| ( in @ SY2505 @ SV445 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1787,plain,
! [SV188: $i,SV337: $i] :
( ( ( in @ ( sK69_X @ SV337 @ SV188 ) @ SV188 )
= $true )
| ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1788,plain,
! [SV188: $i,SV337: $i] :
( ( ( in @ SV337 @ ( sK69_X @ SV337 @ SV188 ) )
= $true )
| ( ( in @ SV337 @ ( setunion @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1789,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1790,plain,
! [SV189: $i > $o,SV423: $i] :
( ( ( SV423
!= ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1791,plain,
! [SV474: $i,SV190: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ ( setadjoin @ SV190 @ SV474 ) ) )
= $true )
| ( ( ( SV498 = SV190 )
| ( in @ SV498 @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1792,plain,
! [SV190: $i] :
( ( ! [SY2134: $i,SY2135: $i] :
( ( SY2135 != SV190 )
| ( in @ SY2135 @ ( setadjoin @ SV190 @ SY2134 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1793,plain,
! [SV190: $i] :
( ( ! [SY2136: $i,SY2137: $i] :
( ~ ( in @ SY2137 @ SY2136 )
| ( in @ SY2137 @ ( setadjoin @ SV190 @ SY2136 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1794,plain,
! [SV338: $i,SV191: $i,SV1: $i,SV475: $i] :
( ( ( in @ SV475 @ SV1 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV191
@ ^ [SY2507: $i] : ( in @ ( kpair @ SV475 @ SY2507 ) @ SV338 ) ) )
@ SV191 )
= $true )
| ( ( in @ SV338 @ ( funcSet @ SV1 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1795,plain,
! [SV342: $i > $i > $o,SV5: $i,SV427: $i,SV195: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ SV195 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV427 @ SV499 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SV499 ) )
= $true )
| ( ( in @ SV427 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1796,plain,
! [SV8: $i,SV428: $i,SV345: $i > $i > $o,SV198: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV198 ) )
= $true )
| ( ( ~ ( SV345 @ SV428 @ SV500 )
| ( in @ ( kpair @ SV428 @ SV500 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) )
= $true )
| ( ( in @ SV428 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1797,plain,
! [SV10: $i,SV347: $i,SV200: $i,SV477: $i] :
( ( ( in @ SV477 @ SV200 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV347 @ SV477 ) )
= SV477 )
= $true )
| ( ( in @ SV347 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1798,plain,
! [SV11: $i,SV348: $i,SV201: $i,SV478: $i] :
( ( ( in @ SV478 @ SV201 )
= $false )
| ( ( ( kfst @ ( kpair @ SV348 @ SV478 ) )
= SV348 )
= $true )
| ( ( in @ SV348 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1799,plain,
! [SV12: $i,SV349: $i,SV479: $i,SV501: $i] :
( ( ( in @ SV501 @ SV479 )
= $false )
| ( $true = $true )
| ( ( in @ SV349 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1800,plain,
! [SV21: $i,SV209: $i,SV433: $i,SV355: $i] :
( ( ( SV355 = SV433 )
= $false )
| ( ( SV209 = SV433 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV21 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV355 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV355 @ ( setadjoin @ SV433 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1801,plain,
! [SV35: $i,SV362: $i,SV219: $i,SV480: $i] :
( ( ( in @ SV480 @ SV219 )
= $false )
| ( ( in @ ( kpair @ SV362 @ SV480 ) @ ( cartprod @ SV35 @ SV219 ) )
= $true )
| ( ( in @ SV362 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1802,plain,
! [SV36: $i,SV363: $i,SV220: $i,SV481: $i] :
( ( ( in @ SV481 @ SV220 )
= $false )
| ( ( in @ ( kpair @ SV363 @ SV481 ) @ ( powerset @ ( powerset @ ( binunion @ SV36 @ SV220 ) ) ) )
= $true )
| ( ( in @ SV363 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1803,plain,
! [SV37: $i,SV364: $i,SV221: $i,SV482: $i] :
( ( ( in @ SV482 @ SV221 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV364 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV364 @ ( setadjoin @ SV482 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV37 @ SV221 ) ) ) )
= $true )
| ( ( in @ SV364 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1804,plain,
! [SV38: $i,SV365: $i,SV222: $i,SV483: $i] :
( ( ( in @ SV483 @ SV222 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV365 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV365 @ ( setadjoin @ SV483 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV38 @ SV222 ) ) )
= $true )
| ( ( in @ SV365 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1805,plain,
! [SV39: $i,SV366: $i,SV223: $i,SV484: $i] :
( ( ( in @ SV484 @ SV223 )
= $false )
| ( ( in @ ( setadjoin @ SV366 @ ( setadjoin @ SV484 @ emptyset ) ) @ ( powerset @ ( binunion @ SV39 @ SV223 ) ) )
= $true )
| ( ( in @ SV366 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1806,plain,
! [SV40: $i,SV367: $i,SV224: $i,SV485: $i] :
( ( ( in @ SV485 @ SV224 )
= $false )
| ( ( subset @ ( setadjoin @ SV367 @ ( setadjoin @ SV485 @ emptyset ) ) @ ( binunion @ SV40 @ SV224 ) )
= $true )
| ( ( in @ SV367 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1807,plain,
! [SV235: $i,SV51: $i,SV371: $i] :
( ( ( in @ SV371 @ ( symdiff @ SV51 @ SV235 ) )
= $false )
| ( ( in @ SV371 @ SV235 )
= $false )
| ( ( in @ SV371 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1808,plain,
! [SV284: $i,SV104: $i,SV486: $i,SV454: $i] :
( ( ( SV454 = SV486 )
= $false )
| ( ( ( setadjoin @ SV104 @ SV454 )
= ( setadjoin @ SV284 @ SV486 ) )
= $true )
| ( ( SV104 = SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1809,plain,
! [SV285: $i,SV105: $i,SV487: $i,SV455: $i] :
( ( ( SV455 = SV487 )
= $false )
| ( ( ~ ( in @ SV455 @ SV105 )
| ( in @ SV487 @ SV285 ) )
= $true )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1810,plain,
! [SV434: $i,SV287: $i > $o,SV109: $i] :
( ( ( ( dsetconstr @ SV109
@ ^ [SY2242: $i] : ( SV287 @ SY2242 ) )
= emptyset )
= $false )
| ( ( SV287 @ SV434 )
= $false )
| ( ( in @ SV434 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1811,plain,
! [SV397: $i,SV301: $i > $o,SV128: $i] :
( ( ( ( dsetconstr @ SV128
@ ^ [SY2249: $i] : ( SV301 @ SY2249 ) )
= emptyset )
= $false )
| ( ( SV301 @ SV397 )
= $false )
| ( ( in @ SV397 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1812,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( ~ ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 ) )
= $false )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1813,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( ~ ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) )
= $false )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1695]) ).
thf(1814,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( SV141 @ SV404 )
= $false )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1815,plain,
! [SV141: $i > $o,SV404: $i] :
( ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( ~ ( SV141 @ SV404 ) )
= $true )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1816,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1817,plain,
! [SV437: $i,SV145: $i,SV309: $i > $o] :
( ( ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
| ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1818,plain,
! [SV146: $i,SV310: $i,SV406: $i > $i] :
( ( ( in @ ( SV406 @ ( sK93_Xx @ SV406 @ SV310 @ SV146 ) ) @ SV310 )
= $false )
| ( ( in
@ ( dpsetconstr @ SV146 @ SV310
@ ^ [SY2391: $i,SY2392: $i] :
( ( SV406 @ SY2391 )
= SY2392 ) )
@ ( funcSet @ SV146 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1819,plain,
! [SV311: $i,SV147: $i,SV511: $i] :
( ( ( ! [SY2542: $i] :
( ( SV511 != SY2542 )
| ~ ( in @ SV511 @ SV147 )
| ( in @ SY2542 @ SV311 ) ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1820,plain,
! [SV147: $i,SV311: $i,SV512: $i] :
( ( ( ! [SY2543: $i] :
( ( SV512 != SY2543 )
| ~ ( in @ SY2543 @ SV311 )
| ( in @ SV512 @ SV147 ) ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1821,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ~ ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) ) )
= $true )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1822,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( in @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1823,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( ~ ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 ) )
= $false )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1824,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( ~ ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) )
= $false )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1707]) ).
thf(1825,plain,
! [SV457: $i > $o,SV151: $i,SV488: $i] :
( ( ( in @ SV488 @ SV151 )
= $false )
| ( ( ~ ( SV457 @ SV488 )
| ( in @ SV488
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1826,plain,
! [SV458: $i > $o,SV151: $i,SV489: $i] :
( ( ( in @ SV489 @ SV151 )
= $false )
| ( ( ~ ( in @ SV489
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) )
| ( SV458 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1827,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1828,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1829,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1830,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1831,plain,
! [SV315: $i,SV154: $i] :
( ( ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2272 @ SV154 )
| ( in @ SY2272 @ SV315 )
| ! [SX3: $o] : SX3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1714]) ).
thf(1832,plain,
! [SV315: $i,SV154: $i] :
( ( ! [SY2274: $i] :
( ~ ( in @ SY2274 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SY2274 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1833,plain,
! [SV315: $i,SV154: $i] :
( ( ! [SY2276: $i] :
( ~ ( in @ SY2276 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2277: $o] :
( ~ SY2277
| ( in @ SY2276 @ SV315 )
| SY2277 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1834,plain,
! [SV315: $i,SV154: $i] :
( ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1835,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
| ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1836,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( SV156 @ SV410 )
= $false )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1837,plain,
! [SV156: $i > $o,SV410: $i] :
( ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( ~ ( SV156 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1838,plain,
! [SV459: $i,SV157: $i,SV491: $i] :
( ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false )
| ( ( ! [SY2514: $i] :
( ~ ( in @ SY2514 @ SV157 )
| ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2515: $i] : ( in @ ( kpair @ SY2514 @ SY2515 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SY2514 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2516: $i] : ( in @ ( kpair @ SY2514 @ SY2516 ) @ SV491 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1839,plain,
! [SV460: $i,SV157: $i,SV492: $i] :
( ( ( in @ SV492 @ ( funcSet @ SV157 @ SV460 ) )
= $false )
| ( ( subset @ SV492 @ ( cartprod @ SV157 @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1840,plain,
! [SV317: $i > $o,SV158: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV158 ) )
= $true )
| ( ( ~ ( SV317 @ SV502 ) )
= $true )
| ( ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1841,plain,
! [SV317: $i > $o,SV158: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV158 ) )
= $true )
| ( ( ~ ( SV317 @ SV503 ) )
= $true )
| ( ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1842,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( in @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV159 )
| ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1843,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( ~ ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 ) )
= $false )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1844,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( ~ ( in @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) @ SV160 )
| ~ ~ ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1845,plain,
! [SV320: $i > $o,SV162: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV162 ) )
= $true )
| ( ( ~ ( SV320 @ SV504 ) )
= $true )
| ( ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(1846,plain,
! [SV320: $i > $o,SV162: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV162 ) )
= $true )
| ( ( ~ ( SV320 @ SV505 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1847,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ( ( sK55_Xx @ SV464 @ SV439 )
!= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1848,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1849,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ( sK51_Xx @ SV465 @ SV440 )
!= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1850,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1851,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
| ~ ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) )
= $false )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1852,plain,
! [SV163: $i,SV513: $i] :
( ( ! [SY2544: $i] :
( ~ ( in @ SV513 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SY2544 @ ( sK15_B @ SV163 ) )
| ! [SY2545: $i] :
( ~ ( in @ SY2545 @ SV513 )
| ( in @ SY2545 @ SY2544 ) )
| ! [SY2546: $i] :
( ~ ( in @ SY2546 @ SY2544 )
| ( in @ SY2546 @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1853,plain,
! [SV163: $i] :
( ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) )
| ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1854,plain,
! [SV164: $i,SV321: $i,SV411: $i] :
( ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1855,plain,
! [SV164: $i,SV411: $i,SV321: $i] :
( ( ( ! [SY2395: $i] :
( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SY2395 @ emptyset ) )
| ~ ( in @ SY2395
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1856,plain,
! [SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1857,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1858,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
| ~ ( ( SV506
!= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) ) ) ) )
= $true )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1859,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1860,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1861,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( SV167 @ SV413 )
= $false )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1862,plain,
! [SV167: $i > $o,SV413: $i] :
( ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( ~ ( SV167 @ SV413 ) )
= $true )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1863,plain,
! [SV168: $i,SV467: $o,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ SV467 @ SV324 @ SV168 ) ) )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1864,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 ) )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1865,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ $true @ SV324 @ SV168 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1866,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1867,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ ( sK31_B @ $false @ SV324 @ SV168 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1868,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1869,plain,
! [SV507: $i] :
( ( ( ~ ( in @ SV507 @ sK1_SY0 ) )
= $true )
| ( ( ! [SY2541: $i] :
( ~ ( in @ SY2541 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SV507 @ SY2541 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SY2541 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1870,plain,
( ( ~ ( in @ sK5_SY1607 @ sK3_SY1596 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1871,plain,
( ( ~ ~ ( sK4_SY1601 @ sK5_SY1607 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1872,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( SV169 @ SV414 )
= $false )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1873,plain,
! [SV169: $i > $o,SV414: $i] :
( ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( ~ ( SV169 @ SV414 ) )
= $true )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1874,plain,
! [SV170: $i,SV325: $i,SV415: $i] :
( ( ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1875,plain,
! [SV170: $i,SV415: $i,SV325: $i] :
( ( ( ! [SY2410: $i] :
( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SY2410 @ emptyset ) )
| ~ ( in @ SY2410
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1876,plain,
! [SV171: $i,SV514: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV514 )
| ~ ( in @ SV514 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1877,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1878,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1879,plain,
! [SV172: $i > $o,SV416: $i] :
( ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( ~ ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1880,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1881,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( SV173 @ SV417 )
= $false )
| ( ( SV173 @ ( sK24_SY91 @ SV417 @ SV173 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1882,plain,
! [SV173: $i > $o,SV417: $i] :
( ( ( SV417
= ( sK24_SY91 @ SV417 @ SV173 ) )
= $false )
| ( ( ~ ( SV173 @ SV417 ) )
= $true )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1883,plain,
! [SV441: $i,SV508: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV508 ) )
= $true )
| ( ( ~ ( in @ SV508 @ SV441 ) )
= $true )
| ( ( in @ SV468 @ ( setunion @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1884,plain,
! [SV442: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) )
| ~ ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 ) )
= $false )
| ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1885,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( ~ ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 ) )
= $false )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1886,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( ~ ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) )
= $false )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1887,plain,
! [SV175: $i,SV515: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV515 )
| ~ ( in @ SV515 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1888,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1889,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1890,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 ) )
= $false )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1891,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) @ SV176 )
| ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1892,plain,
! [SV178: $i,SV509: $i,SV330: $i > $o] :
( ( ( ~ ( SV330 @ SV509 ) )
= $true )
| ( ( ~ ( in @ SV509 @ SV178 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1893,plain,
! [SV178: $i,SV510: $i,SV330: $i > $o] :
( ( ( ~ ( SV330 @ SV510 ) )
= $true )
| ( ( ~ ( in @ SV510 @ SV178 ) )
= $true )
| ( ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1894,plain,
! [SV179: $i,SV331: $i,SV418: $i] :
( ( ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1895,plain,
! [SV179: $i,SV418: $i,SV331: $i] :
( ( ( ! [SY2415: $i] :
( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SY2415 @ emptyset ) )
| ~ ( in @ SY2415
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1896,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( sK9_Xx @ SV180 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1897,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( sK9_Xx @ SV180 ) @ SV180 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1898,plain,
! [SV180: $i] :
( ( ( in @ emptyset @ SV180 )
= $false )
| ( ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 )
= $false )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1899,plain,
! [SV181: $i,SV332: $i,SV419: $i] :
( ( ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1900,plain,
! [SV181: $i,SV419: $i,SV332: $i] :
( ( ( ! [SY2418: $i] :
( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SY2418 @ emptyset ) )
| ~ ( in @ SY2418
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) ) )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1901,plain,
! [SV420: $i,SV182: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ ( sK14_B @ SV182 ) )
| ~ ( in @ SV516 @ SV182 ) )
= $true )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(1902,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( SV183 @ SV421 )
= $false )
| ( ( SV183 @ ( sK20_SY62 @ SV421 @ SV183 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1903,plain,
! [SV183: $i > $o,SV421: $i] :
( ( ( SV421
= ( sK20_SY62 @ SV421 @ SV183 ) )
= $false )
| ( ( ~ ( SV183 @ SV421 ) )
= $true )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1904,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1905,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1906,plain,
! [SV186: $i,SV335: $i] :
( ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
= $false )
| ( ( ~ ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 ) )
= $true )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1907,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
| ~ ( ( SV517
!= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1908,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1909,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1910,plain,
! [SV444: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV472 ) )
= $false )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1785]) ).
thf(1911,plain,
! [SV444: $i,SV472: $i] :
( ( ( ~ ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 ) )
= $false )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1785]) ).
thf(1912,plain,
! [SV445: $i,SV473: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ SV473 )
| ( in @ SV518 @ SV445 ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV445 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1913,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( SV189 @ SV423 )
= $false )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1914,plain,
! [SV189: $i > $o,SV423: $i] :
( ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( ~ ( SV189 @ SV423 ) )
= $true )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1915,plain,
! [SV474: $i,SV190: $i,SV498: $i] :
( ( ( in @ SV498 @ ( setadjoin @ SV190 @ SV474 ) )
= $false )
| ( ( ( SV498 = SV190 )
| ( in @ SV498 @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1916,plain,
! [SV519: $i,SV190: $i] :
( ( ! [SY2547: $i] :
( ( SY2547 != SV190 )
| ( in @ SY2547 @ ( setadjoin @ SV190 @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1917,plain,
! [SV190: $i,SV520: $i] :
( ( ! [SY2548: $i] :
( ~ ( in @ SY2548 @ SV520 )
| ( in @ SY2548 @ ( setadjoin @ SV190 @ SV520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1918,plain,
! [SV342: $i > $i > $o,SV5: $i,SV427: $i,SV195: $i,SV499: $i] :
( ( ( in @ SV499 @ SV195 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV427 @ SV499 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
| ( SV342 @ SV427 @ SV499 ) )
= $true )
| ( ( in @ SV427 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1919,plain,
! [SV8: $i,SV428: $i,SV345: $i > $i > $o,SV198: $i,SV500: $i] :
( ( ( in @ SV500 @ SV198 )
= $false )
| ( ( ~ ( SV345 @ SV428 @ SV500 )
| ( in @ ( kpair @ SV428 @ SV500 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) ) )
= $true )
| ( ( in @ SV428 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1920,plain,
! [SV285: $i,SV487: $i,SV105: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV105 ) )
= $true )
| ( ( in @ SV487 @ SV285 )
= $true )
| ( ( SV455 = SV487 )
= $false )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1921,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( in @ ( sK38_Xx @ SV306 @ SV140 ) @ SV140 )
= $true )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1922,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( ~ ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) ) )
= $true )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1923,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $false )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1924,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( SV141 @ SV404 )
= $false )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( ~ ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1925,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
| ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1926,plain,
! [SV437: $i,SV145: $i,SV309: $i > $o] :
( ( ( ~ ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) ) )
= $false )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1927,plain,
! [SV437: $i,SV145: $i,SV309: $i > $o] :
( ( ( ~ ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1817]) ).
thf(1928,plain,
! [SV311: $i,SV147: $i,SV521: $i,SV511: $i] :
( ( ( ( SV511 != SV521 )
| ~ ( in @ SV511 @ SV147 )
| ( in @ SV521 @ SV311 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1929,plain,
! [SV147: $i,SV311: $i,SV522: $i,SV512: $i] :
( ( ( ( SV512 != SV522 )
| ~ ( in @ SV522 @ SV311 )
| ( in @ SV512 @ SV147 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1930,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
| ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1931,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( in @ ( sK40_Xx @ SV313 @ SV150 ) @ SV150 )
= $true )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1932,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( ~ ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) ) )
= $true )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1933,plain,
! [SV151: $i,SV488: $i,SV457: $i > $o] :
( ( ( ~ ( SV457 @ SV488 ) )
= $true )
| ( ( in @ SV488
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) )
= $true )
| ( ( in @ SV488 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1934,plain,
! [SV458: $i > $o,SV151: $i,SV489: $i] :
( ( ( ~ ( in @ SV489
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) ) )
= $true )
| ( ( SV458 @ SV489 )
= $true )
| ( ( in @ SV489 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1935,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1936,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) )
| ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1937,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1938,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1829]) ).
thf(1939,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
| ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1940,plain,
! [SV315: $i,SV154: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SV523 @ SV154 )
| ( in @ SV523 @ SV315 )
| ! [SX3: $o] : SX3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1941,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ~ ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
| ( in @ SV524 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1942,plain,
! [SV315: $i,SV154: $i,SV525: $i] :
( ( ~ ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
| ! [SY2551: $o] :
( ~ SY2551
| ( in @ SV525 @ SV315 )
| SY2551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(1943,plain,
! [SV315: $i,SV154: $i] :
( ( ( ! [SY2278: $i] :
~ ( in @ SY2278 @ ( binunion @ SV154 @ SV315 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(1944,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1945,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1946,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) )
= $false )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1947,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( SV156 @ SV410 )
= $false )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( ~ ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1948,plain,
! [SV491: $i,SV459: $i,SV157: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV157 )
| ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(1949,plain,
! [SV317: $i > $o,SV158: $i,SV502: $i] :
( ( ( in @ SV502 @ SV158 )
= $false )
| ( ( ~ ( SV317 @ SV502 ) )
= $true )
| ( ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1950,plain,
! [SV317: $i > $o,SV158: $i,SV503: $i] :
( ( ( in @ SV503 @ SV158 )
= $false )
| ( ( ~ ( SV317 @ SV503 ) )
= $true )
| ( ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1951,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( in @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV159 ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1952,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1842]) ).
thf(1953,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( ~ ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 ) )
= $false )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1954,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( ~ ~ ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 ) )
= $false )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1955,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( ~ ( in @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) @ SV160 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(1956,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( ~ ~ ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(1957,plain,
! [SV320: $i > $o,SV162: $i,SV504: $i] :
( ( ( in @ SV504 @ SV162 )
= $false )
| ( ( ~ ( SV320 @ SV504 ) )
= $true )
| ( ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1958,plain,
! [SV320: $i > $o,SV162: $i,SV505: $i] :
( ( ( in @ SV505 @ SV162 )
= $false )
| ( ( ~ ( SV320 @ SV505 ) )
= $true )
| ( ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1959,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1960,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1961,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1962,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1963,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 ) )
= $false )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1964,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) )
= $false )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1965,plain,
! [SV527: $i,SV163: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SV527 @ ( sK15_B @ SV163 ) )
| ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(1966,plain,
! [SV163: $i] :
( ( ~ ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1967,plain,
! [SV163: $i] :
( ( ~ ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1968,plain,
! [SV321: $i,SV164: $i,SV411: $i] :
( ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1969,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV321: $i] :
( ( ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SV528 @ emptyset ) )
| ~ ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(1970,plain,
! [SV322: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1971,plain,
! [SV165: $i > $i > $o,SV322: $i] :
( ( ( ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(1972,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
| ~ ( ( SV506
!= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) ) ) )
= $false )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1973,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1974,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1975,plain,
! [SV413: $i,SV529: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV529 )
| ! [SY2558: $i] :
( ~ ( SV167 @ SY2558 )
| ( SV529 = SY2558 ) ) )
= $true )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(1976,plain,
! [SV413: $i,SV167: $i > $o] :
( ( ( SV167 @ SV413 )
= $false )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( ! [SY2056: $i] :
( ~ ( SV167 @ SY2056 )
| ! [SY2057: $i] :
( ~ ( SV167 @ SY2057 )
| ( SY2056 = SY2057 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1977,plain,
! [SV168: $i,SV467: $o,SV324: $i] :
( ( ( in @ SV324 @ ( sK31_B @ SV467 @ SV324 @ SV168 ) )
= $true )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1863]) ).
thf(1978,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 ) )
= $true )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(1979,plain,
! [SV168: $i,SV324: $i] :
( ( ( in @ SV324 @ ( sK31_B @ $true @ SV324 @ SV168 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1980,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(1981,plain,
! [SV168: $i,SV324: $i] :
( ( ( in @ SV324 @ ( sK31_B @ $false @ SV324 @ SV168 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1867]) ).
thf(1982,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1868]) ).
thf(1983,plain,
! [SV507: $i] :
( ( ( in @ SV507 @ sK1_SY0 )
= $false )
| ( ( ! [SY2541: $i] :
( ~ ( in @ SY2541 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SV507 @ SY2541 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SY2541 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1984,plain,
( ( in @ sK5_SY1607 @ sK3_SY1596 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(1985,plain,
( ( ~ ( sK4_SY1601 @ sK5_SY1607 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1986,plain,
! [SV414: $i,SV530: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV530 )
| ! [SY2559: $i] :
( ~ ( SV169 @ SY2559 )
| ( SV530 = SY2559 ) ) )
= $true )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(1987,plain,
! [SV414: $i,SV169: $i > $o] :
( ( ( SV169 @ SV414 )
= $false )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( ! [SY2061: $i] :
( ~ ( SV169 @ SY2061 )
| ! [SY2062: $i] :
( ~ ( SV169 @ SY2062 )
| ( SY2061 = SY2062 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1988,plain,
! [SV325: $i,SV170: $i,SV415: $i] :
( ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false )
| ( ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1989,plain,
! [SV531: $i,SV170: $i,SV415: $i,SV325: $i] :
( ( ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SV531 @ emptyset ) )
| ~ ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(1990,plain,
! [SV171: $i,SV514: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV514 ) )
= $true )
| ( ( ~ ( in @ SV514 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1991,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1992,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1993,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( ~ ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1994,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) ) )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1995,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1996,plain,
! [SV417: $i,SV173: $i > $o] :
( ( ( SV173 @ SV417 )
= $false )
| ( ( SV417
= ( sK24_SY91 @ SV417 @ SV173 ) )
= $false )
| ( ( SV173 @ ( sK23_Xx @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1997,plain,
! [SV441: $i,SV508: $i,SV468: $i] :
( ( ( in @ SV468 @ SV508 )
= $false )
| ( ( ~ ( in @ SV508 @ SV441 ) )
= $true )
| ( ( in @ SV468 @ ( setunion @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1998,plain,
! [SV442: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) ) )
= $false )
| ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(1999,plain,
! [SV442: $i,SV469: $i] :
( ( ( ~ ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 ) )
= $false )
| ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1884]) ).
thf(2000,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( in @ ( sK35_Xx @ SV327 @ SV174 ) @ SV174 )
= $true )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(2001,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( ~ ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) ) )
= $true )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(2002,plain,
! [SV175: $i,SV515: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV515 ) )
= $true )
| ( ( ~ ( in @ SV515 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2003,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1888]) ).
thf(2004,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(2005,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 ) )
= $false )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2006,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( ~ ~ ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 ) )
= $false )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2007,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) @ SV176 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2008,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( ~ ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 ) )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2009,plain,
! [SV178: $i,SV509: $i,SV330: $i > $o] :
( ( ( SV330 @ SV509 )
= $false )
| ( ( ~ ( in @ SV509 @ SV178 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2010,plain,
! [SV178: $i,SV510: $i,SV330: $i > $o] :
( ( ( SV330 @ SV510 )
= $false )
| ( ( ~ ( in @ SV510 @ SV178 ) )
= $true )
| ( ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2011,plain,
! [SV331: $i,SV179: $i,SV418: $i] :
( ( ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) )
= $false )
| ( ( in @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SV179 )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2012,plain,
! [SV532: $i,SV179: $i,SV418: $i,SV331: $i] :
( ( ( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SV532 @ emptyset ) )
| ~ ( in @ SV532
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2013,plain,
! [SV180: $i] :
( ( ( in @ ( sK9_Xx @ SV180 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(2014,plain,
! [SV180: $i] :
( ( ( in @ ( sK9_Xx @ SV180 ) @ SV180 )
= $true )
| ( ( ~ ( in @ emptyset @ SV180 ) )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(2015,plain,
! [SV180: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ omega )
| ( in @ SV533 @ SV180 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 )
= $false )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2016,plain,
! [SV332: $i,SV181: $i,SV419: $i] :
( ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false )
| ( ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2017,plain,
! [SV534: $i,SV181: $i,SV419: $i,SV332: $i] :
( ( ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SV534 @ emptyset ) )
| ~ ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2018,plain,
! [SV420: $i,SV182: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ ( sK14_B @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ SV516 @ SV182 ) )
= $true )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2019,plain,
! [SV421: $i,SV183: $i > $o] :
( ( ( SV183 @ SV421 )
= $false )
| ( ( SV421
= ( sK20_SY62 @ SV421 @ SV183 ) )
= $false )
| ( ( SV183
@ ( descr
@ ^ [SY2115: $i] : ( SV183 @ SY2115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2020,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2021,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(2022,plain,
! [SV186: $i,SV335: $i] :
( ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV335 )
= $false )
| ( ( in @ ( sK6_Xx @ SV335 @ SV186 ) @ SV186 )
= $false )
| ( ( SV186 = SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(2023,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
| ~ ( ( SV517
!= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2024,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(2025,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
| ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(2026,plain,
! [SV444: $i,SV472: $i] :
( ( ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV472 )
= $true )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(2027,plain,
! [SV444: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 ) )
= $true )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1911]) ).
thf(2028,plain,
! [SV445: $i,SV473: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ SV473 ) )
= $true )
| ( ( in @ SV518 @ SV445 )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV445 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2029,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) )
= $false )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2030,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( SV189 @ SV423 )
= $false )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( ~ ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2031,plain,
! [SV474: $i,SV190: $i,SV498: $i] :
( ( ( SV498 = SV190 )
= $true )
| ( ( in @ SV498 @ SV474 )
= $true )
| ( ( in @ SV498 @ ( setadjoin @ SV190 @ SV474 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2032,plain,
! [SV519: $i,SV190: $i,SV535: $i] :
( ( ( SV535 != SV190 )
| ( in @ SV535 @ ( setadjoin @ SV190 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2033,plain,
! [SV190: $i,SV520: $i,SV536: $i] :
( ( ~ ( in @ SV536 @ SV520 )
| ( in @ SV536 @ ( setadjoin @ SV190 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2034,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i,SV499: $i,SV427: $i] :
( ( ( ~ ( in @ ( kpair @ SV427 @ SV499 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) ) )
= $true )
| ( ( SV342 @ SV427 @ SV499 )
= $true )
| ( ( in @ SV499 @ SV195 )
= $false )
| ( ( in @ SV427 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2035,plain,
! [SV198: $i,SV8: $i,SV500: $i,SV428: $i,SV345: $i > $i > $o] :
( ( ( ~ ( SV345 @ SV428 @ SV500 ) )
= $true )
| ( ( in @ ( kpair @ SV428 @ SV500 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) )
= $true )
| ( ( in @ SV500 @ SV198 )
= $false )
| ( ( in @ SV428 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(2036,plain,
! [SV285: $i,SV487: $i,SV105: $i,SV455: $i] :
( ( ( in @ SV455 @ SV105 )
= $false )
| ( ( in @ SV487 @ SV285 )
= $true )
| ( ( SV455 = SV487 )
= $false )
| ( ( SV105 = SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2037,plain,
! [SV436: $i,SV140: $i,SV306: $i > $o] :
( ( ( SV306 @ ( sK38_Xx @ SV306 @ SV140 ) )
= $false )
| ( ( SV306 @ SV436 )
= $true )
| ( ( in @ SV436 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2038,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) ) )
= $false )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2039,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $false )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1923]) ).
thf(2040,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) )
| ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $false )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2041,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1925]) ).
thf(2042,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( ~ ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1925]) ).
thf(2043,plain,
! [SV437: $i,SV145: $i,SV309: $i > $o] :
( ( ( SV309 @ ( sK73_Xx @ SV309 @ SV145 ) )
= $true )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2044,plain,
! [SV437: $i,SV145: $i,SV309: $i > $o] :
( ( ( in @ ( sK73_Xx @ SV309 @ SV145 ) @ SV145 )
= $true )
| ( ( ( dsetconstr @ SV145
@ ^ [SY2261: $i] : ( SV309 @ SY2261 ) )
= ( setadjoin @ SV437 @ emptyset ) )
= $false )
| ( ( in @ SV437
@ ( dsetconstr @ SV145
@ ^ [SY2262: $i] : ( SV309 @ SY2262 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2045,plain,
! [SV311: $i,SV147: $i,SV521: $i,SV511: $i] :
( ( ( SV511 != SV521 )
= $true )
| ( ( ~ ( in @ SV511 @ SV147 )
| ( in @ SV521 @ SV311 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2046,plain,
! [SV147: $i,SV311: $i,SV522: $i,SV512: $i] :
( ( ( SV512 != SV522 )
= $true )
| ( ( ~ ( in @ SV522 @ SV311 )
| ( in @ SV512 @ SV147 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2047,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( SV407
!= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2048,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 ) )
= $false )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2049,plain,
! [SV438: $i,SV150: $i,SV313: $i > $o] :
( ( ( SV313 @ ( sK40_Xx @ SV313 @ SV150 ) )
= $false )
| ( ( SV313 @ SV438 )
= $true )
| ( ( in @ SV438 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2050,plain,
! [SV151: $i,SV488: $i,SV457: $i > $o] :
( ( ( SV457 @ SV488 )
= $false )
| ( ( in @ SV488
@ ( dsetconstr @ SV151
@ ^ [SY2463: $i] : ( SV457 @ SY2463 ) ) )
= $true )
| ( ( in @ SV488 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2051,plain,
! [SV458: $i > $o,SV151: $i,SV489: $i] :
( ( ( in @ SV489
@ ( dsetconstr @ SV151
@ ^ [SY2465: $i] : ( SV458 @ SY2465 ) ) )
= $false )
| ( ( SV458 @ SV489 )
= $true )
| ( ( in @ SV489 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2052,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $false )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2053,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2054,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK45_SY1644 @ SV152 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2055,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2056,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(2057,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(2058,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2059,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2060,plain,
! [SV315: $i,SV154: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) ) )
= $true )
| ( ( ( in @ SV523 @ SV154 )
| ( in @ SV523 @ SV315 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(2061,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) ) )
= $true )
| ( ( ( in @ SV524 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2062,plain,
! [SV315: $i,SV154: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) ) )
= $true )
| ( ( ! [SY2551: $o] :
( ~ SY2551
| ( in @ SV525 @ SV315 )
| SY2551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2063,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2064,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2065,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) ) )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2066,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) ) )
= $false )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2067,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) )
= $false )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2068,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) )
| ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) )
= $false )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2069,plain,
! [SV491: $i,SV459: $i,SV157: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV157 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2070,plain,
! [SV158: $i,SV502: $i,SV317: $i > $o] :
( ( ( SV317 @ SV502 )
= $false )
| ( ( in @ SV502 @ SV158 )
= $false )
| ( ( SV317 @ ( sK39_Xx @ SV317 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2071,plain,
! [SV158: $i,SV503: $i,SV317: $i > $o] :
( ( ( SV317 @ SV503 )
= $false )
| ( ( in @ SV503 @ SV158 )
= $false )
| ( ( in @ ( sK39_Xx @ SV317 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2072,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( in @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV159 )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2073,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2074,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2075,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( ~ ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 ) )
= $true )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(2076,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( in @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) @ SV160 )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2077,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( ~ ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 ) )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2078,plain,
! [SV162: $i,SV504: $i,SV320: $i > $o] :
( ( ( SV320 @ SV504 )
= $false )
| ( ( in @ SV504 @ SV162 )
= $false )
| ( ( SV320 @ ( sK37_Xx @ SV320 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2079,plain,
! [SV162: $i,SV505: $i,SV320: $i > $o] :
( ( ( SV320 @ SV505 )
= $false )
| ( ( in @ SV505 @ SV162 )
= $false )
| ( ( in @ ( sK37_Xx @ SV320 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2080,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2081,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
| ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2082,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2083,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
| ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2084,plain,
! [SV163: $i,SV466: $i] :
( ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2085,plain,
! [SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 ) )
= $true )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(2086,plain,
! [SV527: $i,SV163: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( sK15_B @ SV163 ) )
| ~ ( in @ SV527 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2087,plain,
! [SV163: $i] :
( ( ! [SY2027: $i] :
( ~ ( in @ SY2027 @ ( sK15_B @ SV163 ) )
| ! [SY2028: $i] :
( ~ ( in @ SY2028 @ SY2027 )
| ( in @ SY2028 @ SV163 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2088,plain,
! [SV163: $i] :
( ( ! [SY2029: $i,SY2030: $i] :
( ~ ( in @ SY2029 @ SV163 )
| ~ ( in @ SY2030 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ~ ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) )
| ~ ( ( in @ SY2029 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) )
| ( in @ SY2030 @ ( sK16_SY1631 @ SY2030 @ SY2029 @ SV163 ) ) ) ) )
| ( SY2029 = SY2030 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2089,plain,
! [SV411: $i,SV321: $i,SV164: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2090,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
!= ( setadjoin @ SV528 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2091,plain,
! [SV322: $i,SV539: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2568: $i] :
( ~ ( SV165 @ SY2568 @ SV539 )
| ~ ( in @ SY2568 @ SV322 ) )
| ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2092,plain,
! [SV165: $i > $i > $o,SV322: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 )
| ~ ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2093,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) ) )
= $false )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2094,plain,
! [SV165: $i > $i > $o,SV322: $i,SV506: $i] :
( ( ( ~ ( ( SV506
!= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) ) ) )
= $false )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2095,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2096,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2097,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2098,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2099,plain,
! [SV413: $i,SV529: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV529 ) )
= $true )
| ( ( ! [SY2558: $i] :
( ~ ( SV167 @ SY2558 )
| ( SV529 = SY2558 ) ) )
= $true )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2100,plain,
! [SV413: $i,SV541: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV541 )
| ! [SY2569: $i] :
( ~ ( SV167 @ SY2569 )
| ( SV541 = SY2569 ) ) )
= $true )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2101,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
| ~ ~ SV467 )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2102,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2103,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
| ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2104,plain,
! [SV507: $i,SV542: $i] :
( ( ( ~ ( in @ SV542 @ sK2_SY1590 )
| ~ ( in @ ( kpair @ SV507 @ SV542 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SV542 ) ) )
= $true )
| ( ( in @ SV507 @ sK1_SY0 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2105,plain,
( ( sK4_SY1601 @ sK5_SY1607 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2106,plain,
! [SV414: $i,SV530: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV530 ) )
= $true )
| ( ( ! [SY2559: $i] :
( ~ ( SV169 @ SY2559 )
| ( SV530 = SY2559 ) ) )
= $true )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2107,plain,
! [SV414: $i,SV543: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV543 )
| ! [SY2570: $i] :
( ~ ( SV169 @ SY2570 )
| ( SV543 = SY2570 ) ) )
= $true )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2108,plain,
! [SV415: $i,SV325: $i,SV170: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2571: $i] : ( in @ ( kpair @ SV544 @ SY2571 ) @ SV415 ) ) )
@ SV325 ) )
= $true )
| ( ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
= $true )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2109,plain,
! [SV531: $i,SV170: $i,SV415: $i,SV325: $i] :
( ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
!= ( setadjoin @ SV531 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2110,plain,
! [SV171: $i,SV514: $i,SV326: $i > $o] :
( ( ( SV326 @ SV514 )
= $false )
| ( ( ~ ( in @ SV514 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2111,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2112,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
| ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2113,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) )
| ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) )
= $false )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2114,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) ) )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2115,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( SV172 @ ( sK46_SY216 @ SV172 ) )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2116,plain,
! [SV468: $i,SV441: $i,SV508: $i] :
( ( ( in @ SV508 @ SV441 )
= $false )
| ( ( in @ SV468 @ SV508 )
= $false )
| ( ( in @ SV468 @ ( setunion @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2117,plain,
! [SV442: $i,SV469: $i] :
( ( ( in @ SV469 @ ( sK8_B @ SV469 @ SV442 ) )
= $true )
| ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2118,plain,
! [SV442: $i,SV469: $i] :
( ( ( in @ ( sK8_B @ SV469 @ SV442 ) @ SV442 )
= $true )
| ( ( in @ SV469 @ ( setunion @ SV442 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2119,plain,
! [SV443: $i,SV174: $i,SV327: $i > $o] :
( ( ( SV327 @ ( sK35_Xx @ SV327 @ SV174 ) )
= $false )
| ( ( SV327 @ SV443 )
= $true )
| ( ( in @ SV443 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2120,plain,
! [SV175: $i,SV515: $i,SV328: $i > $o] :
( ( ( SV328 @ SV515 )
= $false )
| ( ( ~ ( in @ SV515 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2121,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2122,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
| ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2123,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2124,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( ~ ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 ) )
= $true )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2125,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( in @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) @ SV176 )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2126,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( ~ ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 ) )
= $true )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2127,plain,
! [SV330: $i > $o,SV178: $i,SV509: $i] :
( ( ( in @ SV509 @ SV178 )
= $false )
| ( ( SV330 @ SV509 )
= $false )
| ( ( in @ ( sK36_Xx @ SV330 @ SV178 ) @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2128,plain,
! [SV330: $i > $o,SV178: $i,SV510: $i] :
( ( ( in @ SV510 @ SV178 )
= $false )
| ( ( SV330 @ SV510 )
= $false )
| ( ( SV330 @ ( sK36_Xx @ SV330 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2129,plain,
! [SV532: $i,SV179: $i,SV418: $i,SV331: $i] :
( ( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
!= ( setadjoin @ SV532 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV532
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2130,plain,
! [SV180: $i] :
( ( ( in @ emptyset @ SV180 )
= $false )
| ( ( in @ ( sK9_Xx @ SV180 ) @ omega )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2131,plain,
! [SV180: $i] :
( ( ( in @ emptyset @ SV180 )
= $false )
| ( ( in @ ( sK9_Xx @ SV180 ) @ SV180 )
= $true )
| ( ( ! [SY2104: $i] :
( ~ ( in @ SY2104 @ omega )
| ( in @ SY2104 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2132,plain,
! [SV180: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ omega ) )
= $true )
| ( ( in @ SV533 @ SV180 )
= $true )
| ( ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 )
= $false )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2133,plain,
! [SV419: $i,SV332: $i,SV181: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2572: $i] : ( in @ ( kpair @ SV545 @ SY2572 ) @ SV419 ) ) )
@ SV332 ) )
= $true )
| ( ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
= $true )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2134,plain,
! [SV534: $i,SV181: $i,SV419: $i,SV332: $i] :
( ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
!= ( setadjoin @ SV534 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2135,plain,
! [SV420: $i,SV182: $i,SV516: $i] :
( ( ( in @ SV516 @ ( sK14_B @ SV182 ) )
= $false )
| ( ( ~ ( in @ SV516 @ SV182 ) )
= $true )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2136,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2137,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2138,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2139,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2140,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
| ~ ( ( SV517
!= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2141,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) ) )
= $true )
| ( ( ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2142,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2143,plain,
! [SV444: $i,SV472: $i] :
( ( ( in @ ( sK7_Xx @ SV472 @ SV444 ) @ SV444 )
= $false )
| ( ( in @ SV472 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2144,plain,
! [SV445: $i,SV473: $i,SV518: $i] :
( ( ( in @ SV518 @ SV473 )
= $false )
| ( ( in @ SV518 @ SV445 )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV445 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2145,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) ) )
= $false )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2029]) ).
thf(2146,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) )
= $false )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2029]) ).
thf(2147,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) )
| ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) )
= $false )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2148,plain,
! [SV519: $i,SV190: $i,SV535: $i] :
( ( ( SV535 != SV190 )
= $true )
| ( ( in @ SV535 @ ( setadjoin @ SV190 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2149,plain,
! [SV190: $i,SV520: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ SV520 ) )
= $true )
| ( ( in @ SV536 @ ( setadjoin @ SV190 @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2150,plain,
! [SV342: $i > $i > $o,SV195: $i,SV5: $i,SV499: $i,SV427: $i] :
( ( ( in @ ( kpair @ SV427 @ SV499 )
@ ( dpsetconstr @ SV5 @ SV195
@ ^ [SY2360: $i,SY2361: $i] : ( SV342 @ SY2360 @ SY2361 ) ) )
= $false )
| ( ( SV342 @ SV427 @ SV499 )
= $true )
| ( ( in @ SV499 @ SV195 )
= $false )
| ( ( in @ SV427 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2151,plain,
! [SV198: $i,SV8: $i,SV500: $i,SV428: $i,SV345: $i > $i > $o] :
( ( ( SV345 @ SV428 @ SV500 )
= $false )
| ( ( in @ ( kpair @ SV428 @ SV500 )
@ ( dpsetconstr @ SV8 @ SV198
@ ^ [SY2368: $i,SY2369: $i] : ( SV345 @ SY2368 @ SY2369 ) ) )
= $true )
| ( ( in @ SV500 @ SV198 )
= $false )
| ( ( in @ SV428 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2152,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2153,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2154,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) ) )
= $false )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2040]) ).
thf(2155,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ~ ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $false )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2040]) ).
thf(2156,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2157,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( ~ ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2158,plain,
! [SV311: $i,SV147: $i,SV521: $i,SV511: $i] :
( ( ( SV511 = SV521 )
= $false )
| ( ( ~ ( in @ SV511 @ SV147 )
| ( in @ SV521 @ SV311 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2159,plain,
! [SV147: $i,SV311: $i,SV522: $i,SV512: $i] :
( ( ( SV512 = SV522 )
= $false )
| ( ( ~ ( in @ SV522 @ SV311 )
| ( in @ SV512 @ SV147 ) )
= $true )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2160,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( SV407
= ( kpair @ ( sK67_Xx @ SV407 @ SV312 @ SV149 ) @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) ) )
= $true )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2161,plain,
! [SV149: $i,SV312: $i,SV407: $i] :
( ( ( in @ ( sK68_SY1652 @ SV407 @ SV312 @ SV149 ) @ SV312 )
= $true )
| ( ( in @ SV407 @ ( cartprod @ SV149 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2162,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $true )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2163,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ ( sK43_SY210 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2164,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2165,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ( sK44_Xx @ SV152 )
!= ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2166,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2167,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV314 )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2168,plain,
! [SV153: $i,SV314: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 ) )
= $true )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2169,plain,
! [SV315: $i,SV154: $i,SV523: $i] :
( ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false )
| ( ( ( in @ SV523 @ SV154 )
| ( in @ SV523 @ SV315 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2170,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false )
| ( ( ( in @ SV524 @ SV154 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2171,plain,
! [SV315: $i,SV154: $i,SV525: $i] :
( ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false )
| ( ( ! [SY2551: $o] :
( ~ SY2551
| ( in @ SV525 @ SV315 )
| SY2551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2172,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2173,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV409 )
| ( SV490 @ SV546 ) )
= $true )
| ( ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2174,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
| ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2175,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) ) )
= $true )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2176,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( SV156 @ ( sK41_SY203 @ SV156 ) )
= $true )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2177,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) ) )
= $false )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2178,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ ( sK41_SY203 @ SV156 ) ) )
= $false )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2068]) ).
thf(2179,plain,
! [SV491: $i,SV459: $i,SV157: $i,SV526: $i] :
( ( ( in @ SV526 @ SV157 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2180,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
| ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2181,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2182,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i] :
( ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false )
| ( ( ! [SY2519: $i] :
( ~ ( in @ SY2519 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2520: $i] :
( in @ ( kpair @ SY2519 @ SY2520 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SY2519 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2523: $i] :
( in @ ( kpair @ SY2519 @ SY2523 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2183,plain,
! [SV160: $i,SV463: $i,SV495: $i > $i] :
( ( ( in @ ( SV495 @ ( sK87_Xx @ SV495 @ SV463 @ SV160 ) ) @ SV463 )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV160 @ SV463
@ ^ [SY2526: $i,SY2527: $i] :
( ( SV495 @ SY2526 )
= SY2527 ) )
@ ( cartprod @ SV160 @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2184,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
| ~ ( ( SV548
!= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2185,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2186,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2187,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
| ~ ( ( SV549
!= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2188,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2189,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2190,plain,
! [SV163: $i,SV466: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2191,plain,
! [SV163: $i,SV466: $i] :
( ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( ! [SY2489: $i] :
~ ( in @ SY2489 @ SV466 ) )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2192,plain,
! [SV527: $i,SV163: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ~ ( in @ SV527 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2193,plain,
! [SV163: $i,SV551: $i] :
( ( ~ ( in @ SV551 @ ( sK15_B @ SV163 ) )
| ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV551 )
| ( in @ SY2579 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2194,plain,
! [SV163: $i,SV552: $i] :
( ( ! [SY2580: $i] :
( ~ ( in @ SV552 @ SV163 )
| ~ ( in @ SY2580 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SY2580 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SY2580 @ SV552 @ SV163 ) )
| ~ ( in @ SY2580 @ ( sK16_SY1631 @ SY2580 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SY2580 @ SV552 @ SV163 ) )
| ( in @ SY2580 @ ( sK16_SY1631 @ SY2580 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SY2580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2195,plain,
! [SV411: $i,SV321: $i,SV164: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV164 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2196,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2197,plain,
! [SV322: $i,SV539: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2568: $i] :
( ~ ( SV165 @ SY2568 @ SV539 )
| ~ ( in @ SY2568 @ SV322 ) ) )
= $true )
| ( ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2198,plain,
! [SV165: $i > $i > $o,SV322: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 )
| ~ ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2199,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2200,plain,
! [SV165: $i > $i > $o,SV322: $i,SV506: $i] :
( ( ( SV506
!= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2201,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ( in @ SV412 @ SV166 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2202,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2203,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2204,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2205,plain,
! [SV413: $i,SV529: $i,SV167: $i > $o] :
( ( ( SV167 @ SV529 )
= $false )
| ( ( ! [SY2558: $i] :
( ~ ( SV167 @ SY2558 )
| ( SV529 = SY2558 ) ) )
= $true )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2206,plain,
! [SV413: $i,SV541: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV541 ) )
= $true )
| ( ( ! [SY2569: $i] :
( ~ ( SV167 @ SY2569 )
| ( SV541 = SY2569 ) ) )
= $true )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2207,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 ) )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2101]) ).
thf(2208,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ ~ SV467 )
= $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2101]) ).
thf(2209,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2210,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2102]) ).
thf(2211,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2212,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2213,plain,
! [SV507: $i,SV542: $i] :
( ( ( ~ ( in @ SV542 @ sK2_SY1590 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV507 @ SV542 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SV542 ) ) )
= $true )
| ( ( in @ SV507 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2214,plain,
! [SV414: $i,SV530: $i,SV169: $i > $o] :
( ( ( SV169 @ SV530 )
= $false )
| ( ( ! [SY2559: $i] :
( ~ ( SV169 @ SY2559 )
| ( SV530 = SY2559 ) ) )
= $true )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2215,plain,
! [SV414: $i,SV543: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV543 ) )
= $true )
| ( ( ! [SY2570: $i] :
( ~ ( SV169 @ SY2570 )
| ( SV543 = SY2570 ) ) )
= $true )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2216,plain,
! [SV415: $i,SV325: $i,SV170: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV170 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2571: $i] : ( in @ ( kpair @ SV544 @ SY2571 ) @ SV415 ) ) )
@ SV325 )
= $true )
| ( ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
= $true )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2217,plain,
! [SV531: $i,SV170: $i,SV415: $i,SV325: $i] :
( ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2218,plain,
! [SV326: $i > $o,SV171: $i,SV514: $i] :
( ( ( in @ SV514 @ SV171 )
= $false )
| ( ( SV326 @ SV514 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2219,plain,
! [SV171: $i,SV553: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV553 )
| ~ ( in @ SV553 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2220,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2221,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2222,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) ) )
= $false )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2223,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ ( sK46_SY216 @ SV172 ) ) )
= $false )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2113]) ).
thf(2224,plain,
! [SV416: $i,SV554: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ SV554 )
| ( ( sK46_SY216 @ SV172 )
= SV554 ) )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2225,plain,
! [SV328: $i > $o,SV175: $i,SV515: $i] :
( ( ( in @ SV515 @ SV175 )
= $false )
| ( ( SV328 @ SV515 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2226,plain,
! [SV175: $i,SV555: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV555 )
| ~ ( in @ SV555 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2227,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2228,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2229,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2230,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i] :
( ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false )
| ( ( ! [SY2528: $i] :
( ~ ( in @ SY2528 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2529: $i] :
( in @ ( kpair @ SY2528 @ SY2529 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SY2528 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2532: $i] :
( in @ ( kpair @ SY2528 @ SY2532 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2231,plain,
! [SV176: $i,SV471: $i,SV497: $i > $i] :
( ( ( in @ ( SV497 @ ( sK90_Xx @ SV497 @ SV471 @ SV176 ) ) @ SV471 )
= $false )
| ( ( subset
@ ( dpsetconstr @ SV176 @ SV471
@ ^ [SY2535: $i,SY2536: $i] :
( ( SV497 @ SY2535 )
= SY2536 ) )
@ ( cartprod @ SV176 @ SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2232,plain,
! [SV532: $i,SV179: $i,SV418: $i,SV331: $i] :
( ( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
= ( setadjoin @ SV532 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV532
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2233,plain,
! [SV180: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ omega )
| ( in @ SV557 @ SV180 ) )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2234,plain,
! [SV180: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ omega )
| ( in @ SV558 @ SV180 ) )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ SV180 )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2235,plain,
! [SV180: $i,SV533: $i] :
( ( ( in @ SV533 @ omega )
= $false )
| ( ( in @ SV533 @ SV180 )
= $true )
| ( ( in @ ( setadjoin @ ( sK9_Xx @ SV180 ) @ ( sK9_Xx @ SV180 ) ) @ SV180 )
= $false )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2236,plain,
! [SV419: $i,SV332: $i,SV181: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV181 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2572: $i] : ( in @ ( kpair @ SV545 @ SY2572 ) @ SV419 ) ) )
@ SV332 )
= $true )
| ( ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
= $true )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2237,plain,
! [SV534: $i,SV181: $i,SV419: $i,SV332: $i] :
( ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) ) )
= $true )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2238,plain,
! [SV420: $i,SV182: $i,SV516: $i] :
( ( ( in @ SV516 @ SV182 )
= $false )
| ( ( in @ SV516 @ ( sK14_B @ SV182 ) )
= $false )
| ( ( in @ SV420 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2239,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ( SV422 = SV184 )
| ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2240,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ( SV422 = SV184 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2241,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ! [SY2425: $o] :
( ~ SY2425
| ( in @ SV422 @ SV333 )
| SY2425 ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2242,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2243,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2244,plain,
! [SV187: $i > $o,SV336: $i > $o,SV517: $i] :
( ( ( ~ ( ( SV517
!= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2140]) ).
thf(2245,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) ) )
= $true )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2246,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2247,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) ) )
= $true )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2248,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( SV189 @ ( sK21_Xx @ SV189 ) )
= $true )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2249,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) ) )
= $false )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2250,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ ( sK21_Xx @ SV189 ) ) )
= $false )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2251,plain,
! [SV519: $i,SV190: $i,SV535: $i] :
( ( ( SV535 = SV190 )
= $false )
| ( ( in @ SV535 @ ( setadjoin @ SV190 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2252,plain,
! [SV190: $i,SV520: $i,SV536: $i] :
( ( ( in @ SV536 @ SV520 )
= $false )
| ( ( in @ SV536 @ ( setadjoin @ SV190 @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2253,plain,
! [SV404: $i,SV141: $i > $o,SV559: $i] :
( ( ( ( SV559
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SV559 ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2254,plain,
! [SV404: $i,SV560: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV560 )
| ( SV560
= ( sK32_Xx @ SV141 ) ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2255,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ! [SY1936: $i] :
( ( SY1936
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SY1936 ) ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2256,plain,
! [SV404: $i,SV141: $i > $o] :
( ( ( ! [SY1937: $i] :
( ~ ( SV141 @ SY1937 )
| ( SY1937
= ( sK32_Xx @ SV141 ) ) ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2257,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2258,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
| ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2259,plain,
! [SV311: $i,SV521: $i,SV147: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV147 ) )
= $true )
| ( ( in @ SV521 @ SV311 )
= $true )
| ( ( SV511 = SV521 )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2260,plain,
! [SV147: $i,SV512: $i,SV311: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV311 ) )
= $true )
| ( ( in @ SV512 @ SV147 )
= $true )
| ( ( SV512 = SV522 )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2261,plain,
! [SV408: $i,SV561: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV561 )
| ( ( sK43_SY210 @ SV152 )
= SV561 ) )
= $true )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2262,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2263,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( ~ ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2264,plain,
! [SV153: $i,SV314: $i] :
( ( ( in @ ( sK25_Xx @ SV314 @ SV153 ) @ SV153 )
= $false )
| ( ( SV153 = SV314 )
= $true )
| ( ( in @ ( sK26_Xx @ SV314 @ SV153 ) @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2265,plain,
! [SV315: $i,SV154: $i,SV523: $i] :
( ( ( in @ SV523 @ SV154 )
= $true )
| ( ( ( in @ SV523 @ SV315 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2266,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( in @ SV524 @ SV154 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2267,plain,
! [SV154: $i,SV315: $i,SV525: $i,SV562: $o] :
( ( ( ~ SV562
| ( in @ SV525 @ SV315 )
| SV562 )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2171]) ).
thf(2268,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( ~ $true
| ( in @ SV525 @ SV315 )
| $true )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2171]) ).
thf(2269,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( ~ $false
| ( in @ SV525 @ SV315 )
| $false )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2171]) ).
thf(2270,plain,
! [SV315: $i,SV154: $i,SV537: $i,SV563: $o] :
( ( ( ~ SV563
| ~ SV563
| SV563 )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2172]) ).
thf(2271,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2172]) ).
thf(2272,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2172]) ).
thf(2273,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV409 ) )
= $true )
| ( ( SV490 @ SV546 )
= $true )
| ( ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2274,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2275,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2276,plain,
! [SV410: $i,SV564: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ SV564 )
| ( ( sK41_SY203 @ SV156 )
= SV564 ) )
= $true )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2277,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( ! [SY1987: $i] :
( ~ ( SV156 @ SY1987 )
| ( ( sK41_SY203 @ SV156 )
= SY1987 ) ) )
= $true )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2278,plain,
! [SV410: $i,SV156: $i > $o] :
( ( ( SV156 @ ( sK41_SY203 @ SV156 ) )
= $true )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2178]) ).
thf(2279,plain,
! [SV157: $i,SV491: $i,SV526: $i,SV459: $i] :
( ( ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
| ~ ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) ) )
= $false )
| ( ( in @ SV526 @ SV157 )
= $false )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2280,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2281,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2282,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV160 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2283,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV160 )
| ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2284,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
| ~ ( ( SV548
!= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) ) ) ) )
= $true )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2285,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2286,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
| ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2287,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
| ~ ( ( SV549
!= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) ) ) ) )
= $true )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2187]) ).
thf(2288,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2289,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
| ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2290,plain,
! [SV163: $i,SV466: $i,SV550: $i] :
( ( ( in @ SV550 @ SV466 )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2291,plain,
! [SV163: $i,SV466: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2292,plain,
! [SV527: $i,SV163: $i,SV513: $i] :
( ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( ~ ( in @ SV527 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2293,plain,
! [SV163: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV551 )
| ( in @ SY2579 @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2294,plain,
! [SV567: $i,SV163: $i,SV552: $i] :
( ( ~ ( in @ SV552 @ SV163 )
| ~ ( in @ SV567 @ SV163 )
| ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2295,plain,
! [SV411: $i,SV321: $i,SV164: $i,SV538: $i] :
( ( ( in @ SV538 @ SV164 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2296,plain,
! [SV164: $i,SV411: $i,SV321: $i,SV528: $i] :
( ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( ~ ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) ) )
= $true )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2297,plain,
! [SV322: $i,SV539: $i,SV568: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV568 @ SV539 )
| ~ ( in @ SV568 @ SV322 ) )
= $true )
| ( ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2298,plain,
! [SV165: $i > $i > $o,SV322: $i,SV540: $i] :
( ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 )
| ~ ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2299,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2300,plain,
! [SV165: $i > $i > $o,SV322: $i,SV506: $i] :
( ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( ~ ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 ) )
= $true )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2301,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $true )
| ( ( ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2302,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2303,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2304,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 )
| ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2305,plain,
! [SV413: $i,SV529: $i,SV569: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV569 )
| ( SV529 = SV569 ) )
= $true )
| ( ( SV167 @ SV529 )
= $false )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2306,plain,
! [SV413: $i,SV541: $i,SV167: $i > $o] :
( ( ( SV167 @ SV541 )
= $false )
| ( ( ! [SY2569: $i] :
( ~ ( SV167 @ SY2569 )
| ( SV541 = SY2569 ) ) )
= $true )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2307,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( in @ ( sK31_B @ SV467 @ SV324 @ SV168 ) @ SV168 )
= $true )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2308,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( ( ~ SV467 ) = $true )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2309,plain,
! [SV168: $i,SV324: $i] :
( ( ( in @ ( sK31_B @ $true @ SV324 @ SV168 ) @ SV168 )
= $true )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2310,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2311,plain,
! [SV168: $i,SV324: $i] :
( ( ( in @ ( sK31_B @ $false @ SV324 @ SV168 ) @ SV168 )
= $true )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2312,plain,
! [SV168: $i,SV324: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2313,plain,
! [SV507: $i,SV542: $i] :
( ( ( in @ SV542 @ sK2_SY1590 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV507 @ SV542 ) @ sK3_SY1596 )
| ( sK4_SY1601 @ ( kpair @ SV507 @ SV542 ) ) )
= $true )
| ( ( in @ SV507 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2314,plain,
! [SV414: $i,SV530: $i,SV570: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV570 )
| ( SV530 = SV570 ) )
= $true )
| ( ( SV169 @ SV530 )
= $false )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2315,plain,
! [SV414: $i,SV543: $i,SV169: $i > $o] :
( ( ( SV169 @ SV543 )
= $false )
| ( ( ! [SY2570: $i] :
( ~ ( SV169 @ SY2570 )
| ( SV543 = SY2570 ) ) )
= $true )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2316,plain,
! [SV415: $i,SV325: $i,SV170: $i,SV544: $i] :
( ( ( in @ SV544 @ SV170 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2571: $i] : ( in @ ( kpair @ SV544 @ SY2571 ) @ SV415 ) ) )
@ SV325 )
= $true )
| ( ( in @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SV170 )
= $true )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2317,plain,
! [SV170: $i,SV415: $i,SV325: $i,SV531: $i] :
( ( ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) )
= $false )
| ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( ~ ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) ) )
= $true )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2318,plain,
! [SV514: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV171 )
= $false )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2319,plain,
! [SV171: $i,SV553: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV553 ) )
= $true )
| ( ( ~ ( in @ SV553 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2320,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2321,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2322,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( ! [SY2075: $i] :
( ~ ( SV172 @ SY2075 )
| ( ( sK46_SY216 @ SV172 )
= SY2075 ) ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2323,plain,
! [SV416: $i,SV172: $i > $o] :
( ( ( SV172 @ ( sK46_SY216 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2324,plain,
! [SV416: $i,SV554: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ SV554 ) )
= $true )
| ( ( ( sK46_SY216 @ SV172 )
= SV554 )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2325,plain,
! [SV515: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV515 )
= $false )
| ( ( in @ SV515 @ SV175 )
= $false )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2326,plain,
! [SV175: $i,SV555: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV555 ) )
= $true )
| ( ( ~ ( in @ SV555 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2327,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2328,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2329,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ SV176 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2330,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV176 )
| ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2331,plain,
! [SV179: $i,SV418: $i,SV331: $i,SV532: $i] :
( ( ( in @ SV532
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) )
= $false )
| ( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
= ( setadjoin @ SV532 @ emptyset ) )
= $false )
| ( ( ~ ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) ) )
= $true )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2332,plain,
! [SV180: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ omega ) )
= $true )
| ( ( in @ SV557 @ SV180 )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2333,plain,
! [SV180: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ omega ) )
= $true )
| ( ( in @ SV558 @ SV180 )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ SV180 )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2334,plain,
! [SV419: $i,SV332: $i,SV181: $i,SV545: $i] :
( ( ( in @ SV545 @ SV181 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2572: $i] : ( in @ ( kpair @ SV545 @ SY2572 ) @ SV419 ) ) )
@ SV332 )
= $true )
| ( ( in @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SV181 )
= $true )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2335,plain,
! [SV181: $i,SV419: $i,SV332: $i,SV534: $i] :
( ( ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) )
= $false )
| ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( ~ ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) ) )
= $true )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2336,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( SV422 = SV184 )
= $true )
| ( ( ( in @ SV422 @ SV333 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2337,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( SV422 = SV184 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2338,plain,
! [SV184: $i,SV333: $i,SV422: $i,SV572: $o] :
( ( ( ~ SV572
| ( in @ SV422 @ SV333 )
| SV572 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2241]) ).
thf(2339,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ $true
| ( in @ SV422 @ SV333 )
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2241]) ).
thf(2340,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ $false
| ( in @ SV422 @ SV333 )
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2241]) ).
thf(2341,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV573: $o] :
( ( ( ~ SV573
| ~ SV573
| SV573 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2242]) ).
thf(2342,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2242]) ).
thf(2343,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2242]) ).
thf(2344,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2243]) ).
thf(2345,plain,
! [SV187: $i > $o,SV336: $i > $o,SV517: $i] :
( ( ( SV517
!= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2244]) ).
thf(2346,plain,
! [SV187: $i > $o,SV336: $i > $o] :
( ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) )
| ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2347,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
| ~ ( ( SV574
!= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2348,plain,
! [SV423: $i,SV575: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ SV575 )
| ( ( sK21_Xx @ SV189 )
= SV575 ) )
= $true )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2349,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( ! [SY2131: $i] :
( ~ ( SV189 @ SY2131 )
| ( ( sK21_Xx @ SV189 )
= SY2131 ) ) )
= $true )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2350,plain,
! [SV423: $i,SV189: $i > $o] :
( ( ( SV189 @ ( sK21_Xx @ SV189 ) )
= $true )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2351,plain,
! [SV404: $i,SV141: $i > $o,SV559: $i] :
( ( ( SV559
!= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV141 @ SV559 )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2352,plain,
! [SV404: $i,SV560: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV560 ) )
= $true )
| ( ( SV560
= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2353,plain,
! [SV404: $i,SV141: $i > $o,SV576: $i] :
( ( ( ( SV576
!= ( sK32_Xx @ SV141 ) )
| ( SV141 @ SV576 ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2354,plain,
! [SV404: $i,SV577: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV577 )
| ( SV577
= ( sK32_Xx @ SV141 ) ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2355,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $false )
| ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2356,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2257]) ).
thf(2357,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( ~ ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2358,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2359,plain,
! [SV311: $i,SV521: $i,SV147: $i,SV511: $i] :
( ( ( in @ SV511 @ SV147 )
= $false )
| ( ( in @ SV521 @ SV311 )
= $true )
| ( ( SV511 = SV521 )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2360,plain,
! [SV147: $i,SV512: $i,SV311: $i,SV522: $i] :
( ( ( in @ SV522 @ SV311 )
= $false )
| ( ( in @ SV512 @ SV147 )
= $true )
| ( ( SV512 = SV522 )
= $false )
| ( ( SV147 = SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2361,plain,
! [SV408: $i,SV561: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV561 ) )
= $true )
| ( ( ( sK43_SY210 @ SV152 )
= SV561 )
= $true )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2362,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $false )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2363,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2364,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) )
| ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2365,plain,
! [SV154: $i,SV315: $i,SV523: $i] :
( ( ( in @ SV523 @ SV315 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV523 @ SV154 )
= $true )
| ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2366,plain,
! [SV315: $i,SV154: $i,SV524: $i,SV578: $o] :
( ( ( ~ SV578
| SV578 )
= $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2266]) ).
thf(2367,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2266]) ).
thf(2368,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2266]) ).
thf(2369,plain,
! [SV154: $i,SV315: $i,SV525: $i,SV562: $o] :
( ( ( ~ SV562 ) = $true )
| ( ( ( in @ SV525 @ SV315 )
| SV562 )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2370,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV525 @ SV315 )
| $true )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2371,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV525 @ SV315 )
| $false )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2372,plain,
! [SV315: $i,SV154: $i,SV537: $i,SV563: $o] :
( ( ( ~ SV563 ) = $true )
| ( ( ~ SV563
| SV563 )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2373,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2374,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2375,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV546: $i] :
( ( ( in @ SV546 @ SV409 )
= $false )
| ( ( SV490 @ SV546 )
= $true )
| ( ( in @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV155 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2376,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2377,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) ) )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2275]) ).
thf(2378,plain,
! [SV410: $i,SV564: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ SV564 ) )
= $true )
| ( ( ( sK41_SY203 @ SV156 )
= SV564 )
= $true )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2379,plain,
! [SV410: $i,SV579: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ SV579 )
| ( ( sK41_SY203 @ SV156 )
= SV579 ) )
= $true )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2380,plain,
! [SV157: $i,SV491: $i,SV526: $i,SV459: $i] :
( ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
!= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
= $false )
| ( ( in @ SV526 @ SV157 )
= $false )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2381,plain,
! [SV157: $i,SV459: $i,SV491: $i,SV526: $i] :
( ( ( ~ ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) ) )
= $false )
| ( ( in @ SV526 @ SV157 )
= $false )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2279]) ).
thf(2382,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( in @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) @ SV318 )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2383,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ~ ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2384,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV547: $i] :
( ( ( in @ SV547 @ SV160 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2385,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV160 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2386,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
| ~ ( ( SV548
!= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2387,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) ) )
= $true )
| ( ( ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2388,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2389,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
| ~ ( ( SV549
!= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2390,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) ) )
= $true )
| ( ( ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2391,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2392,plain,
! [SV550: $i,SV466: $i,SV163: $i] :
( ( ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2393,plain,
! [SV163: $i,SV466: $i,SV566: $i] :
( ( ( in @ SV566 @ SV466 )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( ~ ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2394,plain,
! [SV513: $i,SV163: $i,SV527: $i] :
( ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) )
| ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2292]) ).
thf(2395,plain,
! [SV163: $i,SV551: $i] :
( ( ( in @ SV551 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV551 )
| ( in @ SY2579 @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2293]) ).
thf(2396,plain,
! [SV567: $i,SV163: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV163 )
| ~ ( in @ SV567 @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SV567 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2397,plain,
! [SV164: $i,SV411: $i,SV538: $i,SV321: $i] :
( ( ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) ) )
= $false )
| ( ( in @ SV538 @ SV164 )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2398,plain,
! [SV528: $i,SV321: $i,SV164: $i,SV411: $i] :
( ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ! [SY2398: $i] :
( ~ ( in @ SY2398 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2399: $i] : ( in @ ( kpair @ SY2398 @ SY2399 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SY2398 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2400: $i] : ( in @ ( kpair @ SY2398 @ SY2400 ) @ SV411 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2399,plain,
! [SV322: $i,SV539: $i,SV568: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV568 @ SV539 ) )
= $true )
| ( ( ~ ( in @ SV568 @ SV322 ) )
= $true )
| ( ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2400,plain,
! [SV322: $i,SV540: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 )
| ~ ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2401,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2402,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( ~ ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2403,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV166 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2404,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2302]) ).
thf(2405,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2302]) ).
thf(2406,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2407,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2408,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2409,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2410,plain,
! [SV413: $i,SV529: $i,SV569: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV569 ) )
= $true )
| ( ( SV529 = SV569 )
= $true )
| ( ( SV167 @ SV529 )
= $false )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2411,plain,
! [SV413: $i,SV541: $i,SV580: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV580 )
| ( SV541 = SV580 ) )
= $true )
| ( ( SV167 @ SV541 )
= $false )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2412,plain,
! [SV168: $i,SV324: $i,SV467: $o] :
( ( SV467 = $false )
| ( SV467 = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2413,plain,
! [SV168: $i,SV324: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2414,plain,
! [SV168: $i,SV324: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV324 @ ( setunion @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2415,plain,
! [SV542: $i,SV507: $i] :
( ( ( ~ ( in @ ( kpair @ SV507 @ SV542 ) @ sK3_SY1596 ) )
= $true )
| ( ( sK4_SY1601 @ ( kpair @ SV507 @ SV542 ) )
= $true )
| ( ( in @ SV542 @ sK2_SY1590 )
= $false )
| ( ( in @ SV507 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2416,plain,
! [SV414: $i,SV530: $i,SV570: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV570 ) )
= $true )
| ( ( SV530 = SV570 )
= $true )
| ( ( SV169 @ SV530 )
= $false )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2417,plain,
! [SV414: $i,SV543: $i,SV581: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV581 )
| ( SV543 = SV581 ) )
= $true )
| ( ( SV169 @ SV543 )
= $false )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2418,plain,
! [SV531: $i,SV325: $i,SV170: $i,SV415: $i] :
( ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false )
| ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) )
= $false )
| ( ( ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2414: $i] : ( in @ ( kpair @ SY2413 @ SY2414 ) @ SV415 ) ) )
@ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2419,plain,
! [SV514: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $false )
| ( ( SV326 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV171 )
= $false )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2420,plain,
! [SV514: $i,SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV171 )
= $false )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2421,plain,
! [SV171: $i,SV553: $i,SV326: $i > $o] :
( ( ( SV326 @ SV553 )
= $false )
| ( ( ~ ( in @ SV553 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2422,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2423,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
| ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2424,plain,
! [SV416: $i,SV582: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ SV582 )
| ( ( sK46_SY216 @ SV172 )
= SV582 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2425,plain,
! [SV416: $i,SV554: $i,SV172: $i > $o] :
( ( ( SV172 @ SV554 )
= $false )
| ( ( ( sK46_SY216 @ SV172 )
= SV554 )
= $true )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2426,plain,
! [SV515: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $false )
| ( ( SV328 @ SV515 )
= $false )
| ( ( in @ SV515 @ SV175 )
= $false )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2427,plain,
! [SV515: $i,SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV515 )
= $false )
| ( ( in @ SV515 @ SV175 )
= $false )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2428,plain,
! [SV175: $i,SV555: $i,SV328: $i > $o] :
( ( ( SV328 @ SV555 )
= $false )
| ( ( ~ ( in @ SV555 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2429,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2430,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
| ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2431,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV556: $i] :
( ( ( in @ SV556 @ SV176 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2432,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV176 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2433,plain,
! [SV532: $i,SV331: $i,SV179: $i,SV418: $i] :
( ( ( subset @ SV418 @ ( cartprod @ SV179 @ SV331 ) )
= $false )
| ( ( ( dsetconstr @ SV331
@ ^ [SY2416: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2416 ) @ SV418 ) )
= ( setadjoin @ SV532 @ emptyset ) )
= $false )
| ( ( in @ SV532
@ ( dsetconstr @ SV331
@ ^ [SY2417: $i] : ( in @ ( kpair @ ( sK86_SY791 @ SV418 @ SV331 @ SV179 ) @ SY2417 ) @ SV418 ) ) )
= $false )
| ( ( in @ SV418 @ ( funcSet @ SV179 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2434,plain,
! [SV180: $i,SV557: $i] :
( ( ( in @ SV557 @ omega )
= $false )
| ( ( in @ SV557 @ SV180 )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2435,plain,
! [SV180: $i,SV558: $i] :
( ( ( in @ SV558 @ omega )
= $false )
| ( ( in @ SV558 @ SV180 )
= $true )
| ( ( in @ ( sK9_Xx @ SV180 ) @ SV180 )
= $true )
| ( ( in @ emptyset @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2436,plain,
! [SV534: $i,SV332: $i,SV181: $i,SV419: $i] :
( ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false )
| ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) )
= $false )
| ( ( ! [SY2421: $i] :
( ~ ( in @ SY2421 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2422: $i] : ( in @ ( kpair @ SY2421 @ SY2422 ) @ SV419 ) ) )
@ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2437,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( in @ SV422 @ SV333 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2438,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV583: $o] :
( ( ( ~ SV583
| SV583 )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2337]) ).
thf(2439,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2337]) ).
thf(2440,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2337]) ).
thf(2441,plain,
! [SV184: $i,SV333: $i,SV422: $i,SV572: $o] :
( ( ( ~ SV572 ) = $true )
| ( ( ( in @ SV422 @ SV333 )
| SV572 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2442,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV422 @ SV333 )
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2443,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV422 @ SV333 )
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2444,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV573: $o] :
( ( ( ~ SV573 ) = $true )
| ( ( ~ SV573
| SV573 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2445,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2446,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2447,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( SV187 @ SV517 )
= $false )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2448,plain,
! [SV187: $i > $o,SV336: $i > $o,SV517: $i] :
( ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV187 @ SV517 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2449,plain,
! [SV336: $i > $o,SV187: $i > $o] :
( ( ( ! [SY2340: $i] :
( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) )
| ~ ( ( SY2340
!= ( sK59_SY262 @ SY2340 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SY2340 ) ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2450,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
| ~ ( ( SV574
!= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2451,plain,
! [SV423: $i,SV575: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ SV575 ) )
= $true )
| ( ( ( sK21_Xx @ SV189 )
= SV575 )
= $true )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2452,plain,
! [SV423: $i,SV584: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ SV584 )
| ( ( sK21_Xx @ SV189 )
= SV584 ) )
= $true )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2453,plain,
! [SV404: $i,SV141: $i > $o,SV559: $i] :
( ( ( SV559
= ( sK32_Xx @ SV141 ) )
= $false )
| ( ( SV141 @ SV559 )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2454,plain,
! [SV404: $i,SV560: $i,SV141: $i > $o] :
( ( ( SV141 @ SV560 )
= $false )
| ( ( SV560
= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK33_SY147 @ SV404 @ SV141 ) )
= $true )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2455,plain,
! [SV404: $i,SV141: $i > $o,SV576: $i] :
( ( ( SV576
!= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV141 @ SV576 )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2456,plain,
! [SV404: $i,SV577: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV577 ) )
= $true )
| ( ( SV577
= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2457,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $true )
| ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2458,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) )
= $true )
| ( ( in @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) @ SV144 )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2459,plain,
! [SV144: $i,SV405: $i,SV308: $i > $o] :
( ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2357]) ).
thf(2460,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
!= SV405 )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2461,plain,
! [SV408: $i,SV561: $i,SV152: $i > $o] :
( ( ( SV152 @ SV561 )
= $false )
| ( ( ( sK43_SY210 @ SV152 )
= SV561 )
= $true )
| ( ( SV152 @ ( sK44_Xx @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2462,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $true )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2463,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ ( sK43_SY210 @ SV152 ) )
= $true )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2464,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $false )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2465,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ ( sK43_SY210 @ SV152 ) ) )
= $false )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2466,plain,
! [SV154: $i,SV315: $i,SV523: $i,SV585: $o] :
( ( SV585 = $true )
| ( ( in @ SV523 @ SV315 )
= $true )
| ( ( in @ SV523 @ SV154 )
= $true )
| ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2365]) ).
thf(2467,plain,
! [SV154: $i,SV315: $i,SV523: $i] :
( ( $true = $true )
| ( ( in @ SV523 @ SV315 )
= $true )
| ( ( in @ SV523 @ SV154 )
= $true )
| ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2365]) ).
thf(2468,plain,
! [SV154: $i,SV315: $i,SV523: $i] :
( ( $false = $true )
| ( ( in @ SV523 @ SV315 )
= $true )
| ( ( in @ SV523 @ SV154 )
= $true )
| ( ( in @ SV523 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2365]) ).
thf(2469,plain,
! [SV315: $i,SV154: $i,SV524: $i,SV578: $o] :
( ( ( ~ SV578 ) = $true )
| ( SV578 = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2470,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2471,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2472,plain,
! [SV154: $i,SV315: $i,SV525: $i,SV562: $o] :
( ( SV562 = $false )
| ( ( ( in @ SV525 @ SV315 )
| SV562 )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2473,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( $true = $false )
| ( ( ( in @ SV525 @ SV315 )
| $true )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2474,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( $false = $false )
| ( ( ( in @ SV525 @ SV315 )
| $false )
= $true )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2475,plain,
! [SV315: $i,SV154: $i,SV537: $i,SV563: $o] :
( ( SV563 = $false )
| ( ( ~ SV563
| SV563 )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2476,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2477,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2478,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV409 )
| ( SV490 @ SV586 ) )
= $true )
| ( ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2479,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
| ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2480,plain,
! [SV410: $i,SV564: $i,SV156: $i > $o] :
( ( ( SV156 @ SV564 )
= $false )
| ( ( ( sK41_SY203 @ SV156 )
= SV564 )
= $true )
| ( ( SV156 @ ( sK42_Xy @ SV410 @ SV156 ) )
= $true )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2481,plain,
! [SV410: $i,SV579: $i,SV156: $i > $o] :
( ( ( ~ ( SV156 @ SV579 ) )
= $true )
| ( ( ( sK41_SY203 @ SV156 )
= SV579 )
= $true )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2482,plain,
! [SV157: $i,SV491: $i,SV526: $i,SV459: $i] :
( ( ( ( dsetconstr @ SV459
@ ^ [SY2552: $i] : ( in @ ( kpair @ SV526 @ SY2552 ) @ SV491 ) )
= ( setadjoin @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 ) @ emptyset ) )
= $true )
| ( ( in @ SV526 @ SV157 )
= $false )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2483,plain,
! [SV157: $i,SV459: $i,SV491: $i,SV526: $i] :
( ( ( in @ ( sK85_SY753 @ SV526 @ SV491 @ SV459 @ SV157 )
@ ( dsetconstr @ SV459
@ ^ [SY2553: $i] : ( in @ ( kpair @ SV526 @ SY2553 ) @ SV491 ) ) )
= $true )
| ( ( in @ SV526 @ SV157 )
= $false )
| ( ( in @ SV491 @ ( funcSet @ SV157 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2484,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2485,plain,
! [SV494: $i > $i,SV160: $i,SV547: $i,SV462: $i] :
( ( ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) )
= $false )
| ( ( in @ SV547 @ SV160 )
= $false )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2486,plain,
! [SV494: $i > $i,SV462: $i,SV160: $i,SV565: $i] :
( ( ( in @ SV565 @ SV160 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2487,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) ) )
= $false )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2488,plain,
! [SV439: $i > $o,SV464: $i > $o,SV548: $i] :
( ( ( ~ ( ( SV548
!= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2489,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) ) )
= $true )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2490,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2491,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) ) )
= $false )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2492,plain,
! [SV440: $i > $o,SV465: $i > $o,SV549: $i] :
( ( ( ~ ( ( SV549
!= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2493,plain,
! [SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) ) )
= $true )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2494,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2495,plain,
! [SV550: $i,SV466: $i,SV163: $i] :
( ( ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2496,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2497,plain,
! [SV566: $i,SV466: $i,SV163: $i] :
( ( ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2498,plain,
! [SV163: $i,SV527: $i,SV513: $i] :
( ( ( ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV513 )
| ( in @ SY2554 @ SV527 ) ) )
= $true )
| ( ( ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2499,plain,
! [SV163: $i,SV551: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV551 )
| ( in @ SV587 @ SV163 ) )
= $true )
| ( ( in @ SV551 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2500,plain,
! [SV567: $i,SV163: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV163 ) )
= $true )
| ( ( ~ ( in @ SV567 @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SV567 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2501,plain,
! [SV164: $i,SV411: $i,SV538: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
= $false )
| ( ( in @ SV538 @ SV164 )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2502,plain,
! [SV164: $i,SV321: $i,SV411: $i,SV538: $i] :
( ( ( ~ ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) ) )
= $false )
| ( ( in @ SV538 @ SV164 )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2503,plain,
! [SV528: $i,SV411: $i,SV321: $i,SV164: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV164 )
| ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2504,plain,
! [SV322: $i,SV539: $i,SV568: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ SV568 @ SV539 )
= $false )
| ( ( ~ ( in @ SV568 @ SV322 ) )
= $true )
| ( ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2505,plain,
! [SV322: $i,SV540: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 ) )
= $false )
| ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2506,plain,
! [SV165: $i > $i > $o,SV322: $i,SV540: $i] :
( ( ( ~ ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2507,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2401]) ).
thf(2508,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2401]) ).
thf(2509,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) )
| ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2510,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2511,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ( in @ SV412 @ SV166 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2512,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ( in @ SV412 @ SV166 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2513,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 )
| ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2514,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2515,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ! [SY2407: $o] :
( ~ SY2407
| ~ ( in @ SV412 @ SV166 )
| SY2407 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2516,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2517,plain,
! [SV413: $i,SV529: $i,SV569: $i,SV167: $i > $o] :
( ( ( SV167 @ SV569 )
= $false )
| ( ( SV529 = SV569 )
= $true )
| ( ( SV167 @ SV529 )
= $false )
| ( ( SV167 @ ( sK48_SY229 @ SV413 @ SV167 ) )
= $true )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2518,plain,
! [SV413: $i,SV541: $i,SV580: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV580 ) )
= $true )
| ( ( SV541 = SV580 )
= $true )
| ( ( SV167 @ SV541 )
= $false )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2519,plain,
! [SV542: $i,SV507: $i] :
( ( ( in @ ( kpair @ SV507 @ SV542 ) @ sK3_SY1596 )
= $false )
| ( ( sK4_SY1601 @ ( kpair @ SV507 @ SV542 ) )
= $true )
| ( ( in @ SV542 @ sK2_SY1590 )
= $false )
| ( ( in @ SV507 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2520,plain,
! [SV414: $i,SV530: $i,SV570: $i,SV169: $i > $o] :
( ( ( SV169 @ SV570 )
= $false )
| ( ( SV530 = SV570 )
= $true )
| ( ( SV169 @ SV530 )
= $false )
| ( ( SV169 @ ( sK57_SY253 @ SV414 @ SV169 ) )
= $true )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2521,plain,
! [SV414: $i,SV543: $i,SV581: $i,SV169: $i > $o] :
( ( ( ~ ( SV169 @ SV581 ) )
= $true )
| ( ( SV543 = SV581 )
= $true )
| ( ( SV169 @ SV543 )
= $false )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2522,plain,
! [SV531: $i,SV415: $i,SV325: $i,SV170: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV170 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2601: $i] : ( in @ ( kpair @ SV589 @ SY2601 ) @ SV415 ) ) )
@ SV325 ) )
= $true )
| ( ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) )
= $false )
| ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2523,plain,
! [SV514: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $true )
| ( ( SV326 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV171 )
= $false )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2524,plain,
! [SV514: $i,SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) )
= $true )
| ( ( SV326 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV171 )
= $false )
| ( ( in @ ( sK77_Xx @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2525,plain,
! [SV326: $i > $o,SV171: $i,SV553: $i] :
( ( ( in @ SV553 @ SV171 )
= $false )
| ( ( SV326 @ SV553 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2526,plain,
! [SV171: $i,SV590: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV590 )
| ~ ( in @ SV590 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2527,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2528,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ~ ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) ) ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2529,plain,
! [SV416: $i,SV582: $i,SV172: $i > $o] :
( ( ( ~ ( SV172 @ SV582 ) )
= $true )
| ( ( ( sK46_SY216 @ SV172 )
= SV582 )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2530,plain,
! [SV515: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $true )
| ( ( SV328 @ SV515 )
= $false )
| ( ( in @ SV515 @ SV175 )
= $false )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2426]) ).
thf(2531,plain,
! [SV515: $i,SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) )
= $true )
| ( ( SV328 @ SV515 )
= $false )
| ( ( in @ SV515 @ SV175 )
= $false )
| ( ( in @ ( sK71_Xx @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2427]) ).
thf(2532,plain,
! [SV328: $i > $o,SV175: $i,SV555: $i] :
( ( ( in @ SV555 @ SV175 )
= $false )
| ( ( SV328 @ SV555 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2533,plain,
! [SV175: $i,SV591: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV591 )
| ~ ( in @ SV591 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2534,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2535,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ~ ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) ) ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2430]) ).
thf(2536,plain,
! [SV496: $i > $i,SV176: $i,SV556: $i,SV470: $i] :
( ( ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) )
= $false )
| ( ( in @ SV556 @ SV176 )
= $false )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2537,plain,
! [SV496: $i > $i,SV470: $i,SV176: $i,SV571: $i] :
( ( ( in @ SV571 @ SV176 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2538,plain,
! [SV534: $i,SV419: $i,SV332: $i,SV181: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV181 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2602: $i] : ( in @ ( kpair @ SV592 @ SY2602 ) @ SV419 ) ) )
@ SV332 ) )
= $true )
| ( ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) )
= $false )
| ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2539,plain,
! [SV184: $i,SV333: $i,SV422: $i,SV593: $o] :
( ( SV593 = $true )
| ( ( in @ SV422 @ SV333 )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2437]) ).
thf(2540,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( $true = $true )
| ( ( in @ SV422 @ SV333 )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2437]) ).
thf(2541,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( $false = $true )
| ( ( in @ SV422 @ SV333 )
= $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2437]) ).
thf(2542,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV583: $o] :
( ( ( ~ SV583 ) = $true )
| ( SV583 = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2543,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2544,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2545,plain,
! [SV184: $i,SV333: $i,SV422: $i,SV572: $o] :
( ( SV572 = $false )
| ( ( ( in @ SV422 @ SV333 )
| SV572 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2546,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( $true = $false )
| ( ( ( in @ SV422 @ SV333 )
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2547,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( $false = $false )
| ( ( ( in @ SV422 @ SV333 )
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2548,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV573: $o] :
( ( SV573 = $false )
| ( ( ~ SV573
| SV573 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2549,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2550,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2551,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2552,plain,
! [SV336: $i > $o,SV517: $i,SV187: $i > $o] :
( ( ( SV187 @ SV517 )
= $false )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2553,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
| ~ ( ( SV594
!= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) ) ) )
| ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2554,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
| ~ ( ( SV574
!= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2555,plain,
! [SV423: $i,SV575: $i,SV189: $i > $o] :
( ( ( SV189 @ SV575 )
= $false )
| ( ( ( sK21_Xx @ SV189 )
= SV575 )
= $true )
| ( ( SV189 @ ( sK22_SY79 @ SV423 @ SV189 ) )
= $true )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2556,plain,
! [SV423: $i,SV584: $i,SV189: $i > $o] :
( ( ( ~ ( SV189 @ SV584 ) )
= $true )
| ( ( ( sK21_Xx @ SV189 )
= SV584 )
= $true )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2557,plain,
! [SV404: $i,SV141: $i > $o,SV576: $i] :
( ( ( SV576
= ( sK32_Xx @ SV141 ) )
= $false )
| ( ( SV141 @ SV576 )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2558,plain,
! [SV404: $i,SV577: $i,SV141: $i > $o] :
( ( ( SV141 @ SV577 )
= $false )
| ( ( SV577
= ( sK32_Xx @ SV141 ) )
= $true )
| ( ( SV404
= ( sK33_SY147 @ SV404 @ SV141 ) )
= $false )
| ( ( SV141 @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2559,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2560,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2561,plain,
! [SV408: $i,SV595: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV595 )
| ( ( sK43_SY210 @ SV152 )
= SV595 ) )
= $true )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2562,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( ! [SY1971: $i] :
( ~ ( SV152 @ SY1971 )
| ( ( sK43_SY210 @ SV152 )
= SY1971 ) ) )
= $true )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2563,plain,
! [SV408: $i,SV152: $i > $o] :
( ( ( SV152 @ ( sK43_SY210 @ SV152 ) )
= $true )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2564,plain,
! [SV315: $i,SV154: $i,SV524: $i,SV578: $o] :
( ( SV578 = $false )
| ( SV578 = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2565,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2566,plain,
! [SV315: $i,SV154: $i,SV524: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV524 @ SV154 )
= $true )
| ( ( in @ SV524 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2567,plain,
! [SV154: $i,SV562: $o,SV315: $i,SV525: $i] :
( ( ( in @ SV525 @ SV315 )
= $true )
| ( SV562 = $true )
| ( SV562 = $false )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2568,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( in @ SV525 @ SV315 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2569,plain,
! [SV154: $i,SV315: $i,SV525: $i] :
( ( ( in @ SV525 @ SV315 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV525 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2570,plain,
! [SV315: $i,SV154: $i,SV537: $i,SV563: $o] :
( ( ( ~ SV563 ) = $true )
| ( SV563 = $true )
| ( SV563 = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2571,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2572,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2573,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV409 ) )
= $true )
| ( ( SV490 @ SV586 )
= $true )
| ( ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2574,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2575,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2576,plain,
! [SV410: $i,SV579: $i,SV156: $i > $o] :
( ( ( SV156 @ SV579 )
= $false )
| ( ( ( sK41_SY203 @ SV156 )
= SV579 )
= $true )
| ( ( SV410
= ( sK42_Xy @ SV410 @ SV156 ) )
= $false )
| ( ( SV156 @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2577,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
!= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2578,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2484]) ).
thf(2579,plain,
! [SV494: $i > $i,SV160: $i,SV547: $i,SV462: $i] :
( ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
= $false )
| ( ( in @ SV547 @ SV160 )
= $false )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2580,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i,SV547: $i] :
( ( ( ~ ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) )
= $false )
| ( ( in @ SV547 @ SV160 )
= $false )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2581,plain,
! [SV494: $i > $i,SV160: $i,SV565: $i,SV462: $i] :
( ( ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
| ~ ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) )
= $false )
| ( ( in @ SV565 @ SV160 )
= $false )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2582,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2583,plain,
! [SV439: $i > $o,SV464: $i > $o,SV548: $i] :
( ( ( SV548
!= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2584,plain,
! [SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) )
| ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2585,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
| ~ ( ( SV596
!= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2586,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2587,plain,
! [SV440: $i > $o,SV465: $i > $o,SV549: $i] :
( ( ( SV549
!= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2588,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) )
| ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2589,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
| ~ ( ( SV597
!= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2590,plain,
! [SV550: $i,SV466: $i,SV163: $i] :
( ( ( ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2591,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2592,plain,
! [SV566: $i,SV466: $i,SV163: $i] :
( ( ( ~ ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2593,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2594,plain,
! [SV163: $i,SV527: $i,SV513: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV513 )
| ( in @ SV598 @ SV527 ) )
= $true )
| ( ( ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2595,plain,
! [SV163: $i,SV551: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV551 ) )
= $true )
| ( ( in @ SV587 @ SV163 )
= $true )
| ( ( in @ SV551 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2596,plain,
! [SV567: $i,SV163: $i,SV552: $i] :
( ( ( in @ SV552 @ SV163 )
= $false )
| ( ( ~ ( in @ SV567 @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SV567 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2597,plain,
! [SV164: $i,SV411: $i,SV538: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2566: $i] : ( in @ ( kpair @ SV538 @ SY2566 ) @ SV411 ) )
= ( setadjoin @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
= $true )
| ( ( in @ SV538 @ SV164 )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2501]) ).
thf(2598,plain,
! [SV164: $i,SV321: $i,SV411: $i,SV538: $i] :
( ( ( in @ ( sK81_SY667 @ SV538 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2567: $i] : ( in @ ( kpair @ SV538 @ SY2567 ) @ SV411 ) ) )
= $true )
| ( ( in @ SV538 @ SV164 )
= $false )
| ( ( in @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SV164 )
= $true )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2599,plain,
! [SV528: $i,SV411: $i,SV321: $i,SV164: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV164 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2600,plain,
! [SV539: $i,SV165: $i > $i > $o,SV322: $i,SV568: $i] :
( ( ( in @ SV568 @ SV322 )
= $false )
| ( ( SV165 @ SV568 @ SV539 )
= $false )
| ( ( in @ SV539 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2601,plain,
! [SV322: $i,SV540: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV540 )
= $true )
| ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2602,plain,
! [SV165: $i > $i > $o,SV322: $i,SV540: $i] :
( ( ( in @ ( sK11_Xy @ SV540 @ SV322 @ SV165 ) @ SV322 )
= $true )
| ( ( in @ SV540 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( in @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV322 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2603,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2604,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i] :
( ( ( ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2605,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ~ ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2606,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i] :
( ( ( ~ ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2607,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV599: $o] :
( ( SV599 = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2510]) ).
thf(2608,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2510]) ).
thf(2609,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2510]) ).
thf(2610,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $true )
| ( ( ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2611,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2612,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 ) )
= $true )
| ( ( ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2613,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2614,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV600: $o] :
( ( ( ~ SV600
| ~ ( in @ SV412 @ SV166 )
| SV600 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2515]) ).
thf(2615,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true
| ~ ( in @ SV412 @ SV166 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2515]) ).
thf(2616,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false
| ~ ( in @ SV412 @ SV166 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2515]) ).
thf(2617,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2618,plain,
! [SV413: $i,SV541: $i,SV580: $i,SV167: $i > $o] :
( ( ( SV167 @ SV580 )
= $false )
| ( ( SV541 = SV580 )
= $true )
| ( ( SV167 @ SV541 )
= $false )
| ( ( SV413
= ( sK48_SY229 @ SV413 @ SV167 ) )
= $false )
| ( ( SV167 @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2619,plain,
! [SV414: $i,SV543: $i,SV581: $i,SV169: $i > $o] :
( ( ( SV169 @ SV581 )
= $false )
| ( ( SV543 = SV581 )
= $true )
| ( ( SV169 @ SV543 )
= $false )
| ( ( SV414
= ( sK57_SY253 @ SV414 @ SV169 ) )
= $false )
| ( ( SV169 @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2620,plain,
! [SV531: $i,SV415: $i,SV325: $i,SV170: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV170 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2601: $i] : ( in @ ( kpair @ SV589 @ SY2601 ) @ SV415 ) ) )
@ SV325 )
= $true )
| ( ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) )
= $false )
| ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2621,plain,
! [SV553: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2622,plain,
! [SV171: $i,SV590: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV590 ) )
= $true )
| ( ( ~ ( in @ SV590 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2623,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2527]) ).
thf(2624,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ( sK77_Xx @ SV326 @ SV171 )
!= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2625,plain,
! [SV416: $i,SV582: $i,SV172: $i > $o] :
( ( ( SV172 @ SV582 )
= $false )
| ( ( ( sK46_SY216 @ SV172 )
= SV582 )
= $true )
| ( ( ( sK47_Xy @ SV416 @ SV172 )
= SV416 )
= $false )
| ( ( SV172 @ ( sK47_Xy @ SV416 @ SV172 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2626,plain,
! [SV555: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV555 )
= $false )
| ( ( in @ SV555 @ SV175 )
= $false )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2627,plain,
! [SV175: $i,SV591: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV591 ) )
= $true )
| ( ( ~ ( in @ SV591 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2628,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2629,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ( sK71_Xx @ SV328 @ SV175 )
!= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2630,plain,
! [SV496: $i > $i,SV176: $i,SV556: $i,SV470: $i] :
( ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
= $false )
| ( ( in @ SV556 @ SV176 )
= $false )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2631,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i,SV556: $i] :
( ( ( ~ ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) )
= $false )
| ( ( in @ SV556 @ SV176 )
= $false )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2536]) ).
thf(2632,plain,
! [SV496: $i > $i,SV176: $i,SV571: $i,SV470: $i] :
( ( ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
| ~ ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) )
= $false )
| ( ( in @ SV571 @ SV176 )
= $false )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2633,plain,
! [SV534: $i,SV419: $i,SV332: $i,SV181: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV181 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2602: $i] : ( in @ ( kpair @ SV592 @ SY2602 ) @ SV419 ) ) )
@ SV332 )
= $true )
| ( ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) )
= $false )
| ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2634,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV583: $o] :
( ( SV583 = $false )
| ( SV583 = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2635,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2636,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV422 = SV184 )
= $true )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2637,plain,
! [SV184: $i,SV572: $o,SV333: $i,SV422: $i] :
( ( ( in @ SV422 @ SV333 )
= $true )
| ( SV572 = $true )
| ( SV572 = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2638,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( in @ SV422 @ SV333 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2639,plain,
! [SV184: $i,SV333: $i,SV422: $i] :
( ( ( in @ SV422 @ SV333 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2640,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV573: $o] :
( ( ( ~ SV573 ) = $true )
| ( SV573 = $true )
| ( SV573 = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(2641,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2549]) ).
thf(2642,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2643,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
| ~ ( ( SV601
!= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2644,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2645,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( ~ ( ~ ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
| ~ ( ( SV594
!= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2646,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2554]) ).
thf(2647,plain,
! [SV187: $i > $o,SV336: $i > $o,SV574: $i] :
( ( ( ~ ( ( SV574
!= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2554]) ).
thf(2648,plain,
! [SV423: $i,SV584: $i,SV189: $i > $o] :
( ( ( SV189 @ SV584 )
= $false )
| ( ( ( sK21_Xx @ SV189 )
= SV584 )
= $true )
| ( ( SV423
= ( sK22_SY79 @ SV423 @ SV189 ) )
= $false )
| ( ( SV189 @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2649,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $false )
| ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2650,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2559]) ).
thf(2651,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
| ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2652,plain,
! [SV408: $i,SV595: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV595 ) )
= $true )
| ( ( ( sK43_SY210 @ SV152 )
= SV595 )
= $true )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2653,plain,
! [SV408: $i,SV602: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV602 )
| ( ( sK43_SY210 @ SV152 )
= SV602 ) )
= $true )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2654,plain,
! [SV315: $i,SV154: $i,SV537: $i,SV563: $o] :
( ( SV563 = $false )
| ( SV563 = $true )
| ( SV563 = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2655,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2656,plain,
! [SV315: $i,SV154: $i,SV537: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV537 @ ( binunion @ SV154 @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2657,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV586: $i] :
( ( ( in @ SV586 @ SV409 )
= $false )
| ( ( SV490 @ SV586 )
= $true )
| ( ( in @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) @ SV316 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2658,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2574]) ).
thf(2659,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( ~ ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) ) )
= $true )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2575]) ).
thf(2660,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 )
= ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2577]) ).
thf(2661,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2662,plain,
! [SV494: $i > $i,SV160: $i,SV547: $i,SV462: $i] :
( ( ( ( dsetconstr @ SV462
@ ^ [SY2573: $i] :
( in @ ( kpair @ SV547 @ SY2573 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
= ( setadjoin @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
= $true )
| ( ( in @ SV547 @ SV160 )
= $false )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2663,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i,SV547: $i] :
( ( ( in @ ( sK88_SY820 @ SV547 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2576: $i] :
( in @ ( kpair @ SV547 @ SY2576 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) )
= $true )
| ( ( in @ SV547 @ SV160 )
= $false )
| ( ( in @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) @ SV160 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2664,plain,
! [SV494: $i > $i,SV160: $i,SV565: $i,SV462: $i] :
( ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
!= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
= $false )
| ( ( in @ SV565 @ SV160 )
= $false )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2665,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i,SV565: $i] :
( ( ( ~ ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) ) )
= $false )
| ( ( in @ SV565 @ SV160 )
= $false )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2666,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( SV439 @ SV548 )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2667,plain,
! [SV439: $i > $o,SV464: $i > $o,SV548: $i] :
( ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( SV439 @ SV548 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2668,plain,
! [SV464: $i > $o,SV439: $i > $o] :
( ( ( ! [SY2485: $i] :
( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) )
| ~ ( ( SY2485
!= ( sK54_SY238 @ SY2485 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SY2485 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2669,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
| ~ ( ( SV596
!= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) ) ) ) )
= $true )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2670,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( SV465 @ SV549 )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2671,plain,
! [SV440: $i > $o,SV465: $i > $o,SV549: $i] :
( ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( SV465 @ SV549 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2672,plain,
! [SV440: $i > $o,SV465: $i > $o] :
( ( ( ! [SY2487: $i] :
( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) )
| ~ ( ( SY2487
!= ( sK50_SY241 @ SY2487 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SY2487 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2673,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
| ~ ( ( SV597
!= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) ) ) ) )
= $true )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2674,plain,
! [SV550: $i,SV466: $i,SV163: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ ( sK15_B @ SV163 ) )
| ! [SY2603: $i] :
( ~ ( in @ SY2603 @ SV603 )
| ( in @ SY2603 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2675,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2676,plain,
! [SV566: $i,SV466: $i,SV163: $i] :
( ( ( ! [SY2490: $i] :
( ~ ( in @ SY2490 @ ( sK15_B @ SV163 ) )
| ! [SY2491: $i] :
( ~ ( in @ SY2491 @ SY2490 )
| ( in @ SY2491 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SY2490 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2677,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2593]) ).
thf(2678,plain,
! [SV163: $i,SV527: $i,SV513: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV513 ) )
= $true )
| ( ( in @ SV598 @ SV527 )
= $true )
| ( ( ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2679,plain,
! [SV163: $i,SV551: $i,SV587: $i] :
( ( ( in @ SV587 @ SV551 )
= $false )
| ( ( in @ SV587 @ SV163 )
= $true )
| ( ( in @ SV551 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2680,plain,
! [SV552: $i,SV163: $i,SV567: $i] :
( ( ( in @ SV567 @ SV163 )
= $false )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
| ( SV552 = SV567 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2681,plain,
! [SV528: $i,SV411: $i,SV321: $i,SV164: $i,SV588: $i] :
( ( ( in @ SV588 @ SV164 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) ) ) )
= $true )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2682,plain,
! [SV506: $i,SV322: $i,SV604: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2604: $i] :
( ~ ( SV165 @ SY2604 @ SV604 )
| ~ ( in @ SY2604 @ SV322 ) )
| ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2683,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 )
| ~ ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(2684,plain,
! [SV506: $i,SV322: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2297: $i] :
( ! [SY2298: $i] :
( ~ ( SV165 @ SY2298 @ SY2297 )
| ~ ( in @ SY2298 @ SV322 ) )
| ( in @ SY2297 @ ( sK10_B @ SV322 @ SV165 ) ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2685,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i] :
( ( ( ! [SY2299: $i] :
( ~ ( in @ SY2299 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SY2299 )
| ~ ( in @ ( sK11_Xy @ SY2299 @ SV322 @ SV165 ) @ SV322 ) ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2686,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2687,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV606: $o] :
( ( ( ~ SV606
| SV606 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2611]) ).
thf(2688,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2611]) ).
thf(2689,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2611]) ).
thf(2690,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $false )
| ( ( ~ ( in @ SV412 @ SV166 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2691,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2692,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2693,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV600: $o] :
( ( ( ~ SV600 ) = $true )
| ( ( ~ ( in @ SV412 @ SV166 )
| SV600 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2694,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ ( in @ SV412 @ SV166 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2695,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ ( in @ SV412 @ SV166 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2696,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2697,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2698,plain,
! [SV531: $i,SV415: $i,SV325: $i,SV170: $i,SV589: $i] :
( ( ( in @ SV589 @ SV170 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV325
@ ^ [SY2601: $i] : ( in @ ( kpair @ SV589 @ SY2601 ) @ SV415 ) ) )
@ SV325 )
= $true )
| ( ( in @ SV531
@ ( dsetconstr @ SV325
@ ^ [SY2412: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2412 ) @ SV415 ) ) )
= $false )
| ( ( ( dsetconstr @ SV325
@ ^ [SY2411: $i] : ( in @ ( kpair @ ( sK83_SY689 @ SV415 @ SV325 @ SV170 ) @ SY2411 ) @ SV415 ) )
= ( setadjoin @ SV531 @ emptyset ) )
= $false )
| ( ( subset @ SV415 @ ( cartprod @ SV170 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2699,plain,
! [SV553: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $false )
| ( ( SV326 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2700,plain,
! [SV553: $i,SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2701,plain,
! [SV171: $i,SV590: $i,SV326: $i > $o] :
( ( ( SV326 @ SV590 )
= $false )
| ( ( ~ ( in @ SV590 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2702,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(2703,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false )
| ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) )
| ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2704,plain,
! [SV555: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $false )
| ( ( SV328 @ SV555 )
= $false )
| ( ( in @ SV555 @ SV175 )
= $false )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2705,plain,
! [SV555: $i,SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV555 )
= $false )
| ( ( in @ SV555 @ SV175 )
= $false )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2706,plain,
! [SV175: $i,SV591: $i,SV328: $i > $o] :
( ( ( SV328 @ SV591 )
= $false )
| ( ( ~ ( in @ SV591 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2707,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2708,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false )
| ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) )
| ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2709,plain,
! [SV496: $i > $i,SV176: $i,SV556: $i,SV470: $i] :
( ( ( ( dsetconstr @ SV470
@ ^ [SY2581: $i] :
( in @ ( kpair @ SV556 @ SY2581 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
= ( setadjoin @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
= $true )
| ( ( in @ SV556 @ SV176 )
= $false )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2710,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i,SV556: $i] :
( ( ( in @ ( sK91_SY856 @ SV556 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2584: $i] :
( in @ ( kpair @ SV556 @ SY2584 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) )
= $true )
| ( ( in @ SV556 @ SV176 )
= $false )
| ( ( in @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) @ SV176 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2711,plain,
! [SV496: $i > $i,SV176: $i,SV571: $i,SV470: $i] :
( ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
!= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
= $false )
| ( ( in @ SV571 @ SV176 )
= $false )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2712,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i,SV571: $i] :
( ( ( ~ ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) ) )
= $false )
| ( ( in @ SV571 @ SV176 )
= $false )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2713,plain,
! [SV534: $i,SV419: $i,SV332: $i,SV181: $i,SV592: $i] :
( ( ( in @ SV592 @ SV181 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV332
@ ^ [SY2602: $i] : ( in @ ( kpair @ SV592 @ SY2602 ) @ SV419 ) ) )
@ SV332 )
= $true )
| ( ( in @ SV534
@ ( dsetconstr @ SV332
@ ^ [SY2420: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2420 ) @ SV419 ) ) )
= $false )
| ( ( ( dsetconstr @ SV332
@ ^ [SY2419: $i] : ( in @ ( kpair @ ( sK84_SY716 @ SV419 @ SV332 @ SV181 ) @ SY2419 ) @ SV419 ) )
= ( setadjoin @ SV534 @ emptyset ) )
= $false )
| ( ( subset @ SV419 @ ( cartprod @ SV181 @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2714,plain,
! [SV333: $i,SV184: $i,SV422: $i,SV573: $o] :
( ( SV573 = $false )
| ( SV573 = $true )
| ( SV573 = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2715,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2716,plain,
! [SV333: $i,SV184: $i,SV422: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV422 @ ( setadjoin @ SV184 @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2717,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
| ~ ( ( SV601
!= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2718,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
| ~ ( ( SV607
!= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(2719,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
| ~ ( ( SV594
!= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2720,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2721,plain,
! [SV187: $i > $o,SV336: $i > $o,SV574: $i] :
( ( ( SV574
!= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2722,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $true )
| ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2723,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) )
= $true )
| ( ( SV308 @ ( sK75_Xy @ SV405 @ SV308 @ SV144 ) )
= $true )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2724,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
!= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $false )
| ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2651]) ).
thf(2725,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( ~ ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) ) )
= $false )
| ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2651]) ).
thf(2726,plain,
! [SV408: $i,SV595: $i,SV152: $i > $o] :
( ( ( SV152 @ SV595 )
= $false )
| ( ( ( sK43_SY210 @ SV152 )
= SV595 )
= $true )
| ( ( SV152 @ ( sK45_SY1644 @ SV152 ) )
= $true )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2727,plain,
! [SV408: $i,SV602: $i,SV152: $i > $o] :
( ( ( ~ ( SV152 @ SV602 ) )
= $true )
| ( ( ( sK43_SY210 @ SV152 )
= SV602 )
= $true )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2728,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV409 )
| ( SV490 @ SV608 ) )
= $true )
| ( ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(2729,plain,
! [SV155: $i,SV316: $i,SV409: $i,SV490: $i > $o] :
( ( ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) )
= $false )
| ( ( ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV409 )
| ( SV490 @ SY2513 ) ) )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2730,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
| ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2731,plain,
! [SV494: $i > $i,SV160: $i,SV565: $i,SV462: $i] :
( ( ( ( dsetconstr @ SV462
@ ^ [SY2587: $i] :
( in @ ( kpair @ SV565 @ SY2587 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2521: $i,SY2522: $i] :
( ( SV494 @ SY2521 )
= SY2522 ) ) ) )
= ( setadjoin @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 ) @ emptyset ) )
= $true )
| ( ( in @ SV565 @ SV160 )
= $false )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2732,plain,
! [SV160: $i,SV462: $i,SV494: $i > $i,SV565: $i] :
( ( ( in @ ( sK88_SY820 @ SV565 @ SV494 @ SV462 @ SV160 )
@ ( dsetconstr @ SV462
@ ^ [SY2590: $i] :
( in @ ( kpair @ SV565 @ SY2590 )
@ ( dpsetconstr @ SV160 @ SV462
@ ^ [SY2524: $i,SY2525: $i] :
( ( SV494 @ SY2524 )
= SY2525 ) ) ) ) )
= $true )
| ( ( in @ SV565 @ SV160 )
= $false )
| ( ( in @ ( SV494 @ ( sK89_Xx @ SV494 @ SV462 @ SV160 ) ) @ SV462 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2733,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2734,plain,
! [SV464: $i > $o,SV548: $i,SV439: $i > $o] :
( ( ( SV439 @ SV548 )
= $false )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2735,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
| ~ ( ( SV609
!= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) ) ) )
| ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(2736,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
| ~ ( ( SV596
!= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2737,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2738,plain,
! [SV440: $i > $o,SV549: $i,SV465: $i > $o] :
( ( ( SV465 @ SV549 )
= $false )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2739,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
| ~ ( ( SV610
!= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) ) ) )
| ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2740,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
| ~ ( ( SV597
!= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2741,plain,
! [SV550: $i,SV466: $i,SV163: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2603: $i] :
( ~ ( in @ SY2603 @ SV603 )
| ( in @ SY2603 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2742,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2743,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2744,plain,
! [SV566: $i,SV466: $i,SV163: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ ( sK15_B @ SV163 ) )
| ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV611 )
| ( in @ SY2605 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(2745,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
| ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2746,plain,
! [SV163: $i,SV527: $i,SV513: $i,SV598: $i] :
( ( ( in @ SV598 @ SV513 )
= $false )
| ( ( in @ SV598 @ SV527 )
= $true )
| ( ( ! [SY2555: $i] :
( ~ ( in @ SY2555 @ SV527 )
| ( in @ SY2555 @ SV513 ) ) )
= $true )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2747,plain,
! [SV163: $i,SV552: $i,SV567: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2748,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV588: $i,SV321: $i] :
( ( ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) ) )
= $false )
| ( ( in @ SV588 @ SV164 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2749,plain,
! [SV506: $i,SV322: $i,SV604: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2604: $i] :
( ~ ( SV165 @ SY2604 @ SV604 )
| ~ ( in @ SY2604 @ SV322 ) ) )
= $true )
| ( ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2750,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 )
| ~ ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(2751,plain,
! [SV506: $i,SV322: $i,SV612: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2606: $i] :
( ~ ( SV165 @ SY2606 @ SV612 )
| ~ ( in @ SY2606 @ SV322 ) )
| ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(2752,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
| ~ ( ~ ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 )
| ~ ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(2753,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV614: $o] :
( ( SV614 = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2686]) ).
thf(2754,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $true = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2686]) ).
thf(2755,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $false = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2686]) ).
thf(2756,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV606: $o] :
( ( ( ~ SV606 ) = $true )
| ( SV606 = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2757,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(2758,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(2759,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV166 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2690]) ).
thf(2760,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 )
| ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2761,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2762,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV600: $o] :
( ( SV600 = $false )
| ( ( ~ ( in @ SV412 @ SV166 )
| SV600 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2763,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $false )
| ( ( ~ ( in @ SV412 @ SV166 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2764,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $false )
| ( ( ~ ( in @ SV412 @ SV166 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2765,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ! [SY2408: $o] :
( ~ SY2408
| ( in @ SV412 @ SV323 )
| SY2408 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2696]) ).
thf(2766,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2697]) ).
thf(2767,plain,
! [SV553: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $true )
| ( ( SV326 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2768,plain,
! [SV553: $i,SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) )
= $true )
| ( ( SV326 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV171 )
= $false )
| ( ( in @ ( sK78_SY1660 @ SV326 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2769,plain,
! [SV326: $i > $o,SV171: $i,SV590: $i] :
( ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ SV590 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2770,plain,
! [SV171: $i,SV615: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV615 )
| ~ ( in @ SV615 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(2771,plain,
! [SV171: $i,SV326: $i > $o] :
( ( ( ! [SY2317: $i] :
( ~ ( SV326 @ SY2317 )
| ~ ( in @ SY2317 @ SV171 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2772,plain,
! [SV555: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $true )
| ( ( SV328 @ SV555 )
= $false )
| ( ( in @ SV555 @ SV175 )
= $false )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2773,plain,
! [SV555: $i,SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) )
= $true )
| ( ( SV328 @ SV555 )
= $false )
| ( ( in @ SV555 @ SV175 )
= $false )
| ( ( in @ ( sK72_SY1655 @ SV328 @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2774,plain,
! [SV328: $i > $o,SV175: $i,SV591: $i] :
( ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ SV591 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2775,plain,
! [SV175: $i,SV616: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV616 )
| ~ ( in @ SV616 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2776,plain,
! [SV175: $i,SV328: $i > $o] :
( ( ( ! [SY2321: $i] :
( ~ ( SV328 @ SY2321 )
| ~ ( in @ SY2321 @ SV175 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2777,plain,
! [SV496: $i > $i,SV176: $i,SV571: $i,SV470: $i] :
( ( ( ( dsetconstr @ SV470
@ ^ [SY2593: $i] :
( in @ ( kpair @ SV571 @ SY2593 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2530: $i,SY2531: $i] :
( ( SV496 @ SY2530 )
= SY2531 ) ) ) )
= ( setadjoin @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 ) @ emptyset ) )
= $true )
| ( ( in @ SV571 @ SV176 )
= $false )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2778,plain,
! [SV176: $i,SV470: $i,SV496: $i > $i,SV571: $i] :
( ( ( in @ ( sK91_SY856 @ SV571 @ SV496 @ SV470 @ SV176 )
@ ( dsetconstr @ SV470
@ ^ [SY2596: $i] :
( in @ ( kpair @ SV571 @ SY2596 )
@ ( dpsetconstr @ SV176 @ SV470
@ ^ [SY2533: $i,SY2534: $i] :
( ( SV496 @ SY2533 )
= SY2534 ) ) ) ) )
= $true )
| ( ( in @ SV571 @ SV176 )
= $false )
| ( ( in @ ( SV496 @ ( sK92_Xx @ SV496 @ SV470 @ SV176 ) ) @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2712]) ).
thf(2779,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
| ~ ( ( SV601
!= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2780,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
| ~ ( ( SV607
!= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2781,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2782,plain,
! [SV187: $i > $o,SV336: $i > $o,SV594: $i] :
( ( ( ~ ( ( SV594
!= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2783,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( SV187 @ SV574 )
= $false )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2784,plain,
! [SV187: $i > $o,SV336: $i > $o,SV574: $i] :
( ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV187 @ SV574 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2785,plain,
! [SV405: $i,SV308: $i > $o,SV144: $i] :
( ( ( ( dsetconstr @ SV144
@ ^ [SY2258: $i] : ( SV308 @ SY2258 ) )
= ( setadjoin @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 ) @ emptyset ) )
= $true )
| ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2724]) ).
thf(2786,plain,
! [SV144: $i,SV308: $i > $o,SV405: $i] :
( ( ( in @ ( sK74_SY503 @ SV405 @ SV308 @ SV144 )
@ ( dsetconstr @ SV144
@ ^ [SY2259: $i] : ( SV308 @ SY2259 ) ) )
= $true )
| ( ( ( sK75_Xy @ SV405 @ SV308 @ SV144 )
= SV405 )
= $false )
| ( ( SV308 @ SV405 )
= $false )
| ( ( in @ SV405 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2725]) ).
thf(2787,plain,
! [SV408: $i,SV602: $i,SV152: $i > $o] :
( ( ( SV152 @ SV602 )
= $false )
| ( ( ( sK43_SY210 @ SV152 )
= SV602 )
= $true )
| ( ( ( sK44_Xx @ SV152 )
= ( sK45_SY1644 @ SV152 ) )
= $false )
| ( ( SV152 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2788,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV409 ) )
= $true )
| ( ( SV490 @ SV608 )
= $true )
| ( ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2789,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ SV409 )
| ( SV490 @ SV617 ) )
= $true )
| ( ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) )
= $false )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2790,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2791,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2730]) ).
thf(2792,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2793,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2794,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2795,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( ~ ( ~ ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
| ~ ( ( SV609
!= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) ) ) ) )
= $true )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2796,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) ) )
= $false )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2797,plain,
! [SV439: $i > $o,SV464: $i > $o,SV596: $i] :
( ( ( ~ ( ( SV596
!= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2736]) ).
thf(2798,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(2799,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(2800,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2801,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( ~ ( ~ ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
| ~ ( ( SV610
!= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) ) ) ) )
= $true )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2802,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) ) )
= $false )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2803,plain,
! [SV440: $i > $o,SV465: $i > $o,SV597: $i] :
( ( ( ~ ( ( SV597
!= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2804,plain,
! [SV550: $i,SV466: $i,SV163: $i,SV603: $i] :
( ( ( in @ SV603 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( ! [SY2603: $i] :
( ~ ( in @ SY2603 @ SV603 )
| ( in @ SY2603 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2805,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2806,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(2807,plain,
! [SV566: $i,SV466: $i,SV163: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ ( sK15_B @ SV163 ) ) )
= $true )
| ( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV611 )
| ( in @ SY2605 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2744]) ).
thf(2808,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2809,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2745]) ).
thf(2810,plain,
! [SV163: $i,SV598: $i,SV513: $i,SV527: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV527 )
| ( in @ SV618 @ SV513 ) )
= $true )
| ( ( in @ SV598 @ SV527 )
= $true )
| ( ( in @ SV598 @ SV513 )
= $false )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(2811,plain,
! [SV163: $i,SV552: $i,SV567: $i] :
( ( ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2812,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV588: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
!= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
= $false )
| ( ( in @ SV588 @ SV164 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2813,plain,
! [SV528: $i,SV164: $i,SV321: $i,SV411: $i,SV588: $i] :
( ( ( ~ ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) ) )
= $false )
| ( ( in @ SV588 @ SV164 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2814,plain,
! [SV506: $i,SV322: $i,SV604: $i,SV619: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV619 @ SV604 )
| ~ ( in @ SV619 @ SV322 ) )
= $true )
| ( ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(2815,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV605: $i] :
( ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 )
| ~ ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2816,plain,
! [SV506: $i,SV322: $i,SV612: $i,SV165: $i > $i > $o] :
( ( ( ! [SY2606: $i] :
( ~ ( SV165 @ SY2606 @ SV612 )
| ~ ( in @ SY2606 @ SV322 ) ) )
= $true )
| ( ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2751]) ).
thf(2817,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) ) )
= $true )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 )
| ~ ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(2818,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV606: $o] :
( ( SV606 = $false )
| ( SV606 = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2819,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2820,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV412 @ SV166 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2821,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2822,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 ) )
= $true )
| ( ( ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2760]) ).
thf(2823,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV323 ) )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(2824,plain,
! [SV323: $i,SV600: $o,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV166 ) )
= $true )
| ( SV600 = $true )
| ( SV600 = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2825,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV166 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2826,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV166 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2827,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV620: $o] :
( ( ( ~ SV620
| ( in @ SV412 @ SV323 )
| SV620 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2765]) ).
thf(2828,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $true
| ( in @ SV412 @ SV323 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2765]) ).
thf(2829,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $false
| ( in @ SV412 @ SV323 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2765]) ).
thf(2830,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV621: $o] :
( ( ( ~ SV621
| ~ SV621
| SV621 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2766]) ).
thf(2831,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2766]) ).
thf(2832,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2766]) ).
thf(2833,plain,
! [SV590: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV590 )
= $false )
| ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2834,plain,
! [SV171: $i,SV615: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV615 ) )
= $true )
| ( ( ~ ( in @ SV615 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2835,plain,
! [SV171: $i,SV622: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV622 )
| ~ ( in @ SV622 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(2836,plain,
! [SV591: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV591 )
= $false )
| ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2837,plain,
! [SV175: $i,SV616: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV616 ) )
= $true )
| ( ( ~ ( in @ SV616 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(2838,plain,
! [SV175: $i,SV623: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV623 )
| ~ ( in @ SV623 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(2839,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2840,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV601: $i] :
( ( ( ~ ( ( SV601
!= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2841,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
| ~ ( ( SV607
!= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2842,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2843,plain,
! [SV187: $i > $o,SV336: $i > $o,SV594: $i] :
( ( ( SV594
!= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2844,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(2845,plain,
! [SV336: $i > $o,SV574: $i,SV187: $i > $o] :
( ( ( SV187 @ SV574 )
= $false )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2846,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV608: $i] :
( ( ( in @ SV608 @ SV409 )
= $false )
| ( ( SV490 @ SV608 )
= $true )
| ( ( in @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) @ SV409 )
= $true )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2847,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV617: $i] :
( ( ( ~ ( in @ SV617 @ SV409 ) )
= $true )
| ( ( SV490 @ SV617 )
= $true )
| ( ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) )
= $false )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(2848,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2849,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
| ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2850,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2851,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2852,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2853,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2854,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
| ~ ( ( SV609
!= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2855,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2796]) ).
thf(2856,plain,
! [SV439: $i > $o,SV464: $i > $o,SV596: $i] :
( ( ( SV596
!= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2857,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2858,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2799]) ).
thf(2859,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2860,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2861,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
| ~ ( ( SV610
!= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2862,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2802]) ).
thf(2863,plain,
! [SV440: $i > $o,SV465: $i > $o,SV597: $i] :
( ( ( SV597
!= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2864,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV603: $i] :
( ( ( ! [SY2603: $i] :
( ~ ( in @ SY2603 @ SV603 )
| ( in @ SY2603 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 )
= $true )
| ( ( in @ SV603 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(2865,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2866,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SV624 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(2867,plain,
! [SV566: $i,SV466: $i,SV163: $i,SV611: $i] :
( ( ( in @ SV611 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV611 )
| ( in @ SY2605 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
| ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2868,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2808]) ).
thf(2869,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ! [SY2492: $i] :
( ~ ( in @ SY2492 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SY2492 @ SV466 ) ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2809]) ).
thf(2870,plain,
! [SV163: $i,SV598: $i,SV513: $i,SV527: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV527 ) )
= $true )
| ( ( in @ SV618 @ SV513 )
= $true )
| ( ( in @ SV598 @ SV527 )
= $true )
| ( ( in @ SV598 @ SV513 )
= $false )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2871,plain,
! [SV163: $i,SV552: $i,SV567: $i] :
( ( ( ~ ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2811]) ).
thf(2872,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2811]) ).
thf(2873,plain,
! [SV528: $i,SV164: $i,SV411: $i,SV588: $i,SV321: $i] :
( ( ( ( dsetconstr @ SV321
@ ^ [SY2599: $i] : ( in @ ( kpair @ SV588 @ SY2599 ) @ SV411 ) )
= ( setadjoin @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 ) @ emptyset ) )
= $true )
| ( ( in @ SV588 @ SV164 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2874,plain,
! [SV528: $i,SV164: $i,SV321: $i,SV411: $i,SV588: $i] :
( ( ( in @ ( sK81_SY667 @ SV588 @ SV411 @ SV321 @ SV164 )
@ ( dsetconstr @ SV321
@ ^ [SY2600: $i] : ( in @ ( kpair @ SV588 @ SY2600 ) @ SV411 ) ) )
= $true )
| ( ( in @ SV588 @ SV164 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV321
@ ^ [SY2397: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2397 ) @ SV411 ) ) )
= $false )
| ( ( ( dsetconstr @ SV321
@ ^ [SY2396: $i] : ( in @ ( kpair @ ( sK82_SY661 @ SV411 @ SV321 @ SV164 ) @ SY2396 ) @ SV411 ) )
= ( setadjoin @ SV528 @ emptyset ) )
= $false )
| ( ( subset @ SV411 @ ( cartprod @ SV164 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2875,plain,
! [SV506: $i,SV322: $i,SV604: $i,SV619: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV619 @ SV604 ) )
= $true )
| ( ( ~ ( in @ SV619 @ SV322 ) )
= $true )
| ( ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(2876,plain,
! [SV506: $i,SV322: $i,SV605: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 )
| ~ ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2877,plain,
! [SV506: $i,SV322: $i,SV612: $i,SV625: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV625 @ SV612 )
| ~ ( in @ SV625 @ SV322 ) )
= $true )
| ( ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(2878,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV613: $i] :
( ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( ~ ( ~ ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 )
| ~ ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 ) ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2817]) ).
thf(2879,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV626: $o] :
( ( SV626 = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2821]) ).
thf(2880,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2821]) ).
thf(2881,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $true )
| ( ( in @ SV412 @ SV166 )
= $false )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2821]) ).
thf(2882,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $false )
| ( ( ( in @ SV412 @ SV323 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2883,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $false )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2884,plain,
! [SV323: $i,SV600: $o,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $false )
| ( SV600 = $true )
| ( SV600 = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2885,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2886,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( in @ SV412 @ SV166 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(2887,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV620: $o] :
( ( ( ~ SV620 ) = $true )
| ( ( ( in @ SV412 @ SV323 )
| SV620 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2888,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV412 @ SV323 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(2889,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV412 @ SV323 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(2890,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV621: $o] :
( ( ( ~ SV621 ) = $true )
| ( ( ~ SV621
| SV621 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(2891,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(2892,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2893,plain,
! [SV590: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $false )
| ( ( SV326 @ SV590 )
= $false )
| ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2894,plain,
! [SV590: $i,SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV590 )
= $false )
| ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2895,plain,
! [SV171: $i,SV615: $i,SV326: $i > $o] :
( ( ( SV326 @ SV615 )
= $false )
| ( ( ~ ( in @ SV615 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2896,plain,
! [SV171: $i,SV622: $i,SV326: $i > $o] :
( ( ( ~ ( SV326 @ SV622 ) )
= $true )
| ( ( ~ ( in @ SV622 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(2897,plain,
! [SV591: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $false )
| ( ( SV328 @ SV591 )
= $false )
| ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(2898,plain,
! [SV591: $i,SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV591 )
= $false )
| ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(2899,plain,
! [SV175: $i,SV616: $i,SV328: $i > $o] :
( ( ( SV328 @ SV616 )
= $false )
| ( ( ~ ( in @ SV616 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2900,plain,
! [SV175: $i,SV623: $i,SV328: $i > $o] :
( ( ( ~ ( SV328 @ SV623 ) )
= $true )
| ( ( ~ ( in @ SV623 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2901,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2839]) ).
thf(2902,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV601: $i] :
( ( ( SV601
!= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(2903,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2904,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV607: $i] :
( ( ( ~ ( ( SV607
!= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2905,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2906,plain,
! [SV187: $i > $o,SV336: $i > $o,SV594: $i] :
( ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV187 @ SV594 ) )
= $true )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2907,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
| ~ ( ( SV627
!= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(2908,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2909,plain,
! [SV155: $i,SV316: $i,SV490: $i > $o,SV409: $i,SV617: $i] :
( ( ( in @ SV617 @ SV409 )
= $false )
| ( ( SV490 @ SV617 )
= $true )
| ( ( SV490 @ ( kpair @ ( sK94_Xx @ SV490 @ SV409 @ SV316 @ SV155 ) @ ( sK95_SY1693 @ SV490 @ SV409 @ SV316 @ SV155 ) ) )
= $false )
| ( ( subset @ SV409 @ ( cartprod @ SV155 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2910,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
= $true )
| ( ( ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(2911,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $true )
| ( ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2912,plain,
! [SV548: $i,SV439: $i > $o,SV628: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV628 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV628 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(2913,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2852]) ).
thf(2914,plain,
! [SV548: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2853]) ).
thf(2915,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( ~ ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) ) )
= $false )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2916,plain,
! [SV439: $i > $o,SV464: $i > $o,SV609: $i] :
( ( ( ~ ( ( SV609
!= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) ) ) )
= $false )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2917,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( SV439 @ SV596 )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2918,plain,
! [SV439: $i > $o,SV464: $i > $o,SV596: $i] :
( ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( SV439 @ SV596 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2919,plain,
! [SV549: $i,SV465: $i > $o,SV629: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV629 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV629 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(2920,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2921,plain,
! [SV549: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2922,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( ~ ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) ) )
= $false )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(2923,plain,
! [SV440: $i > $o,SV465: $i > $o,SV610: $i] :
( ( ( ~ ( ( SV610
!= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) ) ) )
= $false )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(2924,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2925,plain,
! [SV440: $i > $o,SV465: $i > $o,SV597: $i] :
( ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( SV465 @ SV597 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2926,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV603: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV603 )
| ( in @ SV630 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 )
= $true )
| ( ( in @ SV603 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2927,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2928,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2929,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
= $true )
| ( ( ~ ( in @ SV624 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(2930,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV611: $i] :
( ( ( ! [SY2605: $i] :
( ~ ( in @ SY2605 @ SV611 )
| ( in @ SY2605 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 )
= $true )
| ( ( in @ SV611 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(2931,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
| ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(2932,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
| ~ ( in @ SV631 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(2933,plain,
! [SV163: $i,SV598: $i,SV513: $i,SV527: $i,SV618: $i] :
( ( ( in @ SV618 @ SV527 )
= $false )
| ( ( in @ SV618 @ SV513 )
= $true )
| ( ( in @ SV598 @ SV527 )
= $true )
| ( ( in @ SV598 @ SV513 )
= $false )
| ( ( in @ SV513 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ SV527 @ ( sK15_B @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2934,plain,
! [SV163: $i,SV552: $i,SV567: $i] :
( ( ( in @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) @ ( sK15_B @ SV163 ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2935,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2936,plain,
! [SV506: $i,SV322: $i,SV604: $i,SV619: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ SV619 @ SV604 )
= $false )
| ( ( ~ ( in @ SV619 @ SV322 ) )
= $true )
| ( ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(2937,plain,
! [SV506: $i,SV322: $i,SV605: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 ) )
= $false )
| ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2938,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV605: $i] :
( ( ( ~ ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2939,plain,
! [SV506: $i,SV322: $i,SV612: $i,SV625: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ SV625 @ SV612 ) )
= $true )
| ( ( ~ ( in @ SV625 @ SV322 ) )
= $true )
| ( ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(2940,plain,
! [SV506: $i,SV322: $i,SV613: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 )
| ~ ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2941,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(2942,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV632: $o] :
( ( ( ~ SV632
| SV632 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2883]) ).
thf(2943,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2883]) ).
thf(2944,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2883]) ).
thf(2945,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV620: $o] :
( ( SV620 = $false )
| ( ( ( in @ SV412 @ SV323 )
| SV620 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2946,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $true = $false )
| ( ( ( in @ SV412 @ SV323 )
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2947,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $false = $false )
| ( ( ( in @ SV412 @ SV323 )
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2948,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV621: $o] :
( ( SV621 = $false )
| ( ( ~ SV621
| SV621 )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2949,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2950,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2951,plain,
! [SV590: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $true )
| ( ( SV326 @ SV590 )
= $false )
| ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(2952,plain,
! [SV590: $i,SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) )
= $true )
| ( ( SV326 @ SV590 )
= $false )
| ( ( in @ SV590 @ SV171 )
= $false )
| ( ( SV326 @ ( sK77_Xx @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2953,plain,
! [SV326: $i > $o,SV171: $i,SV615: $i] :
( ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ SV615 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(2954,plain,
! [SV171: $i,SV622: $i,SV326: $i > $o] :
( ( ( SV326 @ SV622 )
= $false )
| ( ( ~ ( in @ SV622 @ SV171 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2955,plain,
! [SV591: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $true )
| ( ( SV328 @ SV591 )
= $false )
| ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(2956,plain,
! [SV591: $i,SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) )
= $true )
| ( ( SV328 @ SV591 )
= $false )
| ( ( in @ SV591 @ SV175 )
= $false )
| ( ( SV328 @ ( sK71_Xx @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(2957,plain,
! [SV328: $i > $o,SV175: $i,SV616: $i] :
( ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ SV616 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(2958,plain,
! [SV175: $i,SV623: $i,SV328: $i > $o] :
( ( ( SV328 @ SV623 )
= $false )
| ( ( ~ ( in @ SV623 @ SV175 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2959,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( SV336 @ SV601 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(2960,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV601: $i] :
( ( ( SV601
= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV601 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2961,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(2962,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV607: $i] :
( ( ( SV607
!= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2904]) ).
thf(2963,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(2964,plain,
! [SV336: $i > $o,SV594: $i,SV187: $i > $o] :
( ( ( SV187 @ SV594 )
= $false )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) )
| ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(2965,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
| ~ ( ( SV627
!= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(2966,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
| ~ ( ( SV633
!= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(2967,plain,
! [SV159: $i,SV318: $i,SV493: $i > $o,SV461: $i > $o] :
( ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $false )
| ( ( ~ ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) ) )
= $true )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(2968,plain,
! [SV548: $i,SV439: $i > $o,SV628: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV628 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV628 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(2969,plain,
! [SV548: $i,SV439: $i > $o,SV634: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV634 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV634 ) )
= $true )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(2970,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(2971,plain,
! [SV439: $i > $o,SV464: $i > $o,SV609: $i] :
( ( ( SV609
!= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(2972,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(2973,plain,
! [SV464: $i > $o,SV596: $i,SV439: $i > $o] :
( ( ( SV439 @ SV596 )
= $false )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(2974,plain,
! [SV549: $i,SV465: $i > $o,SV629: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV629 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV629 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(2975,plain,
! [SV549: $i,SV465: $i > $o,SV635: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV635 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV635 ) )
= $true )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(2976,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2922]) ).
thf(2977,plain,
! [SV440: $i > $o,SV465: $i > $o,SV610: $i] :
( ( ( SV610
!= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2978,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2979,plain,
! [SV440: $i > $o,SV597: $i,SV465: $i > $o] :
( ( ( SV465 @ SV597 )
= $false )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2980,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV603: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV603 ) )
= $true )
| ( ( in @ SV630 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 )
= $true )
| ( ( in @ SV603 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(2981,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(2982,plain,
! [SV550: $i,SV163: $i,SV466: $i] :
( ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(2983,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV624: $i] :
( ( ( in @ SV624 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $false )
| ( ( ~ ( in @ SV624 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2984,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV611: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV611 )
| ( in @ SV636 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 )
= $true )
| ( ( in @ SV611 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(2985,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(2986,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( ~ ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(2987,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( sK17_SY1618 @ SV466 @ SV163 ) ) )
= $true )
| ( ( ~ ( in @ SV631 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(2988,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
| ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(2989,plain,
! [SV506: $i,SV604: $i,SV165: $i > $i > $o,SV322: $i,SV619: $i] :
( ( ( in @ SV619 @ SV322 )
= $false )
| ( ( SV165 @ SV619 @ SV604 )
= $false )
| ( ( in @ SV604 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(2990,plain,
! [SV506: $i,SV322: $i,SV605: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV605 )
= $true )
| ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(2991,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV605: $i] :
( ( ( in @ ( sK11_Xy @ SV605 @ SV322 @ SV165 ) @ SV322 )
= $true )
| ( ( in @ SV605 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $true )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(2992,plain,
! [SV506: $i,SV322: $i,SV612: $i,SV625: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ SV625 @ SV612 )
= $false )
| ( ( ~ ( in @ SV625 @ SV322 ) )
= $true )
| ( ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(2993,plain,
! [SV506: $i,SV322: $i,SV613: $i,SV165: $i > $i > $o] :
( ( ( ~ ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 ) )
= $false )
| ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2940]) ).
thf(2994,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV613: $i] :
( ( ( ~ ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 ) )
= $false )
| ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2940]) ).
thf(2995,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV637: $o] :
( ( SV637 = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2941]) ).
thf(2996,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $true = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2941]) ).
thf(2997,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $false = $true )
| ( ( in @ SV412 @ SV323 )
= $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2941]) ).
thf(2998,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV632: $o] :
( ( ( ~ SV632 ) = $true )
| ( SV632 = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(2999,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3000,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(3001,plain,
! [SV166: $i,SV620: $o,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $true )
| ( SV620 = $true )
| ( SV620 = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3002,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3003,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( ( in @ SV412 @ SV323 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3004,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV621: $o] :
( ( ( ~ SV621 ) = $true )
| ( SV621 = $true )
| ( SV621 = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3005,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3006,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3007,plain,
! [SV615: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV615 )
= $false )
| ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3008,plain,
! [SV326: $i > $o,SV171: $i,SV622: $i] :
( ( ( in @ SV622 @ SV171 )
= $false )
| ( ( SV326 @ SV622 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) ) )
= $true )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3009,plain,
! [SV616: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV616 )
= $false )
| ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3010,plain,
! [SV328: $i > $o,SV175: $i,SV623: $i] :
( ( ( in @ SV623 @ SV175 )
= $false )
| ( ( SV328 @ SV623 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) ) )
= $true )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3011,plain,
! [SV517: $i,SV187: $i > $o,SV601: $i,SV336: $i > $o] :
( ( ( SV336 @ SV601 )
= $false )
| ( ( SV601
= ( sK58_SY265 @ SV601 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3012,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( SV336 @ SV607 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3013,plain,
! [SV517: $i,SV187: $i > $o,SV336: $i > $o,SV607: $i] :
( ( ( SV607
= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV607 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3014,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
| ~ ( ( SV638
!= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3015,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o] :
( ( ( ! [SY2341: $i] :
( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) )
| ~ ( ( SY2341
!= ( sK58_SY265 @ SY2341 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SY2341 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2964]) ).
thf(3016,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
| ~ ( ( SV627
!= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3017,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
| ~ ( ( SV633
!= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3018,plain,
! [SV159: $i,SV318: $i,SV461: $i > $o,SV493: $i > $o] :
( ( ( SV493 @ ( sK63_SY1651 @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $false )
| ( ( SV461 @ ( sK62_Xx @ SV493 @ SV461 @ SV318 @ SV159 ) )
= $false )
| ( ( ( dsetconstr @ SV159
@ ^ [SY2472: $i] : ( SV461 @ SY2472 ) )
= ( dsetconstr @ SV318
@ ^ [SY2518: $i] : ( SV493 @ SY2518 ) ) )
= $true )
| ( ( SV159 = SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3019,plain,
! [SV548: $i,SV439: $i > $o,SV628: $i,SV464: $i > $o] :
( ( ( SV464 @ SV628 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV628 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3020,plain,
! [SV548: $i,SV439: $i > $o,SV634: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV634 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV634 )
= $true )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3021,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3022,plain,
! [SV439: $i > $o,SV464: $i > $o,SV609: $i] :
( ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( SV439 @ SV609 ) )
= $true )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3023,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3024,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3025,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3026,plain,
! [SV549: $i,SV465: $i > $o,SV629: $i,SV440: $i > $o] :
( ( ( SV440 @ SV629 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV629 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3027,plain,
! [SV549: $i,SV465: $i > $o,SV635: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV635 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV635 )
= $true )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3028,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( SV465 @ SV610 )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3029,plain,
! [SV440: $i > $o,SV465: $i > $o,SV610: $i] :
( ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( SV465 @ SV610 ) )
= $true )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3030,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2978]) ).
thf(3031,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2978]) ).
thf(3032,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3033,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV603: $i,SV630: $i] :
( ( ( in @ SV630 @ SV603 )
= $false )
| ( ( in @ SV630 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV603 )
= $true )
| ( ( in @ SV603 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3034,plain,
! [SV550: $i,SV163: $i,SV466: $i,SV624: $i] :
( ( ( in @ SV624 @ SV466 )
= $false )
| ( ( in @ SV624 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ SV550 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3035,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV611: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV611 ) )
= $true )
| ( ( in @ SV636 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 )
= $true )
| ( ( in @ SV611 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2984]) ).
thf(3036,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( in @ ( sK17_SY1618 @ SV466 @ SV163 ) @ ( sK15_B @ SV163 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3037,plain,
! [SV566: $i,SV163: $i,SV466: $i] :
( ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV466 )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2986]) ).
thf(3038,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV631: $i] :
( ( ( in @ SV631 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $false )
| ( ( ~ ( in @ SV631 @ SV466 ) )
= $true )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3039,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3040,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2988]) ).
thf(3041,plain,
! [SV506: $i,SV612: $i,SV165: $i > $i > $o,SV322: $i,SV625: $i] :
( ( ( in @ SV625 @ SV322 )
= $false )
| ( ( SV165 @ SV625 @ SV612 )
= $false )
| ( ( in @ SV612 @ ( sK10_B @ SV322 @ SV165 ) )
= $true )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3042,plain,
! [SV506: $i,SV322: $i,SV613: $i,SV165: $i > $i > $o] :
( ( ( SV165 @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV613 )
= $true )
| ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3043,plain,
! [SV506: $i,SV165: $i > $i > $o,SV322: $i,SV613: $i] :
( ( ( in @ ( sK11_Xy @ SV613 @ SV322 @ SV165 ) @ SV322 )
= $true )
| ( ( in @ SV613 @ ( sK10_B @ SV322 @ SV165 ) )
= $false )
| ( ( SV506
= ( sK13_SY1613 @ SV506 @ SV322 @ SV165 ) )
= $false )
| ( ( SV165 @ ( sK12_SY29 @ SV322 @ SV165 ) @ SV506 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3044,plain,
! [SV166: $i,SV323: $i,SV412: $i,SV632: $o] :
( ( SV632 = $false )
| ( SV632 = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3045,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3046,plain,
! [SV166: $i,SV323: $i,SV412: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV412 @ SV323 )
= $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3047,plain,
! [SV323: $i,SV166: $i,SV412: $i,SV621: $o] :
( ( SV621 = $false )
| ( SV621 = $true )
| ( SV621 = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3048,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3049,plain,
! [SV323: $i,SV166: $i,SV412: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV412 @ ( symdiff @ SV166 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3050,plain,
! [SV615: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $false )
| ( ( SV326 @ SV615 )
= $false )
| ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3051,plain,
! [SV615: $i,SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV615 )
= $false )
| ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3052,plain,
! [SV622: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
| ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV622 )
= $false )
| ( ( in @ SV622 @ SV171 )
= $false )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3053,plain,
! [SV616: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $false )
| ( ( SV328 @ SV616 )
= $false )
| ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3054,plain,
! [SV616: $i,SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV616 )
= $false )
| ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3055,plain,
! [SV623: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
| ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV623 )
= $false )
| ( ( in @ SV623 @ SV175 )
= $false )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3056,plain,
! [SV517: $i,SV187: $i > $o,SV607: $i,SV336: $i > $o] :
( ( ( SV336 @ SV607 )
= $false )
| ( ( SV607
= ( sK58_SY265 @ SV607 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV517
= ( sK59_SY262 @ SV517 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV517 )
= $false )
| ( ( ( sK60_Xx @ SV336 @ SV187 )
= ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3057,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
| ~ ( ( SV638
!= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3058,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
| ~ ( ( SV639
!= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) ) ) )
| ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3059,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3060,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV627: $i] :
( ( ( ~ ( ( SV627
!= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3061,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
| ~ ( ( SV633
!= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3062,plain,
! [SV548: $i,SV439: $i > $o,SV634: $i,SV464: $i > $o] :
( ( ( SV464 @ SV634 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV634 )
= $true )
| ( ( SV548
= ( sK54_SY238 @ SV548 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV548 )
= $false )
| ( ( ( sK55_Xx @ SV464 @ SV439 )
= ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3063,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3064,plain,
! [SV464: $i > $o,SV609: $i,SV439: $i > $o] :
( ( ( SV439 @ SV609 )
= $false )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( ~ ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3065,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3066,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3024]) ).
thf(3067,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3068,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3069,plain,
! [SV549: $i,SV465: $i > $o,SV635: $i,SV440: $i > $o] :
( ( ( SV440 @ SV635 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV635 )
= $true )
| ( ( SV549
= ( sK50_SY241 @ SV549 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV549 )
= $false )
| ( ( ( sK51_Xx @ SV465 @ SV440 )
= ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3070,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3071,plain,
! [SV440: $i > $o,SV610: $i,SV465: $i > $o] :
( ( ( SV465 @ SV610 )
= $false )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( ~ ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3072,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3030]) ).
thf(3073,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3074,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3075,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3076,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV611: $i,SV636: $i] :
( ( ( in @ SV636 @ SV611 )
= $false )
| ( ( in @ SV636 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $true )
| ( ( in @ ( sK18_SY1632 @ SV466 @ SV163 ) @ SV611 )
= $true )
| ( ( in @ SV611 @ ( sK15_B @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3077,plain,
! [SV566: $i,SV163: $i,SV466: $i,SV631: $i] :
( ( ( in @ SV631 @ SV466 )
= $false )
| ( ( in @ SV631 @ ( sK17_SY1618 @ SV466 @ SV163 ) )
= $false )
| ( ( in @ ( sK19_Xx @ SV466 @ SV163 ) @ SV163 )
= $false )
| ( ( in @ SV566 @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3078,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3079,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
| ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3040]) ).
thf(3080,plain,
! [SV615: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $true )
| ( ( SV326 @ SV615 )
= $false )
| ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3081,plain,
! [SV615: $i,SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) )
= $true )
| ( ( SV326 @ SV615 )
= $false )
| ( ( in @ SV615 @ SV171 )
= $false )
| ( ( SV326 @ ( sK78_SY1660 @ SV326 @ SV171 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3082,plain,
! [SV622: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
!= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $false )
| ( ( SV326 @ SV622 )
= $false )
| ( ( in @ SV622 @ SV171 )
= $false )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3083,plain,
! [SV622: $i,SV171: $i,SV326: $i > $o] :
( ( ( ~ ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) ) )
= $false )
| ( ( SV326 @ SV622 )
= $false )
| ( ( in @ SV622 @ SV171 )
= $false )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3052]) ).
thf(3084,plain,
! [SV616: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $true )
| ( ( SV328 @ SV616 )
= $false )
| ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3053]) ).
thf(3085,plain,
! [SV616: $i,SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) )
= $true )
| ( ( SV328 @ SV616 )
= $false )
| ( ( in @ SV616 @ SV175 )
= $false )
| ( ( SV328 @ ( sK72_SY1655 @ SV328 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3054]) ).
thf(3086,plain,
! [SV623: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
!= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $false )
| ( ( SV328 @ SV623 )
= $false )
| ( ( in @ SV623 @ SV175 )
= $false )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3087,plain,
! [SV623: $i,SV175: $i,SV328: $i > $o] :
( ( ( ~ ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) ) )
= $false )
| ( ( SV328 @ SV623 )
= $false )
| ( ( in @ SV623 @ SV175 )
= $false )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3088,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
| ~ ( ( SV638
!= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3089,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( ~ ( ~ ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
| ~ ( ( SV639
!= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) ) ) ) )
= $true )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3090,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3059]) ).
thf(3091,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV627: $i] :
( ( ( SV627
!= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3092,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3093,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV633: $i] :
( ( ( ~ ( ( SV633
!= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3094,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3063]) ).
thf(3095,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3063]) ).
thf(3096,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) )
| ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3097,plain,
! [SV596: $i,SV439: $i > $o,SV640: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV640 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV640 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3098,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3067]) ).
thf(3099,plain,
! [SV596: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3068]) ).
thf(3100,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3101,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3070]) ).
thf(3102,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) )
| ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3103,plain,
! [SV597: $i,SV465: $i > $o,SV641: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV641 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV641 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3104,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3105,plain,
! [SV597: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3075]) ).
thf(3106,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
= $true )
| ( ( ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3107,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
= $true )
| ( ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3108,plain,
! [SV622: $i,SV326: $i > $o,SV171: $i] :
( ( ( ( dsetconstr @ SV171
@ ^ [SY2318: $i] : ( SV326 @ SY2318 ) )
= ( setadjoin @ ( sK76_SY515 @ SV326 @ SV171 ) @ emptyset ) )
= $true )
| ( ( SV326 @ SV622 )
= $false )
| ( ( in @ SV622 @ SV171 )
= $false )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3109,plain,
! [SV622: $i,SV171: $i,SV326: $i > $o] :
( ( ( in @ ( sK76_SY515 @ SV326 @ SV171 )
@ ( dsetconstr @ SV171
@ ^ [SY2319: $i] : ( SV326 @ SY2319 ) ) )
= $true )
| ( ( SV326 @ SV622 )
= $false )
| ( ( in @ SV622 @ SV171 )
= $false )
| ( ( ( sK77_Xx @ SV326 @ SV171 )
= ( sK78_SY1660 @ SV326 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3110,plain,
! [SV623: $i,SV328: $i > $o,SV175: $i] :
( ( ( ( dsetconstr @ SV175
@ ^ [SY2322: $i] : ( SV328 @ SY2322 ) )
= ( setadjoin @ ( sK70_SY484 @ SV328 @ SV175 ) @ emptyset ) )
= $true )
| ( ( SV328 @ SV623 )
= $false )
| ( ( in @ SV623 @ SV175 )
= $false )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3111,plain,
! [SV623: $i,SV175: $i,SV328: $i > $o] :
( ( ( in @ ( sK70_SY484 @ SV328 @ SV175 )
@ ( dsetconstr @ SV175
@ ^ [SY2323: $i] : ( SV328 @ SY2323 ) ) )
= $true )
| ( ( SV328 @ SV623 )
= $false )
| ( ( in @ SV623 @ SV175 )
= $false )
| ( ( ( sK71_Xx @ SV328 @ SV175 )
= ( sK72_SY1655 @ SV328 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3112,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3113,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV638: $i] :
( ( ( ~ ( ( SV638
!= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3114,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
| ~ ( ( SV639
!= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3115,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( SV336 @ SV627 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3116,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV627: $i] :
( ( ( SV627
= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV627 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3117,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3118,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV633: $i] :
( ( ( SV633
!= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3093]) ).
thf(3119,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3094]) ).
thf(3120,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3095]) ).
thf(3121,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $false )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3122,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ~ ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) ) )
= $false )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3123,plain,
! [SV596: $i,SV439: $i > $o,SV640: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV640 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV640 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3124,plain,
! [SV596: $i,SV439: $i > $o,SV642: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV642 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV642 ) )
= $true )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3125,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3100]) ).
thf(3126,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3127,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $false )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3128,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) ) )
= $false )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3102]) ).
thf(3129,plain,
! [SV597: $i,SV465: $i > $o,SV641: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV641 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV641 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3130,plain,
! [SV597: $i,SV465: $i > $o,SV643: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV643 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV643 ) )
= $true )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3131,plain,
! [SV163: $i,SV567: $i,SV552: $i] :
( ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
= $false )
| ( ( ~ ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) ) )
= $true )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3132,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3133,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV638: $i] :
( ( ( SV638
!= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3134,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( ~ ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) ) )
= $false )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3135,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV639: $i] :
( ( ( ~ ( ( SV639
!= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) ) ) )
= $false )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3136,plain,
! [SV574: $i,SV187: $i > $o,SV627: $i,SV336: $i > $o] :
( ( ( SV336 @ SV627 )
= $false )
| ( ( SV627
= ( sK58_SY265 @ SV627 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3137,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( SV336 @ SV633 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3138,plain,
! [SV574: $i,SV187: $i > $o,SV336: $i > $o,SV633: $i] :
( ( ( SV633
= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV633 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3139,plain,
! [SV609: $i,SV439: $i > $o,SV644: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV644 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV644 ) )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3140,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( ! [SY2486: $i] :
( ~ ( SV464 @ SY2486 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SY2486 ) ) )
= $true )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3141,plain,
! [SV609: $i,SV439: $i > $o,SV464: $i > $o] :
( ( ( SV464 @ ( sK53_SY240 @ SV464 @ SV439 ) )
= $true )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3142,plain,
! [SV596: $i,SV439: $i > $o,SV640: $i,SV464: $i > $o] :
( ( ( SV464 @ SV640 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV640 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3143,plain,
! [SV596: $i,SV439: $i > $o,SV642: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV642 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV642 )
= $true )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3144,plain,
! [SV610: $i,SV465: $i > $o,SV645: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV645 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV645 ) )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3145,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( ! [SY2488: $i] :
( ~ ( SV440 @ SY2488 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SY2488 ) ) )
= $true )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3127]) ).
thf(3146,plain,
! [SV610: $i,SV465: $i > $o,SV440: $i > $o] :
( ( ( SV440 @ ( sK49_SY237 @ SV465 @ SV440 ) )
= $true )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3147,plain,
! [SV597: $i,SV465: $i > $o,SV641: $i,SV440: $i > $o] :
( ( ( SV440 @ SV641 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV641 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3148,plain,
! [SV597: $i,SV465: $i > $o,SV643: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV643 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV643 )
= $true )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3149,plain,
! [SV163: $i,SV552: $i,SV567: $i] :
( ( ( in @ SV567 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
= $false )
| ( ( in @ SV552 @ ( sK16_SY1631 @ SV567 @ SV552 @ SV163 ) )
= $false )
| ( ( SV552 = SV567 )
= $true )
| ( ( in @ SV552 @ SV163 )
= $false )
| ( ( in @ SV567 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3150,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( SV336 @ SV638 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3151,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV638: $i] :
( ( ( SV638
= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV638 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3152,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3153,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV639: $i] :
( ( ( SV639
!= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
= $true )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3135]) ).
thf(3154,plain,
! [SV574: $i,SV187: $i > $o,SV633: $i,SV336: $i > $o] :
( ( ( SV336 @ SV633 )
= $false )
| ( ( SV633
= ( sK58_SY265 @ SV633 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV574
= ( sK59_SY262 @ SV574 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV574 )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3155,plain,
! [SV609: $i,SV439: $i > $o,SV644: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV644 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV644 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3156,plain,
! [SV609: $i,SV439: $i > $o,SV646: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV646 )
| ( ( sK53_SY240 @ SV464 @ SV439 )
= SV646 ) )
= $true )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3157,plain,
! [SV596: $i,SV439: $i > $o,SV642: $i,SV464: $i > $o] :
( ( ( SV464 @ SV642 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV642 )
= $true )
| ( ( SV596
= ( sK54_SY238 @ SV596 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV596 )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3158,plain,
! [SV610: $i,SV465: $i > $o,SV645: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV645 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV645 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3159,plain,
! [SV610: $i,SV465: $i > $o,SV647: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV647 )
| ( ( sK49_SY237 @ SV465 @ SV440 )
= SV647 ) )
= $true )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3160,plain,
! [SV597: $i,SV465: $i > $o,SV643: $i,SV440: $i > $o] :
( ( ( SV440 @ SV643 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV643 )
= $true )
| ( ( SV597
= ( sK50_SY241 @ SV597 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV597 )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $true )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3161,plain,
! [SV594: $i,SV187: $i > $o,SV638: $i,SV336: $i > $o] :
( ( ( SV336 @ SV638 )
= $false )
| ( ( SV638
= ( sK58_SY265 @ SV638 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV187 @ ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $true )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3162,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( SV336 @ SV639 )
= $false )
| ( ( SV336 @ ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3163,plain,
! [SV594: $i,SV187: $i > $o,SV336: $i > $o,SV639: $i] :
( ( ( SV639
= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
= $false )
| ( ( ~ ( SV336 @ SV639 ) )
= $true )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3164,plain,
! [SV609: $i,SV439: $i > $o,SV644: $i,SV464: $i > $o] :
( ( ( SV464 @ SV644 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV644 )
= $true )
| ( ( SV439 @ ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $true )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3165,plain,
! [SV609: $i,SV439: $i > $o,SV646: $i,SV464: $i > $o] :
( ( ( ~ ( SV464 @ SV646 ) )
= $true )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV646 )
= $true )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3166,plain,
! [SV610: $i,SV465: $i > $o,SV645: $i,SV440: $i > $o] :
( ( ( SV440 @ SV645 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV645 )
= $true )
| ( ( SV465 @ ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $true )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3167,plain,
! [SV610: $i,SV465: $i > $o,SV647: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ SV647 ) )
= $true )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV647 )
= $true )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3168,plain,
! [SV594: $i,SV187: $i > $o,SV639: $i,SV336: $i > $o] :
( ( ( SV336 @ SV639 )
= $false )
| ( ( SV639
= ( sK58_SY265 @ SV639 @ SV336 @ SV187 ) )
= $false )
| ( ( ( descr
@ ^ [SY2127: $i] : ( SV187 @ SY2127 ) )
= ( descr
@ ^ [SY2343: $i] : ( SV336 @ SY2343 ) ) )
= $true )
| ( ( SV594
= ( sK59_SY262 @ SV594 @ SV336 @ SV187 ) )
= $false )
| ( ( SV187 @ SV594 )
= $false )
| ( ( SV187 @ ( sK60_Xx @ SV336 @ SV187 ) )
= $false )
| ( ( SV336 @ ( sK61_SY1650 @ SV336 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3169,plain,
! [SV609: $i,SV439: $i > $o,SV646: $i,SV464: $i > $o] :
( ( ( SV464 @ SV646 )
= $false )
| ( ( ( sK53_SY240 @ SV464 @ SV439 )
= SV646 )
= $true )
| ( ( SV609
= ( sK54_SY238 @ SV609 @ SV464 @ SV439 ) )
= $false )
| ( ( SV439 @ SV609 )
= $false )
| ( ( SV439 @ ( sK55_Xx @ SV464 @ SV439 ) )
= $false )
| ( ( SV464 @ ( sK56_SY1649 @ SV464 @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3170,plain,
! [SV610: $i,SV465: $i > $o,SV647: $i,SV440: $i > $o] :
( ( ( SV440 @ SV647 )
= $false )
| ( ( ( sK49_SY237 @ SV465 @ SV440 )
= SV647 )
= $true )
| ( ( SV610
= ( sK50_SY241 @ SV610 @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ SV610 )
= $false )
| ( ( SV440 @ ( sK51_Xx @ SV465 @ SV440 ) )
= $false )
| ( ( SV465 @ ( sK52_SY1647 @ SV465 @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3171,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[494,3170,3169,3168,3166,3164,3162,3161,3160,3157,3154,3150,3149,3147,3146,3142,3141,3137,3136,3126,3120,3115,3111,3110,3109,3108,3107,3105,3099,3085,3084,3081,3080,3077,3076,3073,3069,3066,3062,3056,3049,3048,3047,3046,3045,3044,3043,3042,3041,3037,3036,3034,3033,3026,3019,3018,3012,3011,3003,3002,3001,2997,2996,2995,2991,2990,2989,2982,2981,2959,2956,2955,2952,2951,2934,2933,2921,2914,2911,2909,2886,2885,2884,2881,2880,2879,2874,2873,2858,2851,2846,2820,2819,2818,2787,2786,2785,2778,2777,2773,2772,2768,2767,2755,2754,2753,2732,2731,2726,2723,2722,2716,2715,2714,2713,2710,2709,2698,2679,2663,2662,2660,2657,2656,2655,2654,2648,2639,2638,2637,2636,2635,2634,2625,2619,2618,2609,2608,2607,2602,2601,2600,2598,2597,2576,2569,2568,2567,2566,2565,2564,2563,2558,2557,2555,2541,2540,2539,2531,2530,2524,2523,2520,2519,2517,2483,2482,2480,2468,2467,2466,2463,2461,2458,2457,2454,2453,2435,2434,2433,2425,2414,2413,2412,2382,2375,2360,2359,2350,2334,2323,2316,2311,2309,2307,2278,2264,2252,2251,2248,2238,2235,2231,2183,2176,2167,2166,2163,2161,2160,2151,2150,2144,2143,2128,2127,2125,2119,2118,2117,2116,2115,2105,2079,2078,2076,2072,2071,2070,2056,2051,2050,2049,2044,2043,2037,2036,2031,2026,2022,2019,2011,2000,1996,1984,1981,1979,1977,1931,1921,1902,1881,1839,1822,1818,1811,1810,1808,1807,1806,1805,1804,1803,1802,1801,1800,1799,1798,1797,1794,1788,1787,1782,1780,1774,1728,1701,1698,1694,1692,1691,1687,1686,1685,1684,1683,1682,1681,1667,1666,1665,1649,1637,1636,1600,1580,1579,1572,1571,1569,1563,1560,1551,1550,1547,1546,1545,1544,1543,1542,1541,1539,1538,1531,1530,1529,1527,1526,1525,1524,1428,1427,1425,1424,1411,1409,1408,1404,1403,1401,1397,1391,1383,1382,1380,1376,1373,1367,1292,1291,1290,1289,1288,1287,1280,1279,1278,1277,1276,1273,1270,1269,1268,1267,1263,1259,1257,1256,1255,1248,1247,1245,1244,1240,1235,1230,1229,1219,1213,1212,1165,1129,1107,1106,1105,1104,1103,1102,1086,1071,1034,1025,1024,959,950,949,948,947,946,943,937,931,930,909,901,900,898,895,894,890,886,874,868,867,866,865,864,849,839,748,747,746,720,714,705,654,653,652,560,536,498]) ).
thf(3172,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU682^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:32:06 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.57/19.33 .
% 94.57/19.33
% 94.57/19.33 No.of.Axioms: 0
% 94.57/19.33
% 94.57/19.33 Length.of.Defs: 43977
% 94.57/19.33
% 94.57/19.33 Contains.Choice.Funs: true
% 94.57/19.33 .........................................................................................................................................
% 94.57/19.33
% 94.57/19.33 ********************************
% 94.57/19.33 * All subproblems solved! *
% 94.57/19.33 ********************************
% 94.57/19.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:198,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:3171,loop_count:0,foatp_calls:1,translation:fof_full)
% 94.57/19.33
% 94.57/19.33 %**** Beginning of derivation protocol ****
% 94.57/19.33 % SZS output start CNFRefutation
% See solution above
% 94.57/19.38
% 94.57/19.38 %**** End of derivation protocol ****
% 94.57/19.38 %**** no. of clauses in derivation: 3172 ****
% 94.57/19.38 %**** clause counter: 3171 ****
% 94.57/19.38
% 94.57/19.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:198,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:3171,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------